|
Proof-theoretic Semantics
Proof-theoretic semantics is an approach to the semantics of logic that attempts to locate the meaning of propositions and logical connectives not in terms of interpretations, as in Tarskian approaches to semantics, but in the role that the proposition or logical connective plays within the system of inference. Overview Gerhard Gentzen is the founder of proof-theoretic semantics, providing the formal basis for it in his account of cut-elimination for the sequent calculus, and some provocative philosophical remarks about locating the meaning of logical connectives in their introduction rules within natural deduction. The history of proof-theoretic semantics since then has been devoted to exploring the consequences of these ideas. Dag Prawitz extended Gentzen's notion of analytic proof to natural deduction, and suggested that the value of a proof in natural deduction may be understood as its normal form. This idea lies at the basis of the Curry–Howard isomorphism, and o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal Semantics (logic)
In logic, the semantics of logic or formal semantics is the study of the semantics, or interpretations, of formal and (idealizations of) natural languages usually trying to capture the pre-theoretic notion of entailment. Overview The truth conditions of various sentences we may encounter in arguments will depend upon their meaning, and so logicians cannot completely avoid the need to provide some treatment of the meaning of these sentences. The semantics of logic refers to the approaches that logicians have introduced to understand and determine that part of meaning in which they are interested; the logician traditionally is not interested in the sentence as uttered but in the proposition, an idealised sentence suitable for logical manipulation. Until the advent of modern logic, Aristotle's ''Organon'', especially '' De Interpretatione'', provided the basis for understanding the significance of logic. The introduction of quantification, needed to solve the problem of multi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inversion Principle
Inversion or inversions may refer to: Arts * , a French gay magazine (1924/1925) * ''Inversion'' (artwork), a 2005 temporary sculpture in Houston, Texas * Inversion (music), a term with various meanings in music theory and musical set theory * ''Inversions'' (novel) by Iain M. Banks * ''Inversion'' (video game), a 2012 third person shooter for Xbox 360, PlayStation 3, and PC * ''Inversions'' (EP), the 2014 extended play album by American rock music ensemble The Colourist * ''Inversions'' (album), a 2019 album by Belinda O'Hooley * ''Inversion'' (film), a 2016 Iranian film Linguistics and language * Inversion (linguistics), grammatical constructions where two expressions switch their order of appearance * Inversion (prosody), the reversal of the order of a foot's elements in poetry * Anastrophe, a figure of speech also known as an ''inversion'' Mathematics and logic * Involution (mathematics), a function that is its own inverse (when applied twice, the starting value is ob ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philosophical Logic
Understood in a narrow sense, philosophical logic is the area of logic that studies the application of logical methods to philosophical problems, often in the form of extended logical systems like modal logic. Some theorists conceive philosophical logic in a wider sense as the study of the scope and nature of logic in general. In this sense, philosophical logic can be seen as identical to the philosophy of logic, which includes additional topics like how to define logic or a discussion of the fundamental concepts of logic. The current article treats philosophical logic in the narrow sense, in which it forms one field of inquiry within the philosophy of logic. An important issue for philosophical logic is the question of how to classify the great variety of non-classical logical systems, many of which are of rather recent origin. One form of classification often found in the literature is to distinguish between extended logics and deviant logics. Logic itself can be defined as the s ... [...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] |
Logica Universalis
''Logica Universalis'' is a peer-reviewed academic journal which covers research related to universal logic Originally the expression ''Universal logic'' was coined by analogy with the expression ''Universal algebra''. The first idea was to develop Universal logic as a field of logic that studies the features common to all logical systems, aiming to be .... External links * Logic journals Biannual journals English-language journals Publications established in 2007 Springer Science+Business Media academic journals {{philo-journal-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nissim Francez
Nissim Francez (Hebrew: נסים פרנסיז; born: 19 January 1944) is an Israeli professor, emeritus in the computer science faculty at the Technion, and former head of computational linguistics laboratory in the faculty. Early life and education Nissim Francez was born in Bulgaria. His family emigrated to Israel in 1949. He received his B.Sc. in mathematics and philosophy from the Hebrew University, Jerusalem in 1965. After his military service in the IDF, he studied at the Department of Applied Mathematics at the Weizmann Institute, Rehovot, and received his M.sc. in 1971. He continued his studies there and received his Ph.D. degree in 1976. Francez under the supervision of Prof. Amir Pnueli. Career Francez was a research associate at Queen's University Belfast, Northern Ireland in 1976. A year later he joined the Computer Science Department of the University of Southern California (USC), as an assistant professor. In 1978 He returned to Israel as a lect ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Internet Encyclopedia Of Philosophy
