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  • Software requirements

    Software requirements

    Software requirements for a system are the description of what the system should do, the service or services that it provides and the constraints on its operation. The IEEE Standard Glossary of Software Engineering Terminology defines a requirement as: A condition or capability needed by a user to solve a problem or achieve an objective A condition or capability that must be met or possessed by a system or system component to satisfy a contract, standard, specification, or other formally imposed document A documented representation of a condition or capability as in 1 or 2 The activities related to working with software requirements can broadly be broken down into elicitation, analysis, specification, and management. Note that the wording Software requirements is additionally used in software release notes to explain, which depending on software packages are required for a certain software to be built/installed/used. == Elicitation == Elicitation is the gathering and discovery of requirements from stakeholders and other sources. A variety of techniques can be used such as joint application design (JAD) sessions, interviews, document analysis, focus groups, etc. Elicitation is the first step of requirements development. == Analysis == Analysis is the logical breakdown that proceeds from elicitation. Analysis involves reaching a richer and more precise understanding of each requirement and representing sets of requirements in multiple, complementary ways. Requirements Triage or prioritization of requirements is another activity which often follows analysis. This relates to Agile software development in the planning phase, e.g. by Planning poker, however it might not be the same depending on the context and nature of the project and requirements or product/service that is being built. == Specification == Specification involves representing and storing the collected requirements knowledge in a persistent and well-organized fashion that facilitates effective communication and change management. Use cases, user stories, functional requirements, and visual analysis models are popular choices for requirements specification. == Validation == Validation involves techniques to confirm that the correct set of requirements has been specified to build a solution that satisfies the project's business objectives, and to detect and correct errors in the requirements before implementation. == Management == Requirements change during projects and there are often many of them. Management of this change becomes paramount to ensuring that the correct software is built for the stakeholders. == Tool support for Requirements Engineering == === Tools for Requirements Elicitation, Analysis and Validation === Taking into account that these activities may involve some artifacts such as observation reports (user observation), questionnaires (interviews, surveys and polls), use cases, user stories; activities such as requirement workshops (charrettes), brainstorming, mind mapping, role-playing; and even, prototyping; software products providing some or all of these capabilities can be used to help achieve these tasks. There is at least one author who advocates, explicitly, for mind mapping tools such as FreeMind; and, alternatively, for the use of specification by example tools such as Concordion. Additionally, the ideas and statements resulting from these activities may be gathered and organized with wikis and other collaboration tools such as Trello. The features actually implemented and standards compliance vary from product to product. === Tools for Requirements Specification === A Software requirements specification (SRS) document might be created using general-purpose software like a word processor or one of several specialized tools. Some of these tools can import, edit, export and publish SRS documents. It may help to make SRS documents while following a standardised structure and methodology, such as ISO/IEC/IEEE 29148:2018. Likewise, software may or not use some standard to import or export requirements (such as ReqIF) or not allow these exchanges at all. === Tools for Requirements Document Verification === Tools of this kind verify if there are any errors in a requirements document according to some expected structure or standard. === Tools for Requirements Comparison === Tools of this kind compare two requirement sets according to some expected document structure and standard. === Tools for Requirements Merge and Update === Tools of this kind allow the merging and update of requirement documents. === Tools for Requirements Traceability === Tools of this kind allow tracing requirements to other artifacts such as models and source code (forward traceability) or, to previous ones such as business rules and constraints (backwards traceability). === Tools for Model-Based Software or Systems Requirement Engineering === Model-based systems engineering (MBSE) is the formalised application of modelling to support system requirements, design, analysis, verification and validation activities beginning in the conceptual design phase and continuing throughout development and later lifecycle phases. It is also possible to take a model-based approach for some stages of the requirements engineering and, a more traditional one, for others. Very many combinations might be possible. The level of formality and complexity depends on the underlying methodology involved (for instance, i is much more formal than SysML and, even more formal than UML) === Tools for general Requirements Engineering === Tools in this category may provide some mix of the capabilities mentioned previously and others such as requirement configuration management and collaboration. The features actually implemented and standards compliance vary from product to product. There are even more capable or general tools that support other stages and activities. They are classified as ALM tools.

