AI Art Zeus

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Statistical relational learning

Statistical relational learning (SRL) is a subdiscipline of artificial intelligence and machine learning that is concerned with domain models that exhibit both uncertainty (which can be dealt with using statistical methods) and complex, relational structure. Typically, the knowledge representation formalisms developed in SRL use (a subset of) first-order logic to describe relational properties of a domain in a general manner (universal quantification) and draw upon probabilistic graphical models (such as Bayesian networks or Markov networks) to model the uncertainty; some also build upon the methods of inductive logic programming. Significant contributions to the field have been made since the late 1990s. As is evident from the characterization above, the field is not strictly limited to learning aspects; it is equally concerned with reasoning (specifically probabilistic inference) and knowledge representation. Therefore, alternative terms that reflect the main foci of the field include statistical relational learning and reasoning (emphasizing the importance of reasoning) and first-order probabilistic languages (emphasizing the key properties of the languages with which models are represented). Another term that is sometimes used in the literature is relational machine learning (RML). == Canonical tasks == A number of canonical tasks are associated with statistical relational learning, the most common ones being. collective classification, i.e. the (simultaneous) prediction of the class of several objects given objects' attributes and their relations link prediction, i.e. predicting whether or not two or more objects are related link-based clustering, i.e. the grouping of similar objects, where similarity is determined according to the links of an object, and the related task of collaborative filtering, i.e. the filtering for information that is relevant to an entity (where a piece of information is considered relevant to an entity if it is known to be relevant to a similar entity) social network modelling object identification/entity resolution/record linkage, i.e. the identification of equivalent entries in two or more separate databases/datasets == Representation formalisms == One of the fundamental design goals of the representation formalisms developed in SRL is to abstract away from concrete entities and to represent instead general principles that are intended to be universally applicable. Since there are countless ways in which such principles can be represented, many representation formalisms have been proposed in recent years. In the following, some of the more common ones are listed in alphabetical order: Bayesian logic program BLOG model Markov logic networks Multi-entity Bayesian network Probabilistic logic programs Probabilistic relational model – a Probabilistic Relational Model (PRM) is the counterpart of a Bayesian network in statistical relational learning. Probabilistic soft logic Recursive random field Relational Bayesian network Relational dependency network Relational Markov network Relational Kalman filtering
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Roborace

Roborace was a competition with autonomously driving, electrically powered vehicles. Founded in 2015 by Denis Sverdlov, it aimed to be the first global championship for autonomous cars. From 2017 to 2019, the official CEO was 2016–17 Formula E champion, Lucas Di Grassi, who later became a member of Roborace’s supervisory board. The series tested their technology and race formats at FIA Formula E Championship events during 2016–2018. In 2019 Roborace organized Season Alpha, which consisted of 4 trial racing events with several independent teams competing against each other for the first time. In 2020–21 Roborace held Season Beta with 7 competing teams. All teams utilized the same chassis and powertrain, but they had to develop their own real-time computing algorithms and artificial intelligence technologies. In May 2022, Arrival, the owner of Roborace, confirmed that they were no longer continuing the Roborace programme, but that they were hoping to find alternative funding. In February 2024, after getting its stock delisted from the Nasdaq, Arrival's UK division entered administration, with future plans of a sale of Arrival and all of its affiliated assets. == Cars == === Robocar === The world's first purpose-built autonomous racing car, Robocar, was designed by Daniel Simon, who previously worked on vehicles for movies such as Tron: Legacy and Oblivion, as well as designing the livery for the 2011 HRT Formula One car. Michelin is the official tyre supplier, and the internal computing processors (Drive PX 2) are Nvidia. The chassis itself is shaped like a teardrop, improving aerodynamic efficiency. The car weighs around 1350 kg and is 4.8 metres (16 ft) long and 2 metres (6.6 ft) wide. It has four electric motors, each with a power of 135 kW producing over 500 hp combined, and utilizes a 840V battery. For navigation, it relies on a mixture of optical systems, radars, lidars and ultrasonic sensors. The vehicle has been demonstrated at speeds of almost 300 km/h (190 mph). === DevBot === Development of the Robocar started in early 2016, with a first outing of a test vehicle, the so-called DevBot, following in the summer of the same year. The test car consisted of the same internal units (battery, motor, electronics) used in the Robocar, but were placed in the chassis of a Ginetta LMP3 car without an engine cover in order to provide better cooling and access. DevBot saw its first public outing at the Formula E pre-season tests in Donington Park in August 2016. After battery issues in Hong Kong caused the development team to abandon their demonstration run, the DevBot successfully drove twelve laps around the Moulay El Hassan Formula E circuit in Marrakesh. Other test tracks included Michelin's testing ground in Ladoux and the Silverstone Stowe Circuit. During testing ahead of the 2017 Buenos Aires ePrix, two DevBot cars raced against each other autonomously, resulting in one of the vehicles crashing on a corner. During the 2017–18 Formula E season, Roborace pitched pro-drifter Ryan Tuerck against a DevBot at the Rome ePrix. At the Berlin ePrix, Roborace held the Human + Machine Challenge, the first race for combined teams of human drivers and AIs using a pair of Devbots. === DevBot 2.0 === An upgraded version of DevBot was announced in late 2018, and after private testing made its public debut in 2019 at the inaugural Season Alpha event. DevBot 2.0 uses the same technology as both Robocar and DevBot, with the main changes being a conversion to being driven on the rear axle only, a lower position for the driver for safety reasons and a bespoke composite bodywork. == Seasons == === Testing === ==== 2016–17 Formula E season ==== Roborace appeared at a number of Formula E events during the 2016–17 Formula E season. However, in this period only test drives with two different DevBots took place. Within the framework of the 2017 Buenos Aires ePrix both DevBot vehicles drove against each other on a race track for the first time. There were also DevBot demonstrations at the 2016 Marrakesh ePrix, 2017 Berlin ePrix, 2017 New York City ePrix and 2017 Montreal ePrix. At the 2017 Paris ePrix, the developers also let a Robocar onto the track for the first time, even though the vehicle only drove the track at walking speed. ==== 2017–18 Formula E season ==== At the start of the 2017/18 Formula E season, the Roborace developers once again tested the DevBot during a public time trial between the Roborace CI and the TV presenter Nicki Shields at the 2017 Hong Kong ePrix. As part of a similar time trial at the 2018 Rome ePrix, drift professional Ryan Tuerck also tested the DevBot. The Human + Machine Challenge was created for the Formula E race on the Berlin ePrix. A team of doctoral students from the Technical University of Munich (TUM) and the University of Pisa programmed the software for the Devbot to drive autonomously around the circuit in Berlin. Afterwards both teams in combination with a human driver competed in a public time trial. The vehicle of the team of the Technical University of Munich finished the Human + Machine Challenge with an average lap time of 91.59 seconds, almost four seconds faster than that of the University of Pisa with 95.36 seconds and thus won the Challenge. At the Goodwood Festival of Speed, Robocar became the first ever fully autonomous race car to complete the Goodwood Hill Climb. The vehicle completed the first official autonomous run on 13 July 2018 within the framework of the event. === Season Alpha (2019) === Season Alpha took place at various locations in Europe and North America with the aim of testing several competition formats using the new DevBot 2.0. The first event was held at the Circuito Monteblanco in Spain, and featured the first race between two fully autonomous cars. The events were not broadcast live, instead short clips on YouTube were released. Two teams were competing: Arrival and the Technical University of Munich. On 7 July 2019, the Roborace DevBot 2.0 car set the first ever autonomous official timed run at Goodwood Festival of Speed, with a time of 66.96 s and a top speed of 162.8 km/h (101.2 mph). This is currently the record for autonomous vehicles. Roborace also set the Guinness World Record for having the fastest autonomous car in the world. The Robocar reached a speed of 282.42 km/h (175.49 mph). === Season Beta (2020–21) === The second testing season took place at various locations between September 2020 and October 2021, featuring 16 races and involving mixed reality elements dubbed "Roborace Metaverse", which is based on Roborace's patented technology. The program of Season Beta competitions has gradually complicating rules arranged in a progression of so-called missions. Each mission consists of two racing rounds — one round per day. A mission plan issued by Roborace for each mission defines its objectives, rules, and point-scoring system. The key objective of Season Beta is to come to the point when the majority of competing teams have developed sufficient capability for wheel-to-wheel racing in Season 1. There were 7 teams competing in Season Beta: Arrival Racing (UK/Russia), Autonomous Racing Graz (Austria), MIT Driverless (United States), Acronis SIT (Switzerland), University of Pisa (Italy), PoliMOVE (Italy), CMU (United States).
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Mario Klingemann

