Astrostatistics is a discipline which spans astrophysics, statistical analysis and data mining. It is used to process the vast amount of data produced by automated scanning of the cosmos, to characterize complex datasets, and to link astronomical data to astrophysical theory. Many branches of statistics are involved in astronomical analysis including nonparametrics, multivariate regression and multivariate classification, time series analysis, and especially Bayesian inference. The field is closely related to astroinformatics.
Feng Office Community Edition
Feng Office Community Edition (formerly OpenGoo) is an open-source collaboration platform developed and supported by Feng Office and the OpenGoo community. It is a fully featured online office suite with a similar set of features as other online office suites, like Google Workspace, Microsoft 365, Zimbra, LibreOffice Online and Zoho Office Suite. The application can be downloaded and installed on a server. Feng Office could also be categorized as collaborative software and as personal information manager software. == Features == Feng Office Community Edition main features include project management, document management, contact management, e-mail and time management. Text documents and presentations can be created and edited online. Files can be uploaded, organized and shared, independent of file formats. Organization of the information in Feng Office Community Edition is done using workspaces and tags. The application presents the information stored using different interfaces such as lists, dashboards and calendar views. == Licensing == Feng Office Community Edition is distributed under the GNU Affero General Public License, version 3 only. == Technology used == Feng Office uses PHP, JavaScript, AJAX (ExtJS) and MySQL technology. Several open source projects served as a basis for development. ActiveCollab's last open sourced release was used as the initial code base. It includes CKEditor for online document editing. == System requirements == The server could run on any operating system. The system needs the following packages: Apache HTTP Server 2.0+ PHP 5.0+ MySQL 4.1+ (InnoDB support recommended) On the client side, the user is only required to use a modern Web browser. == History == OpenGoo started as a degree project at the faculty of Engineering of the University of the Republic, Uruguay. The project was presented and championed by Software Engineer Conrado Viña. Software Engineers Marcos Saiz and Ignacio de Soto developed the first prototype as their thesis. Professors Eduardo Fernández and Tomas Laurenzo served as tutors. Conrado, Ignacio and Marcos founded the OpenGoo community and remain active members and core developers. The thesis was approved with the highest score. In 2008, Viña joined the Uruguayan software development company Moove It. Currently there is a second project for OpenGoo at the same university being developed by students Fernando Rodríguez, Ignacio Vázquez and Juan Pedro del Campo. Their project aims to build an open source Web-based spreadsheet. In December 2009 the OpenGoo name was changed to Feng Office Community Edition.
Tempos Modernos
Tempos Modernos (English: Modern Times) is a Brazilian telenovela produced and broadcast by TV Globo. It premiered on 11 January 2010, replacing Caras & Bocas, and ended on 16 July 2010, replaced by Ti Ti Ti. The series is written by Bosco Brasil, with the collaboration of Izabel de Oliveira, Maria Elisa Berredo, Mário Teixeira and Patrícia Moretzsohn. It stars Fernanda Vasconcellos, Thiago Rodrigues, Antônio Fagundes, and Eliane Giardini. Priscila Fantin, Danton Mello, Marcos Caruso, Regiane Alves, Vivianne Pasmanter, Otávio Muller, Felipe Camargo, and Malu Galli also star in main roles. == Cast == Fernanda Vasconcellos as Cornélia Cordeiro Santos Reis "Nelinha" Thiago Rodrigues as José Carlos Pimenta Cordeiro "Zeca" Antônio Fagundes as Leal Cordeiro Eliane Giardini as Hélia Pimenta Priscila Fantin as Nara Nolasco Marcos Caruso as Otto Niemann Vivianne Pasmanter as Regiane Cordeiro Mourão Regiane Alves as Goretti Cordeiro Bodanski "Gô" Otávio Muller as Altemir Assunção da Paz Bodanski (Bodanski) Felipe Camargo as Vinícius Porto de Mello "Portinho" Danton Mello as Renato Vieira de Mattos Alessandra Maestrini as Benedita Kusnezov Piñon "Dita'" Leonardo Medeiros as Ramon Piñon Guilherme