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  • Theano (software)

    Theano (software)

    Theano is a Python library and optimizing compiler for manipulating and evaluating mathematical expressions, especially matrix-valued ones. In Theano, computations are expressed using a NumPy-esque syntax and compiled to run efficiently on either CPU or GPU architectures. == History == Theano is an open source project primarily developed by the Montreal Institute for Learning Algorithms (MILA) at the Université de Montréal. The name of the software references the ancient philosopher Theano, long associated with the development of the golden mean. On 28 September 2017, Pascal Lamblin posted a message from Yoshua Bengio, Head of MILA: major development would cease after the 1.0 release due to competing offerings by strong industrial players. Theano 1.0.0 was then released on 15 November 2017. On 17 May 2018, Chris Fonnesbeck wrote on behalf of the PyMC development team that the PyMC developers will officially assume control of Theano maintenance once the MILA development team steps down. On 29 January 2021, they started using the name Aesara for their fork of Theano. On 29 Nov 2022, the PyMC development team announced that the PyMC developers will fork the Aesara project under the name PyTensor. == Sample code == The following code is the original Theano's example. It defines a computational graph with 2 scalars a and b of type double and an operation between them (addition) and then creates a Python function f that does the actual computation. == Examples == === Matrix Multiplication (Dot Product) === The following code demonstrates how to perform matrix multiplication using Theano, which is essential for linear algebra operations in many machine learning tasks. === Gradient Calculation === The following code uses Theano to compute the gradient of a simple operation (like a neuron) with respect to its input. This is useful in training machine learning models (backpropagation). === Building a Simple Neural Network === The following code shows how to start building a simple neural network. This is a very basic neural network with one hidden layer. === Broadcasting in Theano === The following code demonstrates how broadcasting works in Theano. Broadcasting allows operations between arrays of different shapes without needing to explicitly reshape them.

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  • The Best Free AI Text-to-image Tool for Beginners

    The Best Free AI Text-to-image Tool for Beginners

    Looking for the best AI text-to-image tool? An AI text-to-image tool is software that uses machine learning to help you get more done — it can save you hours every week by automating repetitive work. Most options offer a generous free tier, with paid plans unlocking higher limits, faster processing, and team features. Whether you are a beginner or a pro, the right AI text-to-image tool slots into your workflow and pays for itself fast. This guide breaks down the top picks, their pros and cons, and who each one is best for.

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  • Jian Ma (computational biologist)

    Jian Ma (computational biologist)

    Jian Ma (Chinese: 马坚) is an American computer scientist and computational biologist. He is the Ray and Stephanie Lane Professor of Computational Biology in the School of Computer Science at Carnegie Mellon University. He is a faculty member in the Ray and Stephanie Lane Computational Biology Department. His lab develops AI/ML methods to study the structure and function of the human genome and cellular organization and their implications for health and disease. During his Ph.D. and postdoc training, he developed algorithms to reconstruct the ancestral mammalian genome and evolutionary history. His research group has recently pioneered a series of new machine learning solutions for 3D genome organization, single-cell epigenomics, spatial omics, and complex molecular interactions. His lab also explores large language models to uncover gene regulatory mechanisms and the intricate connections among cellular components, with the aim of driving discovery and guiding experimentation. He received an NSF CAREER award in 2011. In 2020, he was awarded a Guggenheim Fellowship in Computer Science. He received the Allen Newell Award for Research Excellence (2025). He is an elected Fellow of the American Association for the Advancement of Science, the American Institute for Medical and Biological Engineering, the International Society for Computational Biology, and the Association for Computing Machinery. He leads an NIH 4D Nucleome Center to develop machine learning algorithms to better understand the cell nucleus. He served as the Program Chair for RECOMB 2024. He is also a member of the Scientific Advisory Board of the Chan Zuckerberg Biohub Chicago (CZ Biohub Chicago) and the RECOMB Steering Committee. In 2024, he launched the Center for AI-Driven Biomedical Research (AI4BIO) at CMU, which will be a catalyst for innovations at the intersection of AI and biomedicine across the School of Computer Science and campus. == Selected Recent Publications == Chen V#, Yang M#, Cui W, Kim JS, Talwalkar A, and Ma J. Applying interpretable machine learning in computational biology - pitfalls, recommendations and opportunities for new developments. Nature Methods, 21(8):1454-1461, 2024. Xiong K#, Zhang R#, and Ma J. scGHOST: Identifying single-cell 3D genome subcompartments. Nature Methods, 21(5):814-822, 2024. Zhou T, Zhang R, Jia D, Doty RT, Munday AD, Gao D, Xin L, Abkowitz JL, Duan Z, and Ma J. GAGE-seq concurrently profiles multiscale 3D genome organization and gene expression in single cells. Nature Genetics, 56(8):1701-1711, 2024. Zhang Y, Boninsegna L, Yang M, Misteli T, Alber F, and Ma J. Computational methods for analysing multiscale 3D genome organization. Nature Reviews Genetics, 5(2):123-141, 2024. Chidester B#, Zhou T#, Alam S, and Ma J. SPICEMIX enables integrative single-cell spatial modeling of cell identity. Nature Genetics, 55(1):78-88, 2023. [Cover Article] Zhang R#, Zhou T#, and Ma J. Ultrafast and interpretable single-cell 3D genome analysis with Fast-Higashi. Cell Systems, 13(10):P798-807.E6, 2022. [Cover Article] Zhu X#, Zhang Y#, Wang Y, Tian D, Belmont AS, Swedlow JR, and Ma J. Nucleome Browser: An integrative and multimodal data navigation platform for 4D Nucleome. Nature Methods, 19(8):911-913, 2022. Zhang R, Zhou T, and Ma J. Multiscale and integrative single-cell Hi-C analysis with Higashi. Nature Biotechnology, 40:254–261, 2022.