The ''Internet Encyclopedia of Philosophy'' (''IEP'') is a scholarly online encyclopedia, dealing with philosophy, philosophical topics, and philosophers. The IEP combines open access publication with peer reviewed publication of original papers. Contribution is generally by invitation, and contributors are recognized and leading international specialists within their field. History The ''IEP'' was founded by philosopher James Fieser in 1995, operating through a non-profit organization with the aim of providing accessible and scholarly information on philosophy.Kooy, B. 2015. 'Internet Encyclopedia of Philosophy', in ''Reference Review,'' Vol.29, No.4, p.12; see also The current general editors are philosophers James Fieser and Bradley Dowden, with the staff also including numerous area editors as well as volunteers. The entire website was redesigned in the summer of 2009, moving from static HTML pages to the open-source publishing platform ''WordPress''. Organization The i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stanford Encyclopedia Of Philosophy
The ''Stanford Encyclopedia of Philosophy'' (''SEP'') combines an online encyclopedia of philosophy with peer-reviewed publication of original papers in philosophy, freely accessible to Internet users. It is maintained by Stanford University. Each entry is written and maintained by an expert in the field, including professors from many academic institutions worldwide. Authors contributing to the encyclopedia give Stanford University the permission to publish the articles, but retain the copyright to those articles. Approach and history As of August 5th, 2022, the ''SEP'' has 1,774 published entries. Apart from its online status, the encyclopedia uses the traditional academic approach of most encyclopedias and academic journals to achieve quality by means of specialist authors selected by an editor or an editorial committee that is competent (although not necessarily considered specialists) in the field covered by the encyclopedia and peer review. The encyclopedia was created in 1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Truth-conditional Semantics
Truth-conditional semantics is an approach to semantics of natural language that sees meaning (or at least the meaning of assertions) as being the same as, or reducible to, their truth conditions. This approach to semantics is principally associated with Donald Davidson, and attempts to carry out for the semantics of natural language what Tarski's semantic theory of truth achieves for the semantics of logic. Truth-conditional theories of semantics attempt to define the meaning of a given proposition by explaining when the sentence is true. So, for example, because 'snow is white' is true if and only if snow is white, the meaning of 'snow is white' is snow is white. History The first truth-conditional semantics was developed by Donald Davidson in '' Truth and Meaning'' (1967). It applied Tarski's semantic theory of truth to a problem it was not intended to solve, that of giving the meaning of a sentence. Criticism Refutation from necessary truths Scott Soames has harshly critici ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inferential Role Semantics
Inferential role semantics (also conceptual role semantics, functional role semantics, procedural semantics, semantic inferentialism) is an approach to the theory of meaning that identifies the meaning of an expression with its relationship to other expressions (typically its inferential relations with other expressions), in contradistinction to denotationalism, according to which denotations are the primary sort of meaning. Overview Georg Wilhelm Friedrich Hegel is considered an early proponent of what is now called inferentialism.P. Stekeler-Weithofer (2016)"Hegel's Analytic Pragmatism" University of Leipzig, pp. 122–4. He believed that the ground for the axioms and the foundation for the validity of the inferences are the right consequences and that the axioms do not explain the consequence. In its current form, inferential role semantics originated in the work of Wilfrid Sellars. Contemporary proponents of semantic inferentialism include Robert Brandom, Gilbert Harman, Paul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nuel Belnap
Nuel Dinsmore Belnap Jr. (; born 1930) is an American logician and philosopher who has made contributions to the philosophy of logic, temporal logic, and structural proof theory. He taught at the University of Pittsburgh from 1963 until his retirement in 2011. Biography As an undergraduate, Belnap studied at the University of Illinois where he obtained his B.A. He recalled Max Fisch assigned Whitehead readings. After military service he attended Yale University and enjoyed metaphysics. His professors included Paul Weiss, Arthur Pap, Henry Margenau, Frederic Fitch, and Rulon Wells. On a Fulbright Fellowship in 1958 he went to Louvain to study with Canon Robert Feys. Belnap domiciled in Brussels with wife and 2-year-old. Feys directed Belnap to read Wilhelm Ackermann's article on rigorous implication in the ''Journal of Symbolic Logic''. Alan Ross Anderson and Belnap began to discuss relevant implication. In 1960 Anderson told Belnap to write up the work he had done on releva ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logical Harmony
Logical harmony, a name coined by Michael Dummett, is a supposed constraint on the rules of inference that can be used in a given logical system. Overview The logician Gerhard Gentzen proposed that the meanings of logical connectives could be given by the rules for introducing them into discourse. For example, if one believes that ''the sky is blue'' and one also believes that ''grass is green'', then one can introduce the connective ''and'' as follows: ''The sky is blue AND grass is green.'' Gentzen's idea was that having rules like this is what gives meaning to one's words, or at least to certain words. The idea has also been associated with the Wittgensteinian notion that in many cases we can say, '' meaning is use''. Most contemporary logicians prefer to think that the introduction rules and the elimination rules for an expression are equally important. In this case, ''and'' is characterized by the following rules: {, border="1" cellpadding="6" cellspacing="0" align="center" ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |