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Institutional Model Theory
:''This page is about the concept in mathematical logic. For the concepts in sociology, see Institutional theory and Institutional logic''. In mathematical logic, institutional model theory generalizes a large portion of first-order model theory to an arbitrary logical system. Overview The notion of "logical system" here is formalized as an institution. Institutions constitute a model-oriented meta-theory on logical systems similar to how the theory of rings and modules constitute a meta-theory for classical linear algebra. Another analogy can be made with universal algebra versus groups, rings, modules etc. By abstracting away from the realities of the actual conventional logics, it can be noticed that institution theory comes in fact closer to the realities of non-conventional logics. Institutional model theory analyzes and generalizes classical model-theoretic notions and results, like * elementary diagrams * elementary embeddings * ultraproducts, Los' theorem * saturated mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sociology
Sociology is a social science that focuses on society, human social behavior, patterns of Interpersonal ties, social relationships, social interaction, and aspects of culture associated with everyday life. It uses various methods of Empirical research, empirical investigation and critical analysis to develop a body of knowledge about social order and social change. While some sociologists conduct research that may be applied directly to social policy and welfare, others focus primarily on refining the Theory, theoretical understanding of social processes and phenomenology (sociology), phenomenological method. Subject matter can range from Microsociology, micro-level analyses of society (i.e. of individual interaction and agency (sociology), agency) to Macrosociology, macro-level analyses (i.e. of social systems and social structure). Traditional focuses of sociology include social stratification, social class, social mobility, sociology of religion, religion, secularization, S ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Axiomatizable Class
In model theory, a branch of mathematical logic, an elementary class (or axiomatizable class) is a class consisting of all structures satisfying a fixed first-order theory. Definition A class ''K'' of structures of a signature σ is called an elementary class if there is a first-order theory ''T'' of signature σ, such that ''K'' consists of all models of ''T'', i.e., of all σ-structures that satisfy ''T''. If ''T'' can be chosen as a theory consisting of a single first-order sentence, then ''K'' is called a basic elementary class. More generally, ''K'' is a pseudo-elementary class if there is a first-order theory ''T'' of a signature that extends σ, such that ''K'' consists of all σ-structures that are reducts to σ of models of ''T''. In other words, a class ''K'' of σ-structures is pseudo-elementary iff there is an elementary class ''K''' such that ''K'' consists of precisely the reducts to σ of the structures in ''K'''. For obvious reasons, elementary classes are also ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Logic
Mathematical logic is the study of logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power. However, it can also include uses of logic to characterize correct mathematical reasoning or to establish foundations of mathematics. Since its inception, mathematical logic has both contributed to and been motivated by the study of foundations of mathematics. This study began in the late 19th century with the development of axiomatic frameworks for geometry, arithmetic, and Mathematical analysis, analysis. In the early 20th century it was shaped by David Hilbert's Hilbert's program, program to prove the consistency of foundational theories. Results of Kurt Gödel, Gerhard Gentzen, and others provided partial resolution to the program, and clarified the issues involved in pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Computer And System Sciences
The ''Journal of Computer and System Sciences'' (JCSS) is a peer-reviewed scientific journal in the field of computer science. ''JCSS'' is published by Elsevier, and it was started in 1967. Many influential scientific articles have been published in ''JCSS''; these include five papers that have won the Gödel Prize. an 2014 Gödel Prize Its managing editor is |
Jean-Yves Beziau
Jean-Yves is a French masculine given name. Notable persons with that name include: * Jean-Yves André (born 1977), Mauritian footballer * Jean-Yves Anis (born 1980), French footballer * Yves Jean-Bart (born 1947), Haitian football executive * Jean-Yves Berteloot (born 1958), French actor * Jean-Yves Besselat (1943–2012), French politician * Jean-Yves Béziau (born 1965), Swiss professor, mathematician, and researcher * Jean-Yves Bigras (1919–1966), Canadian film director and film editor * Jean-Yves de Blasiis (born 1973), French footballer * Jean-Yves Blondeau (born 1970), French designer * Jean-Yves Bony (born 1955), French politician * Jean-Yves Bosseur (born 1947), French composer and writer * Jean-Yves Bouguet, scientist * Jean-Yves Calvez (1927–2010), French Jesuit priest and philosopher * Jean-Yves Camus (born 1958), French political scientist * Jean-Yves Cartier (born 1949), Canadian ice hockey defenceman * Jean-Yves Chay (born 1948), French football manager and g ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Logic And Computation