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  • Mooky (app)

    Mooky (app)

    Mooky was a location-based social and dating application, designed to help its users to find the perfect match by providing a large scale of filters. Mooky was free of charge. The app made use of mobile devices' geolocation, a feature of smart phones and other devices which allows users to locate other users who are nearby. == History == Mooky was published on Google Play on April 17, 2016, by Mooky BV. The latest version of this application was version 1.0.6. == Overview == === How it works === Mooky used Facebook to build a user profile with photos and basic information, like the user's surname and age. From there on the user had to fill in their Mooky profile, which contains information about the user's height, posture, hair color, eye color, ethnicity and religion. After this the user could select its preferences to find matches nearby. === User verification === Mooky asked their users to take a selfie holding a piece of paper saying 'Mooky'. Mooky would then manually accept or decline the user verification.

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  • METEO System

    METEO System

    The METEO System is a machine translation system specifically designed for the translation of the weather forecasts issued daily by Environment Canada. The system was used from 1981 to 30 September 2001 by Environment Canada to translate forecasts issued in French in the province of Quebec into English and those issued in English in other Canadian provinces into French. Since then, a competitor program has replaced METEO System after an open governmental bid. The system was developed by John Chandioux and was often mentioned as one of the few success stories in the field of machine translation. == History == The METEO System was in operational use at Environment Canada from 1982 to 2001. It stems from a prototype developed in 1975–76 by the TAUM Group, known as TAUM-METEO. The initial motivation to develop that prototype was that a junior translator came to TAUM to ask for help in translating weather bulletins at Environment Canada. Since all official communications emanating from the Canadian government must be available in French and English, because of the Official Languages Act of 1969, and weather bulletins represent a large amount of translation in real time, junior translators had to spend several months producing first draft translations, which were then revised by seniors. That was a difficult and tedious job, because of the specificities of the English and French sublanguages used, and not very rewarding, as the lifetime of a bulletin is only 4 hours. TAUM proposed to build a prototype MT system, and Environment Canada agreed to fund the project. A prototype was ready after a few months, with basic integration in the workflow of translation (source and target bulletins travelled over telex lines at the time and MT happened on a mainframe computer). The first version of the system (METEO 1) went into operation on a Control Data CDC 7600 supercomputer in March 1977. Chandioux then left the TAUM group to manage its operation and improve it, while the TAUM group embarked on a different project (TAUM-aviation, 1977–81). Benoit Thouin made improvements to the initial prototype over the subsequent year, and turned it into an operational system. After three years, METEO 1 had demonstrated the feasibility of microcomputer-based machine translation to the satisfaction of the Canadian government's Translation Bureau of Public Works and Government Services Canada. METEO 1 was formally adopted in 1981, replacing the junior translators in the workflow. Because of the need for high-quality translation, the revision step, done by senior translators, was maintained. The quality, measured as the percentage of edit operations (inserting or deleting a word counts as 1, replacing as 2) on the MT results, reached 85% in 1985. Until that time, the MT part was still implemented as a sequence of Q-systems. The Q-systems formalism is a rule-based SLLP (Specialized Language for Linguistic Programming) invented by Alain Colmerauer in 1967 as he was a postdoc coopérant at the TAUM group. He later invented the Prolog language in 1972 after returning to France and becoming a university professor in Marseille-Luminy. As the engine of the Q-systems is highly non-deterministic, and the manipulated data structures are in some ways too simple, without any types such as string or number, Chandioux encountered limitations in his efforts to raise translation quality and lower computation time to the point he could run it on microcomputers. In 1981, Chandioux created a new SLLP, or metalanguage for linguistic applications, based on the same basic algorithmic ideas as the Q-systems, but more deterministic, and offering typed labels on tree nodes. Following the advice of Bernard Vauquois and Colmerauer, he created GramR, and developed it for microcomputers. In 1982, he could start developing in GramR a new system for translating the weather bulletins on a high-end Cromemco microcomputer. METEO 2 went into operation in 1983. The software then ran in 48Kb of central memory with a 5Mb hard disk for paging. METEO 2 was the first MT application to run on a microcomputer. In 1985, the system had nothing left of the initial prototype, and was officially renamed METEO. It translated about 20 million words per year from English into French, and 10 million words from French into English, with a quality of 97%. Typically, it took 4 minutes for a bulletin in English to be sent from Winnipeg and come back in French after MT and human revision. In 1996, Chandioux developed a special version of his system (METEO 96) which was used to translate the weather forecasts (different kinds of bulletins) issued by the US National Weather Service during the 1996 Summer Olympics in Atlanta. The last known version of the system, METEO 5, dates from 1997 and ran on an IBM PC network under Windows NT. It translated 10 pages per second, but was able to fit into a 1.44Mb floppy disk.

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  • How to Choose an AI Marketing Tool

    How to Choose an AI Marketing Tool

    Curious about the best AI marketing tool? An AI marketing tool is software that uses machine learning to help you get more done — it combines speed, accuracy, and an interface that just works. Hands-on testing shows real-world results vary, so a short free trial is the smartest way to decide. Whether you are a beginner or a pro, the right AI marketing tool slots into your workflow and pays for itself fast. This guide breaks down the top picks, their pros and cons, and who each one is best for.

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  • AI Coding Assistants Reviews: What Actually Works in 2026

    AI Coding Assistants Reviews: What Actually Works in 2026

    Comparing the best AI coding assistant? An AI coding assistant is software that uses machine learning to help you get more done — it lowers the barrier so anyone can produce professional output. Privacy matters too: check whether your data trains the model and whether a no-log or enterprise tier is available. Whether you are a beginner or a pro, the right AI coding assistant slots into your workflow and pays for itself fast. We tested the leading options and ranked them by quality, value, and ease of use.

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  • Continuous Exposure Management

    Continuous Exposure Management

    Continuous Exposure Management (CEM) is a cybersecurity approach that provides continuous, real-time monitoring, assessment, and prioritization of an organization’s security vulnerabilities and exposures. CEM focuses on identifying and mitigating risks by analyzing attack paths and providing recommendations, ensuring organizations maintain a resilient cybersecurity posture. == Overview == CEM platforms enable organizations to detect and remediate cybersecurity exposures, such as vulnerabilities, misconfigurations and weak credentials, across their entire ecosystem, including on-premises, cloud environments, and hybrid infrastructures. By simulating potential attack scenarios and mapping attack paths, these platforms help organizations understand how exposures could be exploited and which ones pose the greatest risk to critical assets. The XM Cyber Continuous Exposure Management platform, for example, integrates automated attack path mapping and contextual risk analysis, allowing security teams to prioritize remediation efforts effectively. In 2023, the platform uncovered over 40 million exposures affecting 11.5 million critical business entities. As cyber threats evolve, CEM platforms are becoming indispensable for modern enterprises. According to Gartner, organizations implementing continuous exposure management are three times less likely to experience a breach by 2026. In addition to risk mapping and simulation, some CEM approaches incorporate automated security validation to verify the exploitability of identified vulnerabilities. Platforms such as Pentera utilize automated security testing to emulate real-world adversary behavior across the network, identifying how security gaps could be leveraged to gain access to critical assets. This process aims to move beyond theoretical risk assessments by providing empirical evidence of exposure, allowing security teams to focus remediation efforts on validated attack vectors. By integrating this validation phase into the broader exposure management lifecycle, organizations can refine their prioritization strategies based on the actual effectiveness of their existing security controls and the proven reachability of their most sensitive data. == Key features == CEM platforms are designed to address the dynamic nature of cybersecurity risks through the following features: Attack Path Simulation: Continuously maps attack paths to critical assets, highlighting exploitable exposures and chokepoints. Risk Prioritization: Focuses on exposures with the highest impact on critical assets, ensuring efficient allocation of resources. Remediation Guidance: Provides clear, actionable recommendations to resolve exposures and strengthen defenses. Integration with Existing Tools: Seamlessly works with Security Information and Event Management (SIEM), ticketing, and Security Orchestration, Automation, and Response (SOAR) systems. Real-time Monitoring: Offers continuous visibility into exposures, ensuring that new ones are quickly identified and addressed.

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  • Julia Hirschberg

    Julia Hirschberg

    Julia Hirschberg is an American computer scientist noted for her research on computational linguistics and natural language processing. She received her first PhD in history from the University of Michigan and the second from the University of Pennsylvania in computer science doing research in Natural Language Processing. She worked at Bell Labs and AT&T Bell Labs from 1985 to 2002 and from 2002 at Columbia University where she is currently the Percy K. and Vida L. W. Hudson Professor of Computer Science. == Biography == Julia Linn Bell Hirschberg received her first Ph.D. degree in history (16th-century Mexico) from University of Michigan in 1976. She served on the History faculty of Smith College from 1974 to 1982. She subsequently shifted to Computer Science studies, receiving her M.S. in Computer and Information Science from University of Pennsylvania in 1982 and a Ph.D. in Computer and Information Science from University of Pennsylvania in 1985. Upon graduation from University of Pennsylvania in 1985, Hirschberg joined AT&T Bell Labs as a Member of Technical staff in the Linguistics Research Department, where she worked on improving prosody assignment for Text-to-Speech Synthesis (TTS) in the Bell Labs TTS system. She was promoted to Department Head in 1994 when she created a new Human Computer Interface Research Lab. She and her department remained at Bell Labs until 1996 when they moved to AT&T Labs Research as part of a corporate reorganization. In 2002, she joined the Columbia University faculty as a professor in the Department of Computer Science. She served as Chair of the Computer Science Department from 2012 to 2018. She still leads classes at Columbia in speech and natural language research and supervises PhD students and a large number of research project students. == Research == Hirschberg's research has included prosody, discourse structure, conversational implicature, text-to-speech synthesis, speech summarization, spoken dialogue systems, emotional speech, deceptive speech, charismatic speech, entrainment, empathetic speech and code-switching. Hirschberg was among the first to combine Natural Language Processing (NLP) approaches to discourse and dialogue with speech research. She pioneered techniques in text analysis for prosody assignment in Text-to-Speech synthesis at Bell laboratories in the 1980s and 1990s, developing corpus-based statistical models based upon syntactic and discourse information which are in general use today in TTS systems. With Janet Pierrehumbert, she developed a theoretical model of intonational meaning. She was a leader in the development of the ToBI conventions for intonational description, which have been extended to numerous languages and which today are the most widely used standard for intonational annotation. Hirschberg has been a pioneer together with Gregory Ward in much experimental work on intonational sources of language meaning and how these interact with pragmatic phenomena, particularly on the meaning of accent (intonational prominent) items and the meaning of intonational contours. She also has innovated in numerous other areas involving prosody and meaning, including the role of grammatical function and surface position in pitch accent location, the use of prosody in disambiguating cue phrases (discourse markers) with Diane Litman, the role of prosody in disambiguation in English, Italian, and Spanish with Cinzia Avesani and Pilar Prieto, and the automatic identification of speech recognition errors using prosodic information, At AT&T Labs she worked with Fernando Pereira, Steve Whittaker, and others on speech search and developing new interfaces for speech navigation. At Columbia, she and her students have continued and extended research on spoken dialogue systems (automatically detecting speech recognition errors and inappropriate system queries, modeling turn-taking behavior, dialogue entrainment, modeling and generating clarification dialogues); on the automatic classification of trust, charisma, deception and emotion from speech; on speech summarization; prosody translation, hedging behavior in text and speech, text-to-speech synthesis, and speech search in low resource languages. She also holds several patents in TTS and in speech search. Corpora she and collaborators have collected include the Boston Directions Corpus, the Columbia SRI Colorado Deception Corpus, and the Columbia Games Corpus. She has served on numerous technical boards and editorial committees. She has served as a member of the Computing Research Association's (CRA) Board of Directors and as co-chair of CRA-W. She is also noted for her leadership in broadening participation in computing. == Awards == Hirschberg's notable honors and awards include: Elected as a member of the National Academy of Artificial Intelligence Academy of Sciences and recipient of the NAAI Artificial Intelligence Exploration Award, 2025 Elected as a Fellow of Asia-Pacific Artificial Intelligence Association (AAIA), 2024. 2020 ISCA Special Service Medal Honorary Doctorate (eredoctoraat) from Tilburg University, Netherlands, 2018. American Academy of Arts and Sciences, 2018. IEEE Fellow, 2017 National Academy of Engineering, 2017 ACM Fellow in 2015 Elected member, American Philosophical Society, 2014. Honorary member, Association for Laboratory Phonology, 2014. Association for Computational Linguistics (ACL) (Founding) Fellow, 2011. International Speech Communication Association (ISCA) Medal for Scientific Achievement, 2011. IEEE James L. Flanagan Speech and Audio Processing Award, 2011. Honorary Doctorate (Hedersdoktorer), KTH (Royal Institute of Technology) Stockholm, Sweden, 2007. AAAI Fellow, 1994. == Publications == A social history of Puebla de Los Ángeles, 1531-60, 1976 Empirical studies on the disambiguation of cue phrases, 1991 Prosody and conversation, 1998 Most recent publications and other information, https://www.cs.columbia.edu/speech/.

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  • Armin B. Cremers

    Armin B. Cremers

    Armin Bernd Cremers (born June 7, 1946) is a German mathematician and computer scientist. He is a professor in the computer science institute at the University of Bonn, Germany. He is most notable for his contributions to several fields of discrete mathematics including formal languages and automata theory. In more recent years he has been recognized for his work in artificial intelligence, machine learning and robotics as well as in geoinformatics and deductive databases. == Life and work == Armin B. Cremers studied mathematics and physics at the University of Karlsruhe, Germany. After his graduate diploma (1971) and PhD (1972), both in mathematics, both summa cum laude, he received his academic lectureship qualification for computer science (1974), all from the University of Karlsruhe. Following an invitation by Seymour Ginsburg, he joined the University of Southern California (USC), Los Angeles, in 1973 where he worked until 1976 as an assistant professor of electrical engineering and computer science. With Ginsburg he initiated Grammar Forms, a new formalism for grammatical families. In 1976 A. B. Cremers returned to Germany and was appointed to full professor of computer science at the University of Dortmund, where he remained until 1990, holding the chair for information systems. During the same time he continued working as a visiting research professor at USC, where together with Thomas N. Hibbard he developed the concept of Data Spaces, a comprehensive computational model, in theory and applications. At the University of Dortmund A. B. Cremers served as chairman of the computer science department and, since early 1985, as vice president for Research and Junior Scientific Staff. In this position he was liaison for the development of the Technology Center Dortmund Archived 2021-05-09 at the Wayback Machine. He was the initiator and founding director of the Center for Expert Systems Dortmund (ZEDO) and the NRW State Research Collaborative in Artificial Intelligence (KI-NRW). From 1988 to 1996 he was also a member of the supervisory board of the German National Research Center for Mathematics and Data Processing (GMD). Since 1990 A. B. Cremers has been professor and director of computer science and head of the research group in artificial intelligence at the University of Bonn. From Bonn he has contributed fundamentally to artificial intelligence and robotics (with Wolfram Burgard, Dieter Fox, Sebastian Thrun among his students), and to the development of software engineering, particularly in civil engineering, and information systems, particularly in the geosciences. The paper "The Interactive Museum Tour-Guide Robot" won the AAAI Classic Paper award of 2016. Together with Matthias Jarke A. B. Cremers established the Bonn-Aachen International Center for Information Technology (B-IT) in 2001 and led this as Founding Scientific Director from the University of Bonn side until his retirement from teaching in 2014. From 2004 to 2008 Cremers was Dean of the School of Mathematics and Natural Sciences, and from April 2009 to July 2014 University Vice President for Planning and Finance. He is member of advisory boards, e.g., as well as Chairman of the University Council of the University of Koblenz-Landau.

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  • Top 10 AI Bug Finders Compared (2026)

    Top 10 AI Bug Finders Compared (2026)

    Trying to pick the best AI bug finder? An AI bug finder is software that uses machine learning to help you get more done — it scales effortlessly from a single task to thousands. The best picks balance beginner-friendly simplicity with the depth power users need, and they ship updates often. Whether you are a beginner or a pro, the right AI bug finder slots into your workflow and pays for itself fast. This guide breaks down the top picks, their pros and cons, and who each one is best for.

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  • Dynamic epistemic logic

    Dynamic epistemic logic

    Dynamic epistemic logic (DEL) is a logical framework dealing with knowledge and information change. Typically, DEL focuses on situations involving multiple agents and studies how their knowledge changes when events occur. These events can change factual properties of the actual world (they are called ontic events): for example a red card is painted in blue. They can also bring about changes of knowledge without changing factual properties of the world (they are called epistemic events): for example, a card is revealed publicly (or privately) to be red. Originally, DEL focused on epistemic events. Only some of the basic ideas are present in this entry of the original DEL framework; more details about DEL in general can be found in the references. Due to the nature of its object of study and its abstract approach, DEL is related and has applications to numerous research areas, such as computer science (artificial intelligence), philosophy (formal epistemology), economics (game theory) and cognitive science. In computer science, DEL is for example very much related to multi-agent systems, which are systems where multiple intelligent agents interact and exchange information. As a combination of dynamic logic and epistemic logic, dynamic epistemic logic is a young field of research. It really started in 1989 with Plaza's logic of public announcement. Independently, Gerbrandy and Groeneveld proposed a system dealing moreover with private announcement and that was inspired by the work of Veltman. Another system was proposed by van Ditmarsch whose main inspiration was the Cluedo game. But the most influential and original system was the system proposed by Baltag, Moss and Solecki. This system can deal with all the types of situations studied in the works above and its underlying methodology is conceptually grounded. This entry will present some of its basic ideas. Formally, DEL extends ordinary epistemic logic by the inclusion of event models to describe actions, and a product update operator that defines how epistemic models are updated as the consequence of executing actions described through event models. Epistemic logic will first be recalled. Then, actions and events will enter into the picture and we will introduce the DEL framework. == Epistemic logic == Epistemic logic is a modal logic dealing with the notions of knowledge and belief. As a logic, it is concerned with understanding the process of reasoning about knowledge and belief: which principles relating the notions of knowledge and belief are intuitively plausible? Like epistemology, it stems from the Greek word ϵ π ι σ τ η μ η {\displaystyle \epsilon \pi \iota \sigma \tau \eta \mu \eta } or ‘episteme’ meaning knowledge. Epistemology is nevertheless more concerned with analyzing the very nature and scope of knowledge, addressing questions such as “What is the definition of knowledge?” or “How is knowledge acquired?”. In fact, epistemic logic grew out of epistemology in the Middle Ages thanks to the efforts of Burley and Ockham. The formal work, based on modal logic, that inaugurated contemporary research into epistemic logic dates back only to 1962 and is due to Hintikka. It then sparked in the 1960s discussions about the principles of knowledge and belief and many axioms for these notions were proposed and discussed. For example, the interaction axioms K p → B p {\displaystyle Kp\rightarrow Bp} and B p → K B p {\displaystyle Bp\rightarrow KBp} are often considered to be intuitive principles: if an agent Knows p {\displaystyle p} then (s)he also Believes p {\displaystyle p} , or if an agent Believes p {\displaystyle p} , then (s)he Knows that (s)he Believes p {\displaystyle p} . More recently, these kinds of philosophical theories were taken up by researchers in economics, artificial intelligence and theoretical computer science where reasoning about knowledge is a central topic. Due to the new setting in which epistemic logic was used, new perspectives and new features such as computability issues were then added to the research agenda of epistemic logic. === Syntax === In the sequel, A G T S = { 1 , … , n } {\displaystyle AGTS=\{1,\ldots ,n\}} is a finite set whose elements are called agents and P R O P {\displaystyle PROP} is a set of propositional letters. The epistemic language is an extension of the basic multi-modal language of modal logic with a common knowledge operator C A {\displaystyle C_{A}} and a distributed knowledge