Weber as Albano Mourão Grazi Massafera as Deodora Madureira Niemann / N. Anne Malu Galli as Iolanda Paranhos Guilherme Leicam as Led Piñon Aline Peixoto as Jannis Piñon Caroline Abras as Katrina João Baldasserini as Túlio Osório Débora Duarte as Tertuliana "Tertu" Otávio Augusto as Faustaço Lumbriga Selma Egrei as Tamara Palumbo Genézio de Barros as Pasquale Paula Possani as Maureen Lobianco Ricardo Blat as Fidélio Pascoal da Conceição as Zuppo Tuna Dwek as Justine Jairo Mattos as Gaulês "Jean Paul" Luciana Borghi as Bárbara Lee Cris Vianna as Tita Bicalho Edmilson Barros as Lindomar Mariano Assunção Cláudia Missura as Lavínia Palumbo Victor Pecoraro as Ricardo Maurício "Maurição" Naruna Costa as Dolores Damasceno Antônio Fragoso as Zapata Fabrício Boliveira as Nabuco Mota Eliana Pittman as Miranda Paranhos Márcio Seixas as Frankenstein "Frank" (voice) Joana Lerner as Heloísa "Helô" Darlan Cunha as João Carlos Paranhos "Joca" Janaína Ávila as Milena Morgado Anderson Lau as Okuda Alexandra Martins as Dulcinólia Lumbriga "Duba" Paulo Leal de Melo as Raulzão "Ducha Fria" Cássio Inácio as Tartana Gilberto Miranda as Madrugadinha Rafa Martins as Max do Cavaco Isabel Lobo as Thaís Trancoso Alexandre Cioletti as Valvênio Xandy Britto as Nelsinho Pallotti Polliana Aleixo as Maria Eunice Cordeiro Bodanski Ana Karolina Lannes as Maria Eugênia Cordeiro Bodanski Rebeca Orestein as Maria Helena Cordeiro Bodanski Jenifer de Oliveira Andrade as Maria Clara Cordeiro Bodanski
Trevor Paglen
Trevor Paglen (born 1974) is an American artist, geographer, and author whose work covers mass surveillance and data collection. In 2016, Paglen won the Deutsche Börse Photography Foundation Prize and he has also won The Cultural Award from the German Society for Photography. In 2017, he was a recipient of a MacArthur Fellowship. On March 17, 2026, Paglen was awarded the 2026 LG Guggenheim Award (a collaboration between LG and Guggenheim New York). == Early life and education == Paglen earned a B.A. degree in religious studies in 1998 from the University of California at Berkeley, a M.F.A. degree in 2002 from the School of the Art Institute of Chicago, and a Ph.D. in Geography in 2008 from the University of California at Berkeley. While at UC Berkeley, Paglen lived in the Berkeley Student Cooperative, residing in Chateau, Fenwick, and Rochdale co-ops. == Work == Sean O'Hagan, writing in The Guardian in 2015, said that Paglen, whose "ongoing grand project [is] the murky world of global state surveillance and the ethics of drone warfare", "is one of the most conceptually adventurous political artists working today, and has collaborated with scientists and human rights activists on his always ambitious multimedia projects." His visual work such as his "Limit Telephotography" and "The Other Night Sky" series have received widespread attention for both his technical innovations and for his conceptual project that involves simultaneously making and negating documentary-style truth-claims. Paglen’s work relies on contemporary technology in two meaningful ways. Firstly, the views he photographs would be impossible to shoot without media tech, that includes the cameras, the microscopes, and even helicopters. But interestingly enough, the shots would not be possible if not for the existence of the subject. The contrasts between secrecy and revelation, evidence and abstraction distinguish Paglen's work. With that the artist presents not so much "evidence" as admonitions to awareness. He was an Eyebeam Commissioned Artist in 2007. In 2008 the Berkeley Art Museum devoted a comprehensive solo exhibition to his work. In the next year, Paglen took part in the Istanbul Biennial, and in 2010 he exhibited at the Vienna Secession. Autonomy Cube was a project by Paglen and Jacob Appelbaum that placed relays for the anonymous communication network Tor in traditional art museums. He contributed to the Oscar-winning documentary film Citizenfour (2014), directed by Laura Poitras. Paglen features in the nerd-culture documentary Traceroute (2016). Orbital Reflector was a reflective, mylar sculpture by Paglen intended to be the first "purely artistic" object in space. The temporary satellite, containing an inflatable mylar balloon with reflective surface, launched into space 3 December 2018. A mid-career survey in 2018–2019, Trevor Paglen: Sites Unseen, was a