Mario Klingemann (born 1970 in Laatzen, Lower Saxony) is a German artist best known for his work involving neural networks, code, and algorithms. Klingemann was a Google Arts and Culture resident from 2016 to 2018, and he is considered as a pioneer in the use of computer learning in the arts. His works examine creativity, culture, and perception through machine learning and artificial intelligence, and have appeared at the Ars Electronica Festival, the Museum of Modern Art New York, the Metropolitan Museum of Art New York, the Photographers’ Gallery London, the Centre Pompidou Paris, and the British Library. Today he lives in Munich, where, in addition to his art under the name "Dog & Pony", he still runs a creative free space between gallery and Wunderkammer with the paper artist Alexandra Lukaschewitz. In 2018 his work The Butcher's Son won the Lumen Prize Gold Award 2018 by working with figurative visual input. Mario Klingemann is part of ONKAOS, the new media artist support programme of SOLO. In collaboration with ONKAOS he has created works such as Memories of Passerby I, the first work made with AI to be auctioned at Sotheby's in 2019. In 2020, Mario Klingemann won an Honorary Mention in the Prix Ars Electronica with his AI installation Appropriate Response. In 2023, Klingemann presented A.I.C.C.A., a performative sculpture in the form of a dog capable of elaborating art critiques thanks to AI programming.
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Legal Knowledge Interchange Format

The Legal Knowledge Interchange Format (LKIF) was developed in the European ESTRELLA project and was designed with the goal of becoming a standard for representing and interchanging policy, legislation and cases, including their justificatory arguments, in the legal domain. LKIF builds on and uses the Web Ontology Language (OWL) for representing concepts and includes a reusable basic ontology of legal concepts. The core of LKIF consists of a combination of OWL-DL and SWRL. LKIF was designed with two main roles in mind: the translation of legal knowledge bases written in different representation formats and formalisms and to be a knowledge representation formalism which could be part of larger architectures for developing legal knowledge systems.
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Software engineering demographics

Software engineers make up a significant portion of the global workforce. As of 2022, there are an estimated 26.9 million professional software engineers worldwide, up from 21 million in 2016. == By country == === United States === In 2023, there were an estimated 1.6 million professional software developers in North America. There are 166 million people employed in the US workforce, making software developers 0.96% of the total workforce. ==== Summary ==== ==== Software engineers vs. traditional engineers ==== The following two tables compare the number of software engineers (611,900 in 2002) versus the number of traditional engineers (1,157,020 in 2002). There are another 1,500,000 people in system analysis, system administration, and computer support, many of whom might be called software engineers. Many systems analysts manage software development teams, and as analysis is an important software engineering role, many of them may be considered software engineers in the near future. This means that the number of software engineers may actually be much higher. It is important to note that the number of software engineers declined by 5 to 10 percent from 2000 to 2002. ==== Computer managers vs. construction and engineering managers ==== Computer and information system managers (264,790) manage software projects, as well as computer operations. Similarly, Construction and engineering managers (413,750) oversee engineering projects, manufacturing plants, and construction sites. Computer management is 64% the size of construction and engineering management. ==== Software engineering educators vs. engineering educators ==== Most people working in the field of computer science, whether making software systems (software engineering) or studying the theoretical and mathematical facts of software systems (computer science), acquire degrees in computer science. According to the U.S. Bureau of Labor Statistics (May 2023 data), there were approximately 44,800 postsecondary computer science teachers and 50,300 engineering teachers, indicating that the computer science educator workforce is nearly 89% as large as that of engineering educators. The combined number of postsecondary chemistry (25,400) and physics (17,100) teachers totaled 42,500, slightly less than the number of computer science educators. ==== Other software and engineering roles ==== ==== Relation to IT demographics ==== Software engineers are part of the much larger software, hardware, application, and operations community. In 2000 in the U.S., there were about 680,000 software engineers and about 10,000,000 IT workers. As of early 2025, there are an estimated 47.2 million software developers worldwide, representing a 50% increase from 31 million in Q1 2022. There are no numbers on testers in the BLS data. === India === There has been a healthy growth in the number of India's IT professionals over the past few years. From a base of 6,800 knowledge workers in 1985–86, the number increased to 522,000 software and services professionals by the end of 2001–02. It is estimated that out of these 528,000 knowledge workers, almost 170,000 are working in the IT software and services export industry; nearly 106,000 are working in the IT enabled services and over 230,000 in user organizations. === Australia === In May 2024, the Australian government reported that 169,300 Australians are employed as software and applications programmers, 17% of who are women. The role grew annually by 8,300 workers. === Russia === According to the Russian government, the number of IT specialists in the country increased by 13% in 2023, reaching approximately 857,000. During the initial phase of the 2022 invasion of Ukraine, an estimated 100,000 IT specialists left Russia.
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Vehicle infrastructure integration

The Vehicle Infrastructure Integration (VII), also known as "Connected Roadways" or "vehicle-to-everything" (V2X) technology, is a United States Department of Transportation initiative that aims to improve road safety by developing technology that connects road vehicles with their environment. This development draws on several disciplines, including transport engineering, electrical engineering, automotive engineering, telematics, and computer science. Although VII specifically covers road transport, similar technologies are under development for other modes of transport. For example, airplanes may use ground-based beacons for automated guidance, allowing the autopilot to fly the plane without human intervention. == Goals == The goal of VII is to establish a communication link between vehicles (via On-Board Equipment, or OBE) and roadside infrastructure (via Roadside Equipment, or RSE) to enhance the safety, efficiency, and convenience of transportation systems. Two potential approaches are the widespread deployment of a dedicated short-range communications (DSRC) link on the 5.9GHz band, and cellular communication (C-V2X). Either of these methods would allow vehicle-to-vehicle (V2V) and vehicle-to-infrastructure (V2I) communication. The initiative has three priorities: Stakeholder evaluation and acceptance of the business model and its deployment schedule, Validation of the technology, with a focus on communications systems, in relation to deployment costs, and Creation of legal structures and policies, especially concerning digital privacy, to improve the system's long-term potential for success. === Safety === Current automotive safety technology relies primarily on vehicle-based radar, lidar, and sonar systems. This technology allows, for instance, a potential reduction in rear-end collisions by monitoring obstacles in front of or behind the vehicle and automatically applying the brakes when necessary. This technology, however, is limited by the sensing range of vehicle-based radar, particularly in angled and left-turn collisions, such as a motorist losing control of the vehicle during an impending head-on collision. The rear-end collisions addressed by current technology are generally less severe than angled, left-turn, or head-on collisions. VII promotes the development of a direct communication link between road vehicles and all other vehicles nearby, allowing for the exchange of information on vehicle speed and orientation or driver awareness and intent. This real-time exchange of information may enable more effective automated emergency maneuvers, such as steering, decelerating, or braking. In addition to nearby vehicle awareness, VII promotes a communication link between vehicles and roadway infrastructure. Such a link may allow for improved real-time traffic information, better queue management, and feedback to vehicles. Existing implementations of VII use vehicle-based sensors that can recognize and respond to roadway markings or signs, automatically adjusting vehicle parameters to follow the recognized instructions. However, this information may also be acquired via roadside beacons or stored in a centralized database accessible to all vehicles. === Efficiency === With a VII system in place, vehicles will be linked together. The headway between vehicles may therefore be reduced so that there is less empty space on the road, increasing the available capacity per lane. More capacity per lane will in turn imply fewer lanes in general, possibly satisfying the community's concerns about the impact of roadway widening. VII will enable precise traffic-signal coordination by tracking vehicle platoons and will benefit from accurate timing by drawing on real-time traffic data covering volume, density, and turning movements. Real-time traffic data can also be used in the design of new roadways or modification of existing systems as the data could be used to provide accurate origin-destination studies and turning-movement counts for uses in transportation forecasting and traffic operations. Such technology would also lead to improvements for transport engineers to address problems whilst reducing the cost of obtaining and compiling data. Tolling is another prospect for VII technology as it could enable roadways to be automatically tolled. Data could be collectively transmitted to road users for in-vehicle display, outlining the lowest cost, shortest distance, and/or fastest route to a destination on the basis of real-time conditions. === Existing applications === To some extent, results along these lines have been achieved in trials performed around the globe, making use of GPS, mobile phone signals, and vehicle registration plates. GPS is becoming standard in many new high-end vehicles and is an option on most new low- and mid-range vehicles. In addition, many users also have mobile phones that transmit trackable signals (and may also be GPS-enabled). Mobile phones can already be traced for purposes of emergency response. GPS and mobile phone tracking, however, do not provide fully reliable data. Furthermore, integrating mobile phones in vehicles may be prohibitively difficult. Data from mobile phones, though useful, might even increase risks to motorists as they tend to look at their phones rather than concentrate on their driving. Automatic registration plate recognition can provide large quantities of data, but continuously tracking a vehicle through a corridor is a difficult task with existing technology. Today's equipment is designed for data acquisition and functions such as enforcement and tolling, not for returning data to vehicles or motorists for response. GPS will nevertheless be one of the key components in VII systems. == Limitations == === Privacy === VII architecture is designed to prevent identification of individual vehicles, with all data exchange between the vehicle and the system occurring anonymously. Exchanges between the vehicles and third parties such as OEMs and toll collectors will occur, but the network traffic will be sent via encrypted tunnels and will therefore not be decipherable by the VII system. Data sharing with law enforcement or Homeland Security was not included in system design as of 2006. === Technical issues === ==== Coordination ==== A major issue facing the deployment of VII is the problem of how to set up the system initially. The costs associated with installing the technology in vehicles and providing communications and power at every intersection are significant. ==== Maintenance ==== Another factor for consideration in regard to the technology's distribution is how to update and maintain the units. Traffic systems are highly dynamic, with new traffic controls implemented every day and roadways constructed or repaired every year. The vehicle-based option could be updated via the internet (preferably wireless) but may subsequently require all users to have access to internet technology. Alternatively, if receivers were placed in all vehicles and the VII system was primarily located along the roadside, information could be stored in a centralized database. This would allow the agency responsible to issue updates at any time. These would then be disseminated to the roadside units for passing motorists. Operationally, this method is currently considered to provide the greatest effectiveness but at a high cost to the authorities. ==== Security ==== Security of the units is another concern, especially in light of the public acceptance issue. Criminals could tamper, remove, or destroy VII units regardless of whether they are installed inside vehicles or along the roadside. Magnets, electric shocks, and malicious software (viruses, hacking, or jamming) could be used to damage VII systems – regardless of whether units are located inside vehicle or along the roadside. == Recent developments == Much of the current research and experimentation is conducted in the United States where coordination is ensured through the Vehicle Infrastructure Integration Consortium; consisting of automobile manufacturers (Ford, General Motors, Daimler Chrysler, Toyota, Nissan, Honda, Volkswagen, BMW), IT suppliers, U.S. Federal and state transportation departments, and professional associations. Trialing is taking place in Michigan and California. The specific applications now being developed under the U.S. initiative are: Warning drivers of unsafe conditions or imminent collisions. Warning drivers if they are about to run off the road or speed around a curve too fast. Informing system operators of real-time congestion, weather conditions and incidents. Providing operators with information on corridor capacity for real-time management, planning and provision of corridor-wide advisories to drivers. In mid-2007, a VII environment covering some 20 square miles (52 km2) near Detroit was used to test 20 prototype VII applications. Several automobile manufacturers are also conducting their own VII research and triali
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Proof assistant