operator D A {\displaystyle D_{A}} . Formally, the epistemic language L EL C {\displaystyle {\mathcal {L}}_{\textsf {EL}}^{C}} is defined inductively by the following grammar in BNF: L EL C : ϕ ::= p ∣ ¬ ϕ ∣ ( ϕ ∧ ϕ ) ∣ K j ϕ ∣ C A ϕ ∣ D A ϕ {\displaystyle {\mathcal {L}}_{\textsf {EL}}^{C}:\phi ~~::=~~p~\mid ~\neg \phi ~\mid ~(\phi \land \phi )~\mid ~K_{j}\phi ~\mid ~C_{A}\phi ~\mid ~D_{A}\phi } where p ∈ P R O P {\displaystyle p\in PROP} , j ∈ A G T S {\displaystyle j\in {AGTS}} and A ⊆ A G T S {\displaystyle A\subseteq {AGTS}} . The basic epistemic language L E L {\displaystyle {\mathcal {L}}_{EL}} is the language L E L C {\displaystyle {\mathcal {L}}_{EL}^{C}} without the common knowledge and distributed knowledge operators. The formula ⊥ {\displaystyle \bot } is an abbreviation for ¬ p ∧ p {\displaystyle \neg p\land p} (for a given p ∈ P R O P {\displaystyle p\in PROP} ), ⟨ K j ⟩ ϕ {\displaystyle \langle K_{j}\rangle \phi } is an abbreviation for ¬ K j ¬ ϕ {\displaystyle \neg K_{j}\neg \phi } , E A ϕ {\displaystyle E_{A}\phi } is an abbreviation for ⋀ j ∈ A K j ϕ {\displaystyle \bigwedge \limits _{j\in A}K_{j}\phi } and C ϕ {\displaystyle C\phi } an abbreviation for C A G T S ϕ {\displaystyle C_{AGTS}\phi } . Group notions: general, common and distributed knowledge. In a multi-agent setting there are three important epistemic concepts: general knowledge, distributed knowledge and common knowledge. The notion of common knowledge was first studied by Lewis in the context of conventions. It was then applied to distributed systems and to game theory, where it allows to express that the rationality of the players, the rules of the game and the set of players are commonly known. General knowledge. General knowledge of ϕ {\displaystyle \phi } means that everybody in the group of agents A G T S {\displaystyle {AGTS}} knows that ϕ {\displaystyle \phi } . Formally, this corresponds to the following formula: E ϕ := ⋀ j ∈ A G T S K j ϕ . {\displaystyle E\phi :={\underset {j\in {AGTS}}{\bigwedge }}K_{j}\phi .} Common knowledge. Common knowledge of ϕ {\displaystyle \phi } means that everybody knows ϕ {\displaystyle \phi } but also that everybody knows that everybody knows ϕ {\displaystyle \phi } , that everybody knows that everybody knows that everybody knows ϕ {\displaystyle \phi } , and so on ad infinitum. Formally, this corresponds to the following formula C ϕ := E ϕ ∧ E E ϕ ∧ E E E ϕ ∧ … {\displaystyle C\phi :=E\phi \land EE\phi \land EEE\phi \land \ldots } As we do not allow infinite conjunction the notion of common knowledge will have to be introduced as a primitive in our language. Before defining the language with this new operator, we are going to give an example introduced by Lewis that illustrates the difference between the notions of general knowledge and common knowledge. Lewis wanted to know what kind of knowledge is needed so that the statement p {\displaystyle p} : “every driver must drive on the right” be a convention among a group of agents. In other words, he wanted to know what kind of knowledge is needed so that everybody feels safe to drive on the right. Suppose there are only two agents i {\displaystyle i} and j {\displaystyle j} . Then everybody knowing p {\displaystyle p} (formally E p {\displaystyle Ep} ) is not enough. Indeed, it might still be possible that the agent i {\displaystyle i} considers possible that the agent j {\displaystyle j} does not know p {\displaystyle p} (formally ¬ K i K j p {\displaystyle \neg K_{i}K_{j}p} ). In that case the agent i {\displaystyle i} will not feel safe to drive on the right because he might consider that the agent j {\displaystyle j} , not knowing p {\displaystyle p} , could drive on the left. To avoid this problem, we could then assume that everybody knows that everybody knows that p {\displaystyle p} (formally E E p {\displaystyle EEp} ). This is again not enough to ensure that everybody feels safe to drive on the right. Indeed, it might still be possible that agent i {\displaystyle i} considers possible that agent j {\displaystyle j} considers possible that agent i {\displaystyle i} does not know p {\displaystyle p} (formally ¬ K i K j K i p {\displaystyle \neg K_{i}K_{j}K_{i}p} ). In that case and from i {\displaystyle i} ’s point of view, j {\displaystyle j} considers possible that i {\displaystyle i} , not knowing p {\displaystyle p} , will drive on the left. So from i {\displaystyle i} ’s point of view, j {\displaystyle j} might drive on the left as well (by the same argument as abov

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