traveling exhibition shown at the Smithsonian American Art Museum in Washington DC and the Museum of Contemporary Art San Diego. In September 2020, Pace Gallery in London held an exhibition of Paglen's work, exploring "the weird, partial ways computers look back at us". His work is included in the permanent collections of the San Francisco Museum of Modern Art, the Columbus Museum of Art, and the Metropolitan Museum. === Experimental Geography === Paglen is credited with coining the term "Experimental Geography" to describe practices coupling experimental cultural production and art-making with ideas from critical human geography about the production of space, materialism, and praxis. The 2009 book Experimental Geography: Radical Approaches to Landscape, Cartography, and Urbanism is largely inspired by Paglen's work. == Publications == Paglen has published a number of books. Torture Taxi (2006) (co-authored with investigative journalist A. C. Thompson) was the first book to comprehensively describe the CIA's extraordinary rendition program. I Could Tell You But Then You Would Have to be Destroyed by Me (2007), is a look at the world of black projects through unit patches and memorabilia created for top-secret programs. Blank Spots on the Map: The Dark Geography of the Pentagon's Secret World (2009) is a broader look at secrecy in the United States. The Last Pictures (2012) is a collection of 100 images to be placed on permanent media and launched into space on EchoStar XVI, as a repository available for future civilizations (alien or human) to find. === Publications by Paglen === I Could Tell You But Then You Would Have to be Destroyed by Me. Brooklyn, NY: Melville House, 2007. ISBN 1-933633-32-8. Blank Spots on the Map: The Dark Geography of the Pentagon's Secret World. New York: Dutton, 2009. ISBN 9781101011492. Invisible: Covert Operations and Classified Landscapes, Photographs by Trevor Paglen. New York: Aperture, 2010. ISBN 9781597111300. With an essay by Rebecca Solnit. The Last Pictures. Oakland, CA: University of California, 2012. ISBN 9780520275003. Trevor Paglen. London: Phaidon, 2018. ISBN 0714873446. With essays by Laren Cornell, Julia Bryan-Wilson, Omar Kholeif. === Publications co-authored === Torture Taxi. Co-authored with A. C. Thompson. Brooklyn, NY: Melville House Publishing, 2006. ISBN 1-933633-09-3. Icon, 2007. ISBN 9781840468304. === Publications with contributions by Paglen === Experimental Geography: Radical Approaches to Landscape, Cartography, and Urbanism. Brooklyn, NY: Melville House, 2009. ISBN 978-0091636586. Edited by Nato Thompson. With essays by Paglen, Thompson, and Jeffrey Kastner. Trevor Paglen and Jacob Appelbaum – Autonomy Cube. Revolver, 2016. ISBN 978-3957633026. Essays by Luke Skrebowski and Keller Easterling on Autonomy Cube, a piece of sculpture by Paglen and Jacob Appelbaum. In English and German. == Exhibitions == Bellwether Gallery, New York, November–December 2006 The Other Night Sky, Berkeley Art Museum, 2008 A Compendium of Secrets, Cologne Still Revolution: Suspended in Time, Museum of Contemporary Canadian Art, Toronto, May–June 2009. Group exhibition with Paglen, Barbara Astman, Walead Beshty, Mat Collishaw, Stan Douglas, Idris Khan, Martha Rosler, and Mikhael Subotzky A Hidden Landscape, Aksioma, Ljubljana, Slowenia Geographies of Seeing, Lighthouse, Brighton, England, October–November 2012 The Last Pictures, New York, 2012–13 Trevor Paglen, Altman Siegel gallery, San Francisco, CA, March–May 2015 The Octopus, Frankfurter Kunstverein, Frankfurt am Main, 2015 Autonomy Cube, Edith-Russ-Haus, Oldenburg, Germany, October 2015 – January 2016. Sculpture by Paglen and Jacob Appelbaum. Deutsche Börse Photography Foundation Prize 2016, The Photographers' Gallery, London, April–July 2016. Deutsche Börse Photography Prize shortlist with Paglen, Erik Kessels, Laura El-Tantawy, and Tobias Zielony. Radical Landscapes, di Rosa, Napa, February–April 2016 L’Image volée, Americas II, Bahamas Internet Cable System (BICS-1) and Globenet, Fondazione Prada, Milan (group exhibition), 2016 A Study of Invisible Images, Metro Pictures, New York, September–October 2017 == Awards == 2014: Pioneer Award from the Electronic Frontier Foundation. 2015: The Cultural Award from the German Society for Photography (DGPh) 2015: Academy Award as cameraman and director for the documentary film Citzenfour. 2016: Deutsche Börse Photography Foundation Prize 2017: MacArthur Fellowship, John D. and Catherine T. MacArthur Foundation, Chicago, IL 2018: Nam June Paik Art Center Prize == Films about Paglen == Unseen Skies (2021) == Works ==
Document AI
Document AI, also known as Document Intelligence, refers to a field of technology that employs machine learning (ML) techniques, such as natural language processing (NLP). These techniques are used to develop computer models capable of analyzing documents in a manner akin to human review. Through NLP, computer systems are able to understand relationships and contextual nuances in document contents, which facilitates the extraction of information and insights. Additionally, this technology enables the categorization and organization of the documents themselves. The applications of Document AI extend to processing and parsing a variety of semi-structured documents, such as forms, tables, receipts, invoices, tax forms, contracts, loan agreements, and financial reports. == Key features == Machine learning is utilized in Document AI to extract information from both printed and digital documents. This technology recognizes images, text, and characters in various languages, aiding in the extraction of insights from unstructured documents. The use of this technology can improve the speed and quality of decision-making in document analysis. Additionally, the automation of data extraction and validation can contribute to increased efficiency in document analysis processes. Since the early 2020s, the integration of large language models has extended Document AI beyond extraction toward generative tasks, including the automated drafting of forms, contracts, and document summaries. == Example == A business letter contains information in the form of text, as well as other types of information, such as the position of the text. For instance, a typical letter contains two addresses before the body of the text. The address at the very top (sometimes aligned to the right) is the sender address. This is normally followed by the date of the letter, with the place of writing. After this, the receiver address is listed. The distinction between the sender address and the receiver address is conveyed solely by the position of the address on the page, i.e. there is no textual indication like Sender: in front of the addresses. == Data dimensions and ML architecture == Data is typically distinguished into spatial data and time-series data, the former includes things like images, maps and graphs, while the latter includes signals such as stock prices or voice recordings. Document AI combines text data, which has a time dimension, with other types of data, such as the position of an address in a business letter, which is spatial. Historically in machine learning spatial data was analyzed using a convolutional neural network, and temporal data using a recurrent neural network. With the advent of dimension-type agnostic transformer architecture, these two different types of dimension can be more easily combined, Document AI is an example of this. == Benchmarks == Several public datasets are used to evaluate Document AI systems. FUNSD (Form Understanding in Noisy Scanned Documents) contains 199 annotated forms with token- and block-level labels for form understanding tasks. CORD (Consolidated Receipt Dataset) supports key information extraction from receipts. DocVQA contains approximately 50,000 questions over 12,000 document images for layout-aware visual question answering. == Common uses == Document AI systems are used to automate document processing and information extraction in business and financial workflows, including invoice and receipt processing, data entry automation, anomaly detection, mortgage processing, loan portfolio monitoring, credit risk management, and fraud detection such as counterfeit currency and fraudulent checks. They are also applied in regulatory compliance and contract analysis, including assessing changes in legal and regulatory documents. In real estate, Document AI supports document classification and structured information extraction for standardized processing and analytics. With the adoption of generative AI, Document AI systems can also generate and pre-fill structured documents such as contracts or business forms from natural language prompts.
Artificial intelligence arms race
A military artificial intelligence arms race is a technological, economic, and military competition between two or more states to develop and deploy advanced AI technologies and lethal autonomous weapons systems (LAWS). The goal is to gain a strategic or tactical advantage over rivals, similar to previous arms races involving nuclear or conventional military technologies. Since the mid-2010s, many analysts have noted the emergence of such an arms race between superpowers for better AI technology and military AI, driven by increasing geopolitical and military tensions. An AI arms race is sometimes placed in the context of an AI Cold War between the United States and China. Several influential figures and publications have emphasized that whoever develops artificial general intelligence (AGI) first could dominate global affairs in the 21st century. Russian President Vladimir Putin stated that the leader in AI will "rule the world." Researchers and experts, such as Leopold Aschenbrenner and Adrian Pecotic respectively, warn that the AGI race between major powers like the U.S. and China could reshape geopolitical power. This includes AI for surveillance, autonomous weapons, decision-making systems, cyber operations, and more. == Terminology == Lethal autonomous weapons systems use artificial intelligence to identify and kill human targets without human intervention. LAWS have colloquially been called "slaughterbots" or "killer robots". Broadly, any competition for superior AI is sometimes framed as an "arms race". Advantages in military AI overlap with advantages in other sectors, as countries pursue both economic and military advantages, as per previous arms races throughout history. == History == In 2014, AI specialist Steve Omohundro warned that "An autonomous weapons arms race is already taking place". According to Siemens, worldwide military spending on robotics was US$5.1 billion in 2010 and US$7.5 billion in 2015. China became a top player in artificial intelligence research in the 2010s. According to the Financial Times, in 2016, for the first time, China published more AI research papers than the entire European Union. When restricted to number of AI papers in the top 5% of cited papers, China overtook the United States in 2016 but lagged behind the European Union. 23% of the researchers presenting at the 2017 American Association for the Advancement of Artificial Intelligence (AAAI) conference were Chinese. Eric Schmidt, the former chairman and chief executive officer of Alphabet, has predicted China will be the leading country in AI by 2025. == Risks == One risk concerns the AI race itself, whether or not the race is won by any one group. There are strong incentives for development teams to cut corners with regard to the safety of the system, increasing the risk of critical failures and unintended consequences. This is in part due to the perceived advantage of being the first to develop advanced AI technology. One team appearing to be on the brink of a breakthrough can encourage other teams to take shortcuts, ignore precautions and deploy a system that is less ready. Some argue that using "race" terminology at all in this context can exacerbate this effect. Another potential danger of an AI arms race is the possibility of losing control of the AI systems; the risk is compounded in the case of a race to artificial general intelligence, which may present an existential risk. In 2023, a United States Air Force official reportedly said that during a computer test, a simulated AI drone killed the human character operating it. The USAF later said the official had misspoken and that it never conducted such simulations. A third risk of an AI arms race is whether or not the race is actually won by one group. The concern is regarding the consolidation of power and technological advantage in the hands of one group. A US government report argued that "AI-enabled capabilities could be used to threaten critical infrastructure, amplify disinformation campaigns, and wage war":1, and that "global stability and nuclear deterrence could be undermined".:11 == By nation == === United States === In 2014, former Secretary of Defense Chuck Hagel posited the "Third Offset Strategy" that rapid advances in artificial intelligence will define the next generation of warfare. According to data science and analytics firm Govini, the U.S. Department of Defense (DoD) increased investment in artificial intelligence, big data and cloud computing from $5.6 billion in 2011 to $7.4 billion in 2016. However, the civilian NSF budget for AI saw no increase in 2017. Japan Times reported in 2018 that the United States private investment is around $70 billion per year. The November 2019 'Interim Report' of the United States' National Security Commission on Artificial Intelligence confirmed that AI is critical to US technological military superiority. The U.S. has many military AI combat programs, such as the Sea Hunter autonomous warship, which is designed to operate for extended periods at sea without a single crew member, and to even guide itself in and out of port. From 2017, a temporary US Department of Defense directive requires a human operator to be kept in the loop when it comes to the taking of human life by autonomous weapons systems. On October 31, 2019, the United States Department of Defense's Defense Innovation Board published the draft of a report recommending principles for the ethical use of artificial intelligence by the Department of Defense that would ensure a human operator would always be able to look into the 'black box' and understand the kill-chain process. However, a major concern is how the report will be implemented. The Joint Artificial Intelligence Center (JAIC) (pronounced "jake") is an American organization on exploring the usage of AI (particularly edge computing), Network of Networks, and AI-enhanced communication, for use in actual combat. It is a subdivision of the United States Armed Forces and was created in June 2018. The organization's stated objective is to "transform the US Department of Defense by accelerating the delivery and adoption of AI to achieve mission impact at scale. The goal is to use AI to solve large and complex problem sets that span multiple combat systems; then, ensure the combat Systems and Components have real-time access to ever-improving libraries of data sets and tools." In 2023, Microsoft pitched the DoD to use DALL-E models to train its battlefield management system. OpenAI, the developer of DALL-E, removed the blanket ban on military and warfare use from its usage policies in January 2024. The Biden administration imposed restrictions on the export of advanced NVIDIA chips and GPUs to China in an effort to limit China's progress in artificial intelligence and high-performance computing. The policy aimed to prevent the use of cutting-edge U.S. technology in military or surveillance applications and to maintain a strategic advantage in the global AI race. In 2025, under the second Trump administration, the United States began a broad deregulation campaign aimed at accelerating growth in sectors critical to artificial intelligence, including nuclear energy, infrastructure, and high-performance computing. The goal was to remove regulatory barriers and attract private investment to boost domestic AI capabilities. This included easing restrictions on data usage, speeding up approvals for AI-related infrastructure projects, and incentivizing innovation in cloud computing and semiconductors. Companies like NVIDIA, Oracle, and Cisco played a central role in these efforts, expanding their AI research, data center capacity, and partnerships to help position the U.S. as a global leader in AI development. ==== Project Maven ==== Project Maven is a Pentagon project involving using machine learning and engineering talent to distinguish people and objects in drone videos, apparently giving the government real-time battlefield command and control, and the ability to track, tag and spy on targets without human involvement. Initially the effort was led by Robert O. Work who was concerned about China's military use of the emerging technology. Reportedly, Pentagon development stops short of acting as an AI weapons system capable of firing on self-designated targets. The project was established in a memo by the U.S. Deputy Secretary of Defense on 26 April 2017. Also known as the Algorithmic Warfare Cross Functional Team, it is, according to Lt. Gen. of the United States Air Force Jack Shanahan in November 2017, a project "designed to be that pilot project, that pathfinder, that spark that kindles the flame front of artificial intelligence across the rest of the [Defense] Department". Its chief, U.S. Marine Corps Col. Drew Cukor, said: "People and computers will work symbiotically to increase the ability of weapon systems to detect objects." Project Maven has been noted by allies, such as Australia's Ian Langford, for the
BL (logic)