In computer science and mathematical logic, a proof assistant or interactive theorem prover is a software tool to assist with the development of formal proofs by human–machine collaboration. This involves some sort of interactive proof editor, or other interface, with which a human can guide the search for proofs, the details of which are stored in, and some steps provided by, a computer. A recent effort within this field is making these tools use artificial intelligence to automate the formalization of ordinary mathematics. == Automated proof checking == Automated proof checking is the process of using software for checking proofs for correctness. It is one of the most developed fields in automated reasoning. Automated proof checking differs from automated theorem proving in that automated proof checking simply mechanically checks the formal workings of an existing proof, instead of trying to develop new proofs or theorems itself. Because of this, the task of automated proof verification is much simpler than that of automated theorem proving, allowing automated proof checking software to be much simpler than automated theorem proving software. Because of this small size, some automated proof checking systems can have less than a thousand lines of core code, and are thus themselves amenable to both hand-checking and automated software verification. The Mizar system, HOL Light, and Metamath are examples of automated proof checking systems. Automated proof checking can be done either as a batch operation, or interactively, as part of an interactive theorem proving system. == History == Automath, which was developed by Nicolaas Govert de Bruijn starting in 1967, is often considered the first proof checker and the first system to utilize the Curry–Howard correspondence between programs and proofs. Automath was used by L.S. van Benthem Jutting in 1977 to formalize Landau's Foundations of Analysis, which was the first formalization of the real numbers. In 1973, Robert Boyer and J Moore published Proving Theorems about LISP Functions which aimed to verify programs, not mathematics. Their theorem prover is now known as ACL2. In the 1970s, Edinburgh LCF introduced the idea of using a functional programming language as the metalanguage for a theorem prover, and led to the HOL family of proof assistants. The 1990s saw the rise of Rocq, (then known as Coq), which has been used for many large-scale formalization projects. Since the late 2010s, Lean, a proof assistant strongly influenced by Rocq, has become another popular choice, especially for formalizing mathematics. == System comparison == ACL2 – a programming language, a first-order logical theory, and a theorem prover (with both interactive and automatic modes) in the Boyer–Moore tradition. HOL theorem provers – A family of tools ultimately derived from the LCF theorem prover. In these systems, the logical core is a library of their programming language. Theorems represent new elements of the language and can only be introduced via "strategies" which guarantee logical correctness. Strategy composition gives users the ability to produce significant proofs with relatively few interactions with the system. Members of the family include: HOL4 – The "primary descendant", still under active development. Support for both Moscow ML and Poly/ML. Has a BSD-style license. HOL Light – A thriving "minimalist fork". OCaml based. ProofPower – Went proprietary, then returned to open source. Based on Standard ML. IMPS, An Interactive Mathematical Proof System. Isabelle is an interactive theorem prover where other systems can be encoded. Isabelle/HOL is its most popular instance, whose foundation is close to that of the HOL prover. Other instances include Isabelle/ZF and Isabelle/FOL. The main code-base is BSD-licensed, but the Isabelle distribution bundles many add-on tools with different licenses. Jape – Java based. Lean is both an interactive theorem prover and a functional, dependently-typed programming language. It is based on the calculus of inductive constructions with non-cumulative universes. Since version 4 (released in 2023), it is self-hosting. It can be used to formalise mathematics (and has a large, coherent library for formal mathematics), but also for software and hardware verification. LEGO Matita – A light system based on the calculus of inductive constructions. MINLOG – A proof assistant based on first-order minimal logic. Mizar – A proof assistant based on first-order logic, in a natural deduction style, and Tarski–Grothendieck set theory. PhoX – A proof assistant based on higher-order logic which is eXtensible. Prototype Verification System (PVS) – a proof language and system based on higher-order logic. Rocq (formerly named Coq) – A popular interactive theorem prover based on the calculus of inductive constructions. Theorem Proving System (TPS) and ETPS – Interactive theorem provers also based on simply typed lambda calculus, but based on an independent formulation of the logical theory and independent implementation. == User interfaces == A commonly used front-end for proof assistants was the Emacs-based Proof General, developed at the University of Edinburgh. Nowadays, many provers include their own editor. Rocq includes RocqIDE, which is based on OCaml/Gtk. Isabelle includes Isabelle/jEdit, which is based on jEdit and the Isabelle/Scala infrastructure for document-oriented proof processing. More recently, Visual Studio Code extensions have been developed for Rocq, Isabelle by Makarius Wenzel, and for Lean 4 by the leanprover developers. == Formalization extent == Freek Wiedijk has been keeping a ranking of proof assistants by the amount of formalized theorems out of a list of 100 well-known theorems. As of September 2025, only six systems have formalized proofs of more than 70% of the theorems, namely Isabelle, HOL Light, Lean, Rocq, Metamath and Mizar. == Notable formalized proofs == The following is a list of notable proofs that have been formalized within proof assistants.
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Speech synthesis