The ''Journal of Logic and Computation'' is a peer-reviewed academic journal focused on logic and computing. It was established in 1990 and is published by Oxford University Press under licence from Professor Dov Gabbay Dov M. Gabbay (; born October 23, 1945) is an Israeli logician. He is Augustus De Morgan Professor Emeritus of Logic at the Group of Logic, Language and Computation, Department of Computer Science, King's College London. Work Gabbay has auth ... as owner of the journal. External links * Publications established in 1990 Computer science journals Logic journals Logic in computer science Formal methods publications Oxford University Press academic journals Bimonthly journals English-language journals {{compu-journal-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Symbolic Logic
The '' Journal of Symbolic Logic'' is a peer-reviewed mathematics journal published quarterly by Association for Symbolic Logic. It was established in 1936 and covers mathematical logic. The journal is indexed by '' Mathematical Reviews'', Zentralblatt MATH, and Scopus. Its 2009 MCQ was 0.28, and its 2009 impact factor The impact factor (IF) or journal impact factor (JIF) of an academic journal is a scientometric index calculated by Clarivate that reflects the yearly mean number of citations of articles published in the last two years in a given journal, as ... was 0.631. External links * Mathematics journals Publications established in 1936 Multilingual journals Quarterly journals Association for Symbolic Logic academic journals Logic journals Cambridge University Press academic journals {{math-journal-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Joseph Goguen
__NOTOC__ Joseph Amadee Goguen ( ; June 28, 1941 – July 3, 2006) was an American computer scientist. He was professor of Computer Science at the University of California and University of Oxford, and held research positions at IBM and SRI International. In the 1960s, along with Lotfi Zadeh, Goguen was one of the earliest researchers in fuzzy logic and made profound contributions to fuzzy set theory. In the 1970s Goguen's work was one of the earliest approaches to the algebraic characterisation of abstract data types and he originated and helped develop the OBJ family of programming languages. He was author of ''A Categorical Manifesto'' and founderBurstall R., "My friend Joseph Goguen", in ''Goguen Festschrift'', K. Futatsugi et al. (Eds.), Lecture Notes in Computer Science 4060, Springer, pp. 25–30 (2006). and Editor-in-Chief of the ''Journal of Consciousness Studies''. His development of institution theory impacted the field of universal logic. Standard implication in p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Completeness Theorem
Complete may refer to: Logic * Completeness (logic) * Completeness of a theory, the property of a theory that every formula in the theory's language or its negation is provable Mathematics * The completeness of the real numbers, which implies that there are no "holes" in the real numbers * Complete metric space, a metric space in which every Cauchy sequence converges * Complete uniform space, a uniform space where every Cauchy net in converges (or equivalently every Cauchy filter converges) * Complete measure, a measure space where every subset of every null set is measurable * Completion (algebra), at an ideal * Completeness (cryptography) * Completeness (statistics), a statistic that does not allow an unbiased estimator of zero * Complete graph, an undirected graph in which every pair of vertices has exactly one edge connecting them * Complete category, a category ''C'' where every diagram from a small category to ''C'' has a limit; it is ''cocomplete'' if every such functor ha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Beth Definability
In mathematical logic, Beth definability is a result that connects implicit definability of a property to its explicit definability. Specifically Beth definability states that the two senses of definability are equivalent. First-order logic has the Beth definability property. Statement For first-order logic, the theorem states that, given a theory ''T'' in the language ''L''' ⊇ ''L'' and a formula ''φ'' in ''L''', then the following are equivalent: * for any two models ''A'' and ''B'' of ''T'' such that ''A'', ''L'' = ''B'', ''L'' (where ''A'', ''L'' is the reduct of ''A'' to ''L''), it is the case that ''A'' ⊨ ''φ'' 'a''if and only if ''B'' ⊨ ''φ'' 'a''(for all tuples ''a'' of ''A'') * ''φ'' is equivalent modulo ''T'' to a formula ''ψ'' in ''L''. Less formally: a property is implicitly definable in a theory in language ''L'' (via a formula ''φ'' of an extended language ''L''') only if that property is explicitly definable in that theory (by formula ''ψ'' in the origi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robinson's Joint Consistency Theorem
Robinson's joint consistency theorem is an important theorem of mathematical logic. It is related to Craig interpolation and Beth definability. The classical formulation of Robinson's joint consistency theorem is as follows: Let T_1 and T_2 be first-order theories. If T_1 and T_2 are consistent and the intersection T_1 \cap T_2 is complete (in the common language of T_1 and T_2), then the union T_1 \cup T_2 is consistent. A theory T is called complete if it decides every formula, meaning that for every sentence \varphi, the theory contains the sentence or its negation but not both (that is, either T \vdash \varphi or T \vdash \neg \varphi). Since the completeness assumption is quite hard to fulfill, there is a variant of the theorem: Let T_1 and T_2 be first-order In mathematics and other formal sciences, first-order or first order most often means either: * "linear" (a polynomial of degree at most one), as in first-order approximation and other calculus uses, where it is contr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