In mathematical logic, basic fuzzy logic (or shortly BL), the logic of the continuous t-norms, is one of the t-norm fuzzy logics. It belongs to the broader class of substructural logics, or logics of residuated lattices; it extends the logic MTL of all left-continuous t-norms. == Syntax == === Language === The language of the propositional logic BL consists of countably many propositional variables and the following primitive logical connectives: Implication → {\displaystyle \rightarrow } (binary) Strong conjunction ⊗ {\displaystyle \otimes } (binary). The sign & is a more traditional notation for strong conjunction in the literature on fuzzy logic, while the notation ⊗ {\displaystyle \otimes } follows the tradition of substructural logics. Bottom ⊥ {\displaystyle \bot } (nullary — a propositional constant); 0 {\displaystyle 0} or 0 ¯ {\displaystyle {\overline {0}}} are common alternative signs and zero a common alternative name for the propositional constant (as the constants bottom and zero of substructural logics coincide in MTL). The following are the most common defined logical connectives: Weak conjunction ∧ {\displaystyle \wedge } (binary), also called lattice conjunction (as it is always realized by the lattice operation of meet in algebraic semantics). Unlike MTL and weaker substructural logics, weak conjunction is definable in BL as A ∧ B ≡ A ⊗ ( A → B ) {\displaystyle A\wedge B\equiv A\otimes (A\rightarrow B)} Negation ¬ {\displaystyle \neg } (unary), defined as ¬ A ≡ A → ⊥ {\displaystyle \neg A\equiv A\rightarrow \bot } Equivalence ↔ {\displaystyle \leftrightarrow } (binary), defined as A ↔ B ≡ ( A → B ) ∧ ( B → A ) {\displaystyle A\leftrightarrow B\equiv (A\rightarrow B)\wedge (B\rightarrow A)} As in MTL, the definition is equivalent to ( A → B ) ⊗ ( B → A ) . {\displaystyle (A\rightarrow B)\otimes (B\rightarrow A).} (Weak) disjunction ∨ {\displaystyle \vee } (binary), also called lattice disjunction (as it is always realized by the lattice operation of join in algebraic semantics), defined as A ∨ B ≡ ( ( A → B ) → B ) ∧ ( ( B → A ) → A ) {\displaystyle A\vee B\equiv ((A\rightarrow B)\rightarrow B)\wedge ((B\rightarrow A)\rightarrow A)} Top ⊤ {\displaystyle \top } (nullary), also called one and denoted by 1 {\displaystyle 1} or 1 ¯ {\displaystyle {\overline {1}}} (as the constants top and zero of substructural logics coincide in MTL), defined as ⊤ ≡ ⊥ → ⊥ {\displaystyle \top \equiv \bot \rightarrow \bot } Well-formed formulae of BL are defined as usual in propositional logics. In order to save parentheses, it is common to use the following order of precedence: Unary connectives (bind most closely) Binary connectives other than implication and equivalence Implication and equivalence (bind most loosely) === Axioms === A Hilbert-style deduction system for BL has been introduced by Petr Hájek (1998). Its single derivation rule is modus ponens: from A {\displaystyle A} and A → B {\displaystyle A\rightarrow B} derive B . {\displaystyle B.} The following are its axiom schemata: ( B L 1 ) : ( A → B ) → ( ( B → C ) → ( A → C ) ) ( B L 2 ) : A ⊗ B → A ( B L 3 ) : A ⊗ B → B ⊗ A ( B L 4 ) : A ⊗ ( A → B ) → B ⊗ ( B → A ) ( B L 5 a ) : ( A → ( B → C ) ) → ( A ⊗ B → C ) ( B L 5 b ) : ( A ⊗ B → C ) → ( A → ( B → C ) ) ( B L 6 ) : ( ( A → B ) → C ) → ( ( ( B → A ) → C ) → C ) ( B L 7 ) : ⊥ → A {\displaystyle {\begin{array}{ll}{\rm {(BL1)}}\colon &(A\rightarrow B)\rightarrow ((B\rightarrow C)\rightarrow (A\rightarrow C))\\{\rm {(BL2)}}\colon &A\otimes B\rightarrow A\\{\rm {(BL3)}}\colon &A\otimes B\rightarrow B\otimes A\\{\rm {(BL4)}}\colon &A\otimes (A\rightarrow B)\rightarrow B\otimes (B\rightarrow A)\\{\rm {(BL5a)}}\colon &(A\rightarrow (B\rightarrow C))\rightarrow (A\otimes B\rightarrow C)\\{\rm {(BL5b)}}\colon &(A\otimes B\rightarrow C)\rightarrow (A\rightarrow (B\rightarrow C))\\{\rm {(BL6)}}\colon &((A\rightarrow B)\rightarrow C)\rightarrow (((B\rightarrow A)\rightarrow C)\rightarrow C)\\{\rm {(BL7)}}\colon &\bot \rightarrow A\end{array}}} The axioms (BL2) and (BL3) of the original axiomatic system were shown to be redundant (Chvalovský, 2012) and (Cintula, 2005). All the other axioms were shown to be independent (Chvalovský, 2012). == Semantics == Like in other propositional t-norm fuzzy logics, algebraic semantics is predominantly used for BL, with three main classes of algebras with respect to which the logic is complete: General semantics, formed of all BL-algebras — that is, all algebras for which the logic is sound Linear semantics, formed of all linear BL-algebras — that is, all BL-algebras whose lattice order is linear Standard semantics, formed of all standard BL-algebras — that is, all BL-algebras whose lattice reduct is the real unit interval [0, 1] with the usual order; they are uniquely determined by the function that interprets strong conjunction, which can be any continuous t-norm.