Speech synthesis is the artificial production of human speech. A computer system used for this purpose is called a speech synthesizer, and can be implemented in software or hardware products. A text-to-speech (TTS) system converts normal language text into speech; other systems render symbolic linguistic representations like phonetic transcriptions into speech. The reverse process is speech recognition. Synthesized speech can be created by concatenating pieces of recorded speech that are stored in a database. Systems differ in the size of the stored speech units; a system that stores phones or diphones provides the largest output range, but may lack clarity. For specific usage domains, the storage of entire words or sentences allows for high-quality output. Alternatively, a synthesizer can incorporate a model of the vocal tract and other human voice characteristics to create a completely "synthetic" voice output. The quality of a speech synthesizer is judged by its similarity to the human voice and by its ability to be understood clearly. An intelligible text-to-speech program allows people with visual impairments or reading disabilities to listen to written words on a home computer. The earliest computer operating system to have included a speech synthesizer was Unix in 1974, through the Unix speak utility. In 2000, Microsoft Sam was the default text-to-speech voice synthesizer used by the narrator accessibility feature, which shipped with all Windows 2000 operating systems, and subsequent Windows XP systems. A text-to-speech system (or "engine") is composed of two parts: a front-end and a back-end. The front-end has two major tasks. First, it converts raw text containing symbols like numbers and abbreviations into the equivalent of written-out words. This process is often called text normalization, pre-processing, or tokenization. The front-end then assigns phonetic transcriptions to each word, and divides and marks the text into prosodic units, like phrases, clauses, and sentences. The process of assigning phonetic transcriptions to words is called text-to-phoneme or grapheme-to-phoneme conversion. Phonetic transcriptions and prosody information together make up the symbolic linguistic representation that is output by the front-end. The back-end—often referred to as the synthesizer—then converts the symbolic linguistic representation into sound. In certain systems, this part includes the computation of the target prosody (pitch contour, phoneme durations), which is then imposed on the output speech. == History == Long before the invention of electronic signal processing, some people tried to build machines to emulate human speech. There were also legends of the existence of "Brazen Heads", such as those involving Pope Silvester II (d. 1003 AD), Albertus Magnus (1198–1280), and Roger Bacon (1214–1294). In 1779, the German-Danish scientist Christian Gottlieb Kratzenstein won the first prize in a competition announced by the Russian Imperial Academy of Sciences and Arts for models he built of the human vocal tract that could produce the five long vowel sounds (in International Phonetic Alphabet notation: [aː], [eː], [iː], [oː] and [uː]). There followed the bellows-operated "acoustic-mechanical speech machine" of Wolfgang von Kempelen of Pressburg, Hungary, described in a 1791 paper. This machine added models of the tongue and lips, enabling it to produce consonants as well as vowels. In 1837, Charles Wheatstone produced a "speaking machine" based on von Kempelen's design, and in 1846, Joseph Faber exhibited the "Euphonia". In 1923, Paget resurrected Wheatstone's design. In the 1930s, Bell Labs developed the vocoder, which automatically analyzed speech into its fundamental tones and resonances. From his work on the vocoder, Homer Dudley developed a keyboard-operated voice-synthesizer called The Voder (Voice Demonstrator), which he exhibited at the 1939 New York World's Fair. Franklin S. Cooper and his colleagues at Haskins Laboratories built the pattern playback in the late 1940s and completed it in 1950. There were several different versions of this hardware device; only one currently survives. The machine converts pictures of the acoustic patterns of speech in the form of a spectrogram back into sound. Using this device, Alvin Liberman and colleagues discovered acoustic cues for the perception of phonetic segments (consonants and vowels). === Electronic devices === The first computer-based speech-synthesis systems originated in the late 1950s. Noriko Umeda et al. developed the first general English text-to-speech system in 1968, at the Electrotechnical Laboratory in Japan. In 1961, physicist John Larry Kelly, Jr and his colleague Louis Gerstman used an IBM 704 computer to synthesize speech, an event among the most prominent in the history of Bell Labs. Kelly's voice recorder synthesizer (vocoder) recreated the song "Daisy Bell", with musical accompaniment from Max Mathews. Coincidentally, Arthur C. Clarke was visiting his friend and colleague John Pierce at the Bell Labs Murray Hill facility. Clarke was so impressed by the demonstration that he used it in the climactic scene of his screenplay for his novel 2001: A Space Odyssey, where the HAL 9000 computer sings the same song as astronaut Dave Bowman puts it to sleep. Despite the success of purely electronic speech synthesis, research into mechanical speech-synthesizers continues. Linear predictive coding (LPC), a form of speech coding, began development with the work of Fumitada Itakura of Nagoya University and Shuzo Saito of Nippon Telegraph and Telephone (NTT) in 1966. Further developments in LPC technology were made by Bishnu S. Atal and Manfred R. Schroeder at Bell Labs during the 1970s. LPC was later the basis for early speech synthesizer chips, such as the Texas Instruments LPC Speech Chips used in the Speak & Spell toys from 1978. In 1975, Fumitada Itakura developed the line spectral pairs (LSP) method for high-compression speech coding, while at NTT. From 1975 to 1981, Itakura studied problems in speech analysis and synthesis based on the LSP method. In 1980, his team developed an LSP-based speech synthesizer chip. LSP is an important technology for speech synthesis and coding, and in the 1990s was adopted by almost all international speech coding standards as an essential component, contributing to the enhancement of digital speech communication over mobile channels and the internet. In 1975, MUSA was released, and was one of the first Speech Synthesis systems. It consisted of a stand-alone computer hardware and a specialized software that enabled it to read Italian. A second version, released in 1978, was also able to sing Italian in an "a cappella" style. Dominant systems in the 1980s and 1990s were the DECtalk system, based largely on the work of Dennis Klatt at MIT, and the Bell Labs system; the latter was one of the first multilingual language-independent systems, making extensive use of natural language processing methods. Handheld electronics featuring speech synthesis began emerging in the 1970s. One of the first was the Telesensory Systems Inc. (TSI) Speech+ portable calculator for the blind in 1976. Other devices had primarily educational purposes, such as the Speak & Spell toy produced by Texas Instruments in 1978. Fidelity released a speaking version of its electronic chess computer in 1979. The first video game to feature speech synthesis was the 1980 shoot 'em up arcade game, Stratovox (known in Japan as Speak & Rescue), from Sun Electronics. The first personal computer game with speech synthesis was Manbiki Shoujo (Shoplifting Girl), released in 1980 for the PET 2001, for which the game's developer, Hiroshi Suzuki, developed a "zero cross" programming technique to produce a synthesized speech waveform. Another early example, the arcade version of Berzerk, also dates from 1980. The Milton Bradley Company produced the first multi-player electronic game using voice synthesis, Milton, in the same year. In 1976, Computalker Consultants released their CT-1 Speech Synthesizer. Designed by D. Lloyd Rice and Jim Cooper, it was an analog synthesizer built to work with microcomputers using the S-100 bus standard. Synthesized voices typically sounded male until 1990, when Ann Syrdal, at AT&T Bell Laboratories, created a female voice. Ray Kurzweil predicted in 2005 that as the cost-performance ratio caused speech synthesizers to become cheaper and more accessible, more people would benefit from the use of text-to-speech programs. === Artificial intelligence === In September 2016, DeepMind released WaveNet, which demonstrated that deep learning models are capable of modeling raw waveforms and generating speech from acoustic features like spectrograms or mel-spectrograms, starting the field of deep learning speech synthesis. Although WaveNet was initially considered to be computationally expensive and slow to be used in consumer products at the time, a year after its
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Knowledge graph embedding

In representation learning, knowledge graph embedding (KGE), also called knowledge representation learning (KRL), or multi-relation learning, is a machine learning task of learning a low-dimensional representation of a knowledge graph's entities and relations while preserving their semantic meaning. Leveraging their embedded representation, knowledge graphs can be used for various applications such as link prediction, triple classification, entity recognition, clustering, and relation extraction. == Definition == A knowledge graph G = { E , R , F } {\displaystyle {\mathcal {G}}=\{E,R,F\}} is a collection of entities E {\displaystyle E} , relations R {\displaystyle R} , and facts F {\displaystyle F} . A fact is a triple ( h , r , t ) ∈ F {\displaystyle (h,r,t)\in F} that denotes a link r ∈ R {\displaystyle r\in R} between the head h ∈ E {\displaystyle h\in E} and the tail t ∈ E {\displaystyle t\in E} of the triple. Another notation that is often used in the literature to represent a triple (or fact) is ⟨ head , relation , tail ⟩ {\displaystyle \langle {\text{head}},{\text{relation}},{\text{tail}}\rangle } . This notation is called the Resource Description Framework (RDF). A knowledge graph represents the knowledge related to a specific domain; leveraging this structured representation, it is possible to infer a piece of new knowledge from it after some refinement steps. However, nowadays, people have to deal with the sparsity of data and the computational inefficiency to use them in a real-world application. The embedding of a knowledge graph is a function that translates each entity and each relation into a vector of a given dimension d {\displaystyle d} , called embedding dimension. It is even possible to embed the entities and relations with different dimensions. The embedding vectors can then be used for other tasks. A knowledge graph embedding is characterized by four aspects: Representation space: The low-dimensional space in which the entities and relations are represented. Scoring function: A measure of the goodness of a triple-embedded representation. Encoding models: The modality in which the embedded representation of the entities and relations interact with each other. Additional information: Any additional information coming from the knowledge graph that can enrich the embedded representation. Usually, an ad hoc scoring function is integrated into the general scoring function for each additional piece of information. == Embedding procedure == All algorithms for creating a knowledge graph embedding follow the same approach. First, the embedding vectors are initialized to random values. Then, they are iteratively optimized using a training set of triples. In each iteration, a batch of size b {\displaystyle b} triples is sampled from the training set, and a triple from it is sampled and corrupted—i.e., a triple that does not represent a true fact in the knowledge graph. The corruption of a triple involves substituting the head or the tail (or both) of the triple with another entity that makes the fact false. The original triple and the corrupted triple are added in the training batch, and then the embeddings are updated, optimizing a scoring function. Iteration stops when a stop condition is reached. Usually, the stop condition depends on the overfitting of the training set. At the end, the learned embeddings should have extracted semantic meaning from the training triples and should correctly predict unseen true facts in the knowledge graph. === Pseudocode === The following is the pseudocode for the general embedding procedure. algorithm Compute entity and relation embeddings input: The training set S = { ( h , r , t ) } {\displaystyle S=\{(h,r,t)\}} , entity set E {\displaystyle E} , relation set R {\displaystyle R} , embedding dimension k {\displaystyle k} output: Entity and relation embeddings initialization: the entities e {\displaystyle e} and relations r {\displaystyle r} embeddings (vectors) are randomly initialized while stop condition do S b a t c h ← s a m p l e ( S , b ) {\displaystyle S_{batch}\leftarrow sample(S,b)} // Sample a batch from the training set for each ( h , r , t ) {\displaystyle (h,r,t)} in S b a t c h {\displaystyle S_{batch}} do ( h ′ , r , t ′ ) ← s a m p l e ( S ′ ) {\displaystyle (h',r,t')\leftarrow sample(S')} // Sample a corrupted fact T b a t c h ← T b a t c h ∪ { ( ( h , r , t ) , ( h ′ , r , t ′ ) ) } {\displaystyle T_{batch}\leftarrow T_{batch}\cup \{((h,r,t),(h',r,t'))\}} end for Update embeddings by minimizing the loss function end while == Performance indicators == These indexes are often used to measure the embedding quality of a model. The simplicity of the indexes makes them very suitable for evaluating the performance of an embedding algorithm even on a large scale. Given Q {\displaystyle {\ce {Q}}} as the set of all ranked predictions of a model, it is possible to define three different performance indexes: Hits@K, MR, and MRR. === Hits@K === Hits@K or in short, H@K, is a performance index that measures the probability to find the correct prediction in the first top K model predictions. Usually, it is used k = 10 {\displaystyle k=10} . Hits@K reflects the accuracy of an embedding model to predict the relation between two given triples correctly. Hits@K = | { q ∈ Q : q < k } | | Q | ∈ [ 0 , 1 ] {\displaystyle ={\frac {|\{q\in Q:q Read more →
Batch normalization

In artificial neural networks, batch normalization (also known as batch norm) is a normalization technique used to make training faster and more stable by adjusting the inputs to each layer—re-centering them around zero and re-scaling them to a standard size. It was introduced by Sergey Ioffe and Christian Szegedy in 2015. Experts still debate why batch normalization works so well. It was initially thought to tackle internal covariate shift, a problem where parameter initialization and changes in the distribution of the inputs of each layer affect the learning rate of the network. However, newer research suggests it doesn’t fix this shift but instead smooths the objective function—a mathematical guide the network follows to improve—enhancing performance. In very deep networks, batch normalization can initially cause a severe gradient explosion—where updates to the network grow uncontrollably large—but this is managed with shortcuts called skip connections in residual networks. Another theory is that batch normalization adjusts data by handling its size and path separately, speeding up training. == Internal covariate shift == Each layer in a neural network has inputs that follow a specific distribution, which shifts during training due to two main factors: the random starting values of the network’s settings (parameter initialization) and the natural variation in the input data. This shifting pattern affecting the inputs to the network’s inner layers is called internal covariate shift. While a strict definition isn’t fully agreed upon, experiments show that it involves changes in the means and variances of these inputs during training. Batch normalization was first developed to address internal covariate shift. During training, as the parameters of preceding layers adjust, the distribution of inputs to the current layer changes accordingly, such that the current layer needs to constantly readjust to new distributions. This issue is particularly severe in deep networks, because small changes in shallower hidden layers will be amplified as they propagate within the network, resulting in significant shift in deeper hidden layers. Batch normalization was proposed to reduced these unwanted shifts to speed up training and produce more reliable models. Beyond possibly tackling internal covariate shift, batch normalization offers several additional advantages. It allows the network to use a higher learning rate—a setting that controls how quickly the network learns—without causing problems like vanishing or exploding gradients, where updates become too small or too large. It also appears to have a regularizing effect, improving the network’s ability to generalize to new data, reducing the need for dropout, a technique used to prevent overfitting (when a model learns the training data too well and fails on new data). Additionally, networks using batch normalization are less sensitive to the choice of starting settings or learning rates, making them more robust and adaptable. == Procedures == === Transformation === In a neural network, batch normalization is achieved through a normalization step that fixes the means and variances of each layer's inputs. Ideally, the normalization would be conducted over the entire training set, but to use this step jointly with stochastic optimization methods, it is impractical to use the global information. Thus, normalization is restrained to each mini-batch in the training process. Let us use B to denote a mini-batch of size m of the entire training set. The empirical mean and variance of B could thus be denoted as μ B = 1 m ∑ i = 1 m x i {\displaystyle \mu _{B}={\frac {1}{m}}\sum _{i=1}^{m}x_{i}} and σ B 2 = 1 m ∑ i = 1 m ( x i − μ B ) 2 {\displaystyle \sigma _{B}^{2}={\frac {1}{m}}\sum _{i=1}^{m}(x_{i}-\mu _{B})^{2}} . For a layer of the network with d-dimensional input, x = ( x ( 1 ) , . . . , x ( d ) ) {\displaystyle x=(x^{(1)},...,x^{(d)})} , each dimension of its input is then normalized (i.e. re-centered and re-scaled) separately, x ^ i ( k ) = x i ( k ) − μ B ( k ) ( σ B ( k ) ) 2 + ϵ {\displaystyle {\hat {x}}_{i}^{(k)}={\frac {x_{i}^{(k)}-\mu _{B}^{(k)}}{\sqrt {\left(\sigma _{B}^{(k)}\right)^{2}+\epsilon }}}} , where k ∈ [ 1 , d ] {\displaystyle k\in [1,d]} and i ∈ [ 1 , m ] {\displaystyle i\in [1,m]} ; μ B ( k ) {\displaystyle \mu _{B}^{(k)}} and σ B ( k ) {\displaystyle \sigma _{B}^{(k)}} are the per-dimension mean and standard deviation, respectively. ϵ {\displaystyle \epsilon } is added in the denominator for numerical stability and is an arbitrarily small positive constant. The resulting normalized activation x ^ ( k ) {\displaystyle {\hat {x}}^{(k)}} have zero mean and unit variance, if ϵ {\displaystyle \epsilon } is not taken into account. To restore the representation power of the network, a transformation step then follows as y i ( k ) = γ ( k ) x ^ i ( k ) + β ( k ) {\displaystyle y_{i}^{(k)}=\gamma ^{(k)}{\hat {x}}_{i}^{(k)}+\beta ^{(k)}} , where the parameters γ ( k ) {\displaystyle \gamma ^{(k)}} and β ( k ) {\displaystyle \beta ^{(k)}} are subsequently learned in the optimization process. Formally, the operation that implements batch normalization is a transform B N γ ( k ) , β ( k ) : x 1... m ( k ) → y 1... m ( k ) {\displaystyle BN_{\gamma ^{(k)},\beta ^{(k)}}:x_{1...m}^{(k)}\rightarrow y_{1...m}^{(k)}} called the Batch Normalizing transform. The output of the BN transform y ( k ) = B N γ ( k ) , β ( k ) ( x ( k ) ) {\displaystyle y^{(k)}=BN_{\gamma ^{(k)},\beta ^{(k)}}(x^{(k)})} is then passed to other network layers, while the normalized output x ^ i ( k ) {\displaystyle {\hat {x}}_{i}^{(k)}} remains internal to the current layer. === Backpropagation === The described BN transform is a differentiable operation, and the gradient of the loss l {\displaystyle l} with respect to the different parameters can be computed directly with the chain rule. Specifically, ∂ l ∂ y i ( k ) {\displaystyle {\frac {\partial l}{\partial y_{i}^{(k)}}}} depends on the choice of activation function, and the gradient against other parameters could be expressed as a function of ∂ l ∂ y i ( k ) {\displaystyle {\frac {\partial l}{\partial y_{i}^{(k)}}}} : ∂ l ∂ x ^ i ( k ) = ∂ l ∂ y i ( k ) γ ( k ) {\displaystyle {\frac {\partial l}{\partial {\hat {x}}_{i}^{(k)}}}={\frac {\partial l}{\partial y_{i}^{(k)}}}\gamma ^{(k)}} , ∂ l ∂ γ ( k ) = ∑ i = 1 m ∂ l ∂ y i ( k ) x ^ i ( k ) {\displaystyle {\frac {\partial l}{\partial \gamma ^{(k)}}}=\sum _{i=1}^{m}{\frac {\partial l}{\partial y_{i}^{(k)}}}{\hat {x}}_{i}^{(k)}} , ∂ l ∂ β ( k ) = ∑ i = 1 m ∂ l ∂ y i ( k ) {\displaystyle {\frac {\partial l}{\partial \beta ^{(k)}}}=\sum _{i=1}^{m}{\frac {\partial l}{\partial y_{i}^{(k)}}}} , ∂ l ∂ σ B ( k ) 2 = ∑ i = 1 m ∂ l ∂ y i ( k ) ( x i ( k ) − μ B ( k ) ) ( − γ ( k ) 2 ( σ B ( k ) 2 + ϵ ) − 3 / 2 ) {\displaystyle {\frac {\partial l}{\partial \sigma _{B}^{(k)^{2}}}}=\sum _{i=1}^{m}{\frac {\partial l}{\partial y_{i}^{(k)}}}(x_{i}^{(k)}-\mu _{B}^{(k)})\left(-{\frac {\gamma ^{(k)}}{2}}(\sigma _{B}^{(k)^{2}}+\epsilon )^{-3/2}\right)} , ∂ l ∂ μ B ( k ) = ∑ i = 1 m ∂ l ∂ y i ( k ) − γ ( k ) σ B ( k ) 2 + ϵ + ∂ l ∂ σ B ( k ) 2 1 m ∑ i = 1 m ( − 2 ) ⋅ ( x i ( k ) − μ B ( k ) ) {\displaystyle {\frac {\partial l}{\partial \mu _{B}^{(k)}}}=\sum _{i=1}^{m}{\frac {\partial l}{\partial y_{i}^{(k)}}}{\frac {-\gamma ^{(k)}}{\sqrt {\sigma _{B}^{(k)^{2}}+\epsilon }}}+{\frac {\partial l}{\partial \sigma _{B}^{(k)^{2}}}}{\frac {1}{m}}\sum _{i=1}^{m}(-2)\cdot (x_{i}^{(k)}-\mu _{B}^{(k)})} , and ∂ l ∂ x i ( k ) = ∂ l ∂ x ^ i ( k ) 1 σ B ( k ) 2 + ϵ + ∂ l ∂ σ B ( k ) 2 2 ( x i ( k ) − μ B ( k ) ) m + ∂ l ∂ μ B ( k ) 1 m {\displaystyle {\frac {\partial l}{\partial x_{i}^{(k)}}}={\frac {\partial l}{\partial {\hat {x}}_{i}^{(k)}}}{\frac {1}{\sqrt {\sigma _{B}^{(k)^{2}}+\epsilon }}}+{\frac {\partial l}{\partial \sigma _{B}^{(k)^{2}}}}{\frac {2(x_{i}^{(k)}-\mu _{B}^{(k)})}{m}}+{\frac {\partial l}{\partial \mu _{B}^{(k)}}}{\frac {1}{m}}} . === Inference === During the training stage, the normalization steps depend on the mini-batches to ensure efficient and reliable training. However, in the inference stage, this dependence is not useful any more. Instead, the normalization step in this stage is computed with the population statistics such that the output could depend on the input in a deterministic manner. The population mean, E [ x ( k ) ] {\displaystyle E[x^{(k)}]} , and variance, Var ⁡ [ x ( k ) ] {\displaystyle \operatorname {Var} [x^{(k)}]} , are computed as: E [ x ( k ) ] = E B [ μ B ( k ) ] {\displaystyle E[x^{(k)}]=E_{B}[\mu _{B}^{(k)}]} , and Var ⁡ [ x ( k ) ] = m m − 1 E B [ ( σ B ( k ) ) 2 ] {\displaystyle \operatorname {Var} [x^{(k)}]={\frac {m}{m-1}}E_{B}[\left(\sigma _{B}^{(k)}\right)^{2}]} . The population statistics thus is a complete representation of the mini-batches. The BN transform in the inference step thus becomes y ( k ) = B N γ ( k ) , β ( k ) inf ( x ( k ) ) = γ ( k ) x ( k ) − E [ x ( k ) ] Var ⁡ [ x ( k ) ] + ϵ + β
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T-norm fuzzy logics

T-norm fuzzy logics are a family of non-classical logics, informally delimited by having a semantics that takes the real unit interval [0, 1] for the system of truth values and functions called t-norms for permissible interpretations of conjunction. They are mainly used in applied fuzzy logic and fuzzy set theory as a theoretical basis for approximate reasoning. T-norm fuzzy logics belong in broader classes of fuzzy logics and many-valued logics. In order to generate a well-behaved implication, the t-norms are usually required to be left-continuous; logics of left-continuous t-norms further belong in the class of substructural logics, among which they are marked with the validity of the law of prelinearity, (A → B) ∨ (B → A). Both propositional and first-order (or higher-order) t-norm fuzzy logics, as well as their expansions by modal and other operators, are studied. Logics that restrict the t-norm semantics to a subset of the real unit interval (for example, finitely valued Łukasiewicz logics) are usually included in the class as well. Important examples of t-norm fuzzy logics are monoidal t-norm logic (MTL) of all left-continuous t-norms, basic logic (BL) of all continuous t-norms, product fuzzy logic of the product t-norm, or the nilpotent minimum logic of the nilpotent minimum t-norm. Some independently motivated logics belong among t-norm fuzzy logics, too, for example Łukasiewicz logic (which is the logic of the Łukasiewicz t-norm) or Gödel–Dummett logic (which is the logic of the minimum t-norm). == Motivation == As members of the family of fuzzy logics, t-norm fuzzy logics primarily aim at generalizing classical two-valued logic by admitting intermediary truth values between 1 (truth) and 0 (falsity) representing degrees of truth of propositions. The degrees are assumed to be real numbers from the unit interval [0, 1]. In propositional t-norm fuzzy logics, propositional connectives are stipulated to be truth-functional, that is, the truth value of a complex proposition formed by a propositional connective from some constituent propositions is a function (called the truth function of the connective) of the truth values of the constituent propositions. The truth functions operate on the set of truth degrees (in the standard semantics, on the [0, 1] interval); thus the truth function of an n-ary propositional connective c is a function Fc: [0, 1]n → [0, 1]. Truth functions generalize truth tables of propositional connectives known from classical logic to operate on the larger system of truth values. T-norm fuzzy logics impose certain natural constraints on the truth function of conjunction. The truth function ∗ : [ 0 , 1 ] 2 → [ 0 , 1 ] {\displaystyle \colon [0,1]^{2}\to [0,1]} of conjunction is assumed to satisfy the following conditions: Commutativity, that is, x ∗ y = y ∗ x {\displaystyle xy=yx} for all x and y in [0, 1]. This expresses the assumption that the order of fuzzy propositions is immaterial in conjunction, even if intermediary truth degrees are admitted. Associativity, that is, ( x ∗ y ) ∗ z = x ∗ ( y ∗ z ) {\displaystyle (xy)z=x(yz)} for all x, y, and z in [0, 1]. This expresses the assumption that the order of performing conjunction is immaterial, even if intermediary truth degrees are admitted. Monotony, that is, if x ≤ y {\displaystyle x\leq y} then x ∗ z ≤ y ∗ z {\displaystyle xz\leq yz} for all x, y, and z in [0, 1]. This expresses the assumption that increasing the truth degree of a conjunct should not decrease the truth degree of the conjunction. Neutrality of 1, that is, 1 ∗ x = x {\displaystyle 1x=x} for all x in [0, 1]. This assumption corresponds to regarding the truth degree 1 as full truth, conjunction with which does not decrease the truth value of the other conjunct. Together with the previous conditions this condition ensures that also 0 ∗ x = 0 {\displaystyle 0x=0} for all x in [0, 1], which corresponds to regarding the truth degree 0 as full falsity, conjunction with which is always fully false. Continuity of the function ∗ {\displaystyle } (the previous conditions reduce this requirement to the continuity in either argument). Informally this expresses the assumption that microscopic changes of the truth degrees of conjuncts should not result in a macroscopic change of the truth degree of their conjunction. This condition, among other things, ensures a good behavior of (residual) implication derived from conjunction; to ensure the good behavior, however, left-continuity (in either argument) of the function ∗ {\displaystyle } is sufficient. In general t-norm fuzzy logics, therefore, only left-continuity of ∗ {\displaystyle } is required, which expresses the assumption that a microscopic decrease of the truth degree of a conjunct should not macroscopically decrease the truth degree of conjunction. These assumptions make the truth function of conjunction a left-continuous t-norm, which explains the name of the family of fuzzy logics (t-norm based). Particular logics of the family can make further assumptions about the behavior of conjunction (for example, Gödel–Dummett logic requires its idempotence) or other connectives (for example, the logic IMTL (involutive monoidal t-norm logic) requires the involutiveness of negation). All left-continuous t-norms ∗ {\displaystyle } have a unique residuum, that is, a binary function ⇒ {\displaystyle \Rightarrow } such that for all x, y, and z in [0, 1], x ∗ y ≤ z {\displaystyle xy\leq z} if and only if x ≤ y ⇒ z . {\displaystyle x\leq y\Rightarrow z.} The residuum of a left-continuous t-norm can explicitly be defined as ( x ⇒ y ) = sup { z ∣ z ∗ x ≤ y } . {\displaystyle (x\Rightarrow y)=\sup\{z\mid zx\leq y\}.} This ensures that the residuum is the pointwise largest function such that for all x and y, x ∗ ( x ⇒ y ) ≤ y . {\displaystyle x(x\Rightarrow y)\leq y.} The latter can be interpreted as a fuzzy version of the modus ponens rule of inference. The residuum of a left-continuous t-norm thus can be characterized as the weakest function that makes the fuzzy modus ponens valid, which makes it a suitable truth function for implication in fuzzy logic. Left-continuity of the t-norm is the necessary and sufficient condition for this relationship between a t-norm conjunction and its residual implication to hold. Truth functions of further propositional connectives can be defined by means of the t-norm and its residuum, for instance the residual negation ¬ x = ( x ⇒ 0 ) {\displaystyle \neg x=(x\Rightarrow 0)} or bi-residual equivalence x ⇔ y = ( x ⇒ y ) ∗ ( y ⇒ x ) . {\displaystyle x\Leftrightarrow y=(x\Rightarrow y)(y\Rightarrow x).} Truth functions of propositional connectives may also be introduced by additional definitions: the most usual ones are the minimum (which plays a role of another conjunctive connective), the maximum (which plays a role of a disjunctive connective), or the Baaz Delta operator, defined in [0, 1] as Δ x = 1 {\displaystyle \Delta x=1} if x = 1 {\displaystyle x=1} and Δ x = 0 {\displaystyle \Delta x=0} otherwise. In this way, a left-continuous t-norm, its residuum, and the truth functions of additional propositional connectives determine the truth values of complex propositional formulae in [0, 1]. Formulae that always evaluate to 1 are called tautologies with respect to the given left-continuous t-norm ∗ , {\displaystyle ,} or ∗ - {\displaystyle {\mbox{-}}} tautologies. The set of all ∗ - {\displaystyle {\mbox{-}}} tautologies is called the logic of the t-norm ∗ , {\displaystyle ,} as these formulae represent the laws of fuzzy logic (determined by the t-norm) that hold (to degree 1) regardless of the truth degrees of atomic formulae. Some formulae are tautologies with respect to a larger class of left-continuous t-norms; the set of such formulae is called the logic of the class. Important t-norm logics are the logics of particular t-norms or classes of t-norms, for example: Łukasiewicz logic is the logic of the Łukasiewicz t-norm x ∗ y = max ( x + y − 1 , 0 ) {\displaystyle xy=\max(x+y-1,0)} Gödel–Dummett logic is the logic of the minimum t-norm x ∗ y = min ( x , y ) {\displaystyle xy=\min(x,y)} Product fuzzy logic is the logic of the product t-norm x ∗ y = x ⋅ y {\displaystyle xy=x\cdot y} Monoidal t-norm logic MTL is the logic of (the class of) all left-continuous t-norms Basic fuzzy logic BL is the logic of (the class of) all continuous t-norms It turns out that many logics of particular t-norms and classes of t-norms are axiomatizable. The completeness theorem of the axiomatic system with respect to the corresponding t-norm semantics on [0, 1] is then called the standard completeness of the logic. Besides the standard real-valued semantics on [0, 1], the logics are sound and complete with respect to general algebraic semantics, formed by suitable classes of prelinear commutative bounded integral residuated lattices. == History == Some particular t-norm fuzzy logics have been introduced and investigated long before the family was re
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Fuzzy pay-off method for real option valuation

The fuzzy pay-off method for real option valuation (FPOM or pay-off method) is a method for valuing real options, developed by Mikael Collan, Robert Fullér, and József Mezei; and published in 2009. It is based on the use of fuzzy logic and fuzzy numbers for the creation of the possible pay-off distribution of a project (real option). The structure of the method is similar to the probability theory based Datar–Mathews method for real option valuation, but the method is not based on probability theory and uses fuzzy numbers and possibility theory in framing the real option valuation problem. == Method == The Fuzzy pay-off method derives the real option value from a pay-off distribution that is created by using three or four cash-flow scenarios (most often created by an expert or a group of experts). The pay-off distribution is created simply by assigning each of the three cash-flow scenarios a corresponding definition with regards to a fuzzy number (triangular fuzzy number for three scenarios and a trapezoidal fuzzy number for four scenarios). This means that the pay-off distribution is created without any simulation whatsoever. This makes the procedure easy and transparent. The scenarios used are a minimum possible scenario (the lowest possible outcome), the maximum possible scenario (the highest possible outcome) and a best estimate (most likely to happen scenario) that is mapped as a fully possible scenario with a full degree of membership in the set of possible outcomes, or in the case of four scenarios used - two best estimate scenarios that are the upper and lower limit of the interval that is assigned a full degree of membership in the set of possible outcomes. The main observations that lie behind the model for deriving the real option value are the following: The fuzzy NPV of a project is (equal to) the pay-off distribution of a project value that is calculated with fuzzy numbers. The mean value of the positive values of the fuzzy NPV is the "possibilistic" mean value of the positive fuzzy NPV values. Real option value, ROV, calculated from the fuzzy NPV is the "possibilistic" mean value of the positive fuzzy NPV values multiplied with the positive area of the fuzzy NPV over the total area of the fuzzy NPV. The real option formula can then be written simply as: R O V = A ( P o s ) A ( P o s ) + A ( N e g ) × E [ A + ] {\displaystyle \mathrm {ROV} ={\frac {A(\mathrm {Pos} )}{A(\mathrm {Pos} )+A(\mathrm {Neg} )}}\times E[A_{+}]} where A(Pos) is the area of the positive part of the fuzzy distribution, A(Neg) is the area of the negative part of the fuzzy distribution, and E[A+] is the mean value of the positive part of the distribution. It can be seen that when the distribution is totally positive, the real options value reduces to the expected (mean) value, E[A+]. As can be seen, the real option value can be derived directly from the fuzzy NPV, without simulation. At the same time, simulation is not an absolutely necessary step in the Datar–Mathews method, so the two methods are not very different in that respect. But what is totally different is that the Datar–Mathews method is based on probability theory and as such has a very different foundation from the pay-off method that is based on possibility theory: the way that the two models treat uncertainty is fundamentally different. == Use of the method == The pay-off method for real option valuation is very easy to use compared to the other real option valuation methods and it can be used with the most commonly used spreadsheet software without any add-ins. The method is useful in analyses for decision making regarding investments that have an uncertain future, and especially so if the underlying data is in the form of cash-flow scenarios. The method is less useful if optimal timing is the objective. The method is flexible and accommodates easily both one-stage investments and multi-stage investments (compound real options). The method has been taken into use in some large international industrial companies for the valuation of research and development projects and portfolios. In these analyses triangular fuzzy numbers are used. Other uses of the method so far are, for example, R&D project valuation IPR valuation, valuation of M&A targets and expected synergies, valuation and optimization of M&A strategies, valuation of area development (construction) projects, valuation of large industrial real investments. The use of the pay-off method is lately taught within the larger framework of real options, for example at the Lappeenranta University of Technology and at the Tampere University of Technology in Finland.
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ARD Sounds

ARD Sounds (until March 2026: ARD Audiothek) is the joint audio portal of the state broadcasting stations of the ARD and Deutschlandradio on the Internet. The service was officially launched as a mobile app on November 8, 2017, on the occasion of the ARD Radio Play Days in Karlsruhe. A beta web version has also been available since November 2018; it replaces the radio features in the ARD Mediathek, which has since offered only video content. Editorial support for the ARD Audiothek is provided by the ARD, the online editorial team in Mainz. In April 2018, the ARD Audiothek won the German Digital Award in silver in the category "Mobile Apps - User Experience / Usability". Within a year, the mobile app version had been installed more than 510,000 times and had around 21 million audio views. The Android app recorded more than 100,000 downloads in October 2019, according to the Google Play Store.
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Fuzzy number

A fuzzy number is a generalization of a regular real number in the sense that it does not refer to one single value but rather to a connected set of possible values, where each possible value has its own weight between 0 and 1. This weight is called the membership function. A fuzzy number is thus a special case of a convex, normalized fuzzy set of the real line. Just like fuzzy logic is an extension of Boolean logic (which uses absolute truth and falsehood only, and nothing in between), fuzzy numbers are an extension of real numbers. Calculations with fuzzy numbers allow the incorporation of uncertainty on parameters, properties, geometry, initial conditions, etc. The arithmetic calculations on fuzzy numbers are implemented using fuzzy arithmetic operations, which can be done by two different approaches: (1) interval arithmetic approach; and (2) the extension principle approach. A fuzzy number is equal to a fuzzy interval. The degree of fuzziness is determined by the a-cut which is also called the fuzzy spread.
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Shyster (expert system)

SHYSTER is a legal expert system developed at the Australian National University in Canberra in 1993. It was written as the doctoral dissertation of James Popple under the supervision of Robin Stanton, Roger Clarke, Peter Drahos, and Malcolm Newey. A full technical report of the expert system, and a book further detailing its development and testing have also been published. SHYSTER emphasises its pragmatic approach, and posits that a legal expert system need not be based upon a complex model of legal reasoning in order to produce useful advice. Although SHYSTER attempts to model the way in which lawyers argue with cases, it does not attempt to model the way in which lawyers decide which cases to use in those arguments. SHYSTER is of a general design, permitting its operation in different legal domains. It was designed to provide advice in areas of case law that have been specified by a legal expert using a bespoke specification language. Its knowledge of the law is acquired, and represented, as information about cases. It produces its advice by examining, and arguing about, the similarities and differences between cases. It derives its name from Shyster: a slang word for someone who acts in a disreputable, unethical, or unscrupulous way, especially in the practice of law and politics. == Methods == SHYSTER is a specific example of a general category of legal expert systems, broadly defined as systems that make use of artificial intelligence (AI) techniques to solve legal problems. Legal AI systems can be divided into two categories: legal retrieval systems and legal analysis systems. SHYSTER belongs to the latter category of legal analysis systems. Legal analysis systems can be further subdivided into two categories: judgment machines and legal expert systems. SHYSTER again belongs to the latter category of legal expert systems. A legal expert system, as Popple uses the term, is a system capable of performing at a level expected of a lawyer: "AI systems which merely assist a lawyer in coming to legal conclusions or preparing legal arguments are not here considered to be legal expert systems; a legal expert system must exhibit some legal expertise itself." Designed to operate in more than one legal domain, and be of specific use to the common law of Australia, SHYSTER accounts for statute law, case law, and the doctrine of precedent in areas of private law. Whilst it accommodates statute law, it is primarily a case-based system, in contradistinction to rule-based systems like MYCIN. More specifically, it was designed in a manner enabling it to be linked with a rule-based system to form a hybrid system. Although case-based reasoning possesses an advantage over rule-based systems by the elimination of complex semantic networks, it suffers from intractable theoretical obstacles: without some further theory it cannot be predicted what features of a case will turn out to be relevant. Users of SHYSTER therefore require some legal expertise. Richard Susskind argues that "jurisprudence can and ought to supply the models of law and legal reasoning that are required for computerized [sic] implementation in the process of building all expert systems in law". Popple, however, believes jurisprudence is of limited value to developers of legal expert systems. He posits that a lawyer must have a model of the law (maybe unarticulated) which includes assumptions about the nature of law and legal reasoning, but that model need not rest on basic philosophical foundations. It may be a pragmatic model, developed through experience within the legal system. Many lawyers perform their work with little or no jurisprudential knowledge, and there is no evidence to suggest that they are worse, or better, at their jobs than lawyers well-versed in jurisprudence. The fact that many lawyers have mastered the process of legal reasoning, without having been immersed in jurisprudence, suggests that it may indeed be possible to develop legal expert systems of good quality without jurisprudential insight. As a pragmatic legal expert system SHYSTER is the embodiment of this belief. A further example of SHYSTER’s pragmatism is its simple knowledge representation structure. This structure was designed to facilitate specification of different areas of case law using a specification language. Areas of case law are specified in terms of the cases and attributes of importance in those areas. SHYSTER weights its attributes and checks for dependence between them. In order to choose cases upon which to construct its opinions, SHYSTER calculates distances between cases and uses these distances to determine which of the leading cases are nearest to the instant case. To this end SHYSTER can be seen to adopt and expand upon nearest neighbor search methods used in pattern recognition. These nearest cases are used to produce an argument (based on similarities and differences between the cases) about the likely outcome in the instant case. This argument relies on the doctrine of precedent; it assumes that the instant case will be decided the same way as was the nearest case. SHYSTER then uses information about these nearest cases to construct a report. The report that SHYSTER generates makes a prediction and justifies that prediction by reference only to cases and their similarities and differences: the calculations that SHYSTER performs in coming to its opinion do not appear in that opinion. Safeguards are employed to warn users if SHYSTER doubts the veracity of its advice. == Results == SHYSTER was tested in four different and disparate areas of case law. Four specifications were written, each representing an area of Australian law: an aspect of the law of trover; the meaning of "authorization [sic]" in copyright law of Australia; the categorisation of employment contracts; and the implication of natural justice in administrative decision-making. SHYSTER was evaluated under five headings: its usefulness, its generality, the quality of its advice, its limitations, and possible enhancements that could be made to it. Despite its simple knowledge representation structure, it has shown itself capable of producing good advice, and its simple structure has facilitated the specification of different areas of law. Appreciating the difficulties encountered by legal expert systems developers in adequately representing legal knowledge can assist in appreciating the shortcomings of digital rights management technologies. Some academics believe future digital rights management systems may become sophisticated enough to permit exceptions to copyright law. To this end SHYSTER's attempt to model "authorization [sic]" in the Copyright Act can be viewed as pioneering work in this field. The term "authorization [sic]" is undefined in the Copyright Act. Consequently, a number of cases have been before the courts seeking answers as to what conduct amounts to authorisation. The main contexts in which the issue has arisen are analogous to permitted exceptions to copyright currently prevented by most digital rights management technologies: "home taping of recorded materials, photocopying in educational institutions and performing works in public". When applied to one case concerning compact cassettes, SHYSTER successfully agreed that Amstrad did not authorise the infringement. 'shyster-myci'n Popple highlighted the most obvious avenue of future research using SHYSTER as the development of a rule-based system, and the linking together of that rule-based system with the existing case-based system to form a hybrid system. This intention was eventually realised by Thomas O’Callaghan, the creator of SHYSTER-MYCIN: a hybrid legal expert system first presented at ICAIL '03, 24–28 June 2003 in Edinburgh, Scotland. MYCIN is an existing medical expert system, which was adapted for use with SHYSTER. MYCIN’s controversial "certainty factor" is not used in SHYSTER-MYCIN. The reason for this is the difficulty in scientifically establishing how certain a fact is in a legal domain. The rule-based approach of the MYCIN part is used to reason with the provisions of an Act of Parliament only. This hybrid system enables the case-based system (SHYSTER) to determine open textured concepts when required by the rule-based system (MYCIN). The ultimate conclusion of this joint endeavour is that a hybrid approach is preferred in the creation of legal expert systems where "it is appropriate to use rule-based reasoning when dealing with statutes, and…case-based reasoning when dealing with cases".
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