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Register Log in FAQ CiteULike News Discussion Journals Browse current issues Groups Search groups Tag categorical_logic [1 article] Recent papers classified by the tag categorical_logic. Categorical and Kripke semantics for constructive S4 modal logic Vol. 2142 (2001), pp. 292-307. by Natasha Alechina , Michael Mendler , Valeria de Paiva , Eike Ritter posted to kripke by on 2007-12-13 10:03:50 as Note: You may cite this page as: http://www.citeulike.org/tag/categorical_logic RIS BibTeX RSS Related Tags Tags related to: categorical_logic Filter: kripke CiteULike organises scholarly (or academic) papers or literature and provides bibliographic (which means it makes bibliographies) for universities and higher education establishments. It helps undergraduates and postgraduates. People studying for PhDs or in postdoctoral (postdoc) positions. The service is similar in scope to EndNote or RefWorks or any other reference manager like BibTeX, but it is a social bookmarking service for scientists and humanities researchers.

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var wgNotice = ""; var wgNoticeLocal = ""; var wgNoticeLang = "en"; var wgNoticeProject = "wikipedia"; Categorical logic From Wikipedia, the free encyclopedia Jump to: navigation search Categorical logic is a branch of category theory within mathematics , adjacent to mathematical logic but in fact more notable for its connections to theoretical computer science . In broad terms, categorical logic represents both syntax and semantics by a category , and an interpretation by a functor. The categorical framework provides a rich conceptual background for logical and type-theoretic constructions. The subject has been recognisable in these terms since around Categorical logic originated with Bill Lawvere 's Functorial Semantics of Algebraic Theories (1963), and Elementary Theory of the Category of Sets (1964). Lawvere recognised the Grothendieck topos , introduced in algebraic topology as a generalised space, as a generalisation of the category of sets ( Quantifiers and Sheaves (1970)). With Myles Tierney, Lawvere then developed the notion of elementary topos , thus establishing the fruitful field of topos theory , which provides a unified categorical treatment of the syntax and semantics of higher-order predicate logic. The resulting logic is formally intuitionistic. Andre Joyal is credited, in the term Kripke–Joyal semantics, with the observation that the sheaf models for predicate logic, provided by topos theory, generalise

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Indopedia Main Page FORUM Help ... Log in The Indology CMS Categories Mathematical logic Category theory Theoretical computer science ... Wikipedia Article Category:Categorical logic ज्ञानकोश: - The Indological Knowledgebase Articles in category "Categorical logic" There are 3 articles in this category. C Categorical logic S Stone's representation theorem for Boolean algebras T Topos Retrieved from " http://www.indopedia.org/Category:Categorical_logic.html This page has been accessed 15 times. This page was last modified 07:39, 29 Oct 2004 by Indopedia user User:. Articles started before 24 Dec 2004 are outsourced from Wikipedia, the free encyclopedia, and occasionally developed by Indopedia authors. All Wikipedia content available under GFDL 1.2 . For Indopedia-specific content, ask the permission of the particular Indopedian. Recommended browser - Internet Explorer 6. Recommended Font to see diacritics - VU Arial. Edit this page Discuss this page Page history What links here ... About Indopedia Find: This page has been accessed 15 times. This page was last modified 07:39, 29 Oct 2004 by Indopedia user User:. Articles started before 24 Dec 2004 are outsourced from Wikipedia, the free encyclopedia, and occasionally developed by Indopedia authors. All Wikipedia content available under GFDL 1.2

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The Language of Mathematics - Dictionary and Research Guide Provided by Search: Add to Favorites Categorical logic Categorical logic is a branch of category theory within mathematics, adjacent to mathematical logic but in fact more notable for its connections to theoretical computer science. In broad terms, it is a theory about the transition from a type theory, understood to be within an intuitionistic logic or constructive mathematics setting, to a category, by means of a translation that respects both the syntax and the intended computational meaning of type-theoretic constructions. Wikipedia and Wikis Categorical logic - Wikipedia http://en.wikipedia.org/wiki/Categorical_logic Keywords and Synonyms Categorical logic, Categorical semantics More topics about: Categorical logic Edit this page Add new links, rate and edit existing links, or make suggestions. - Staff Explore related topics: Curry-Howard Stephen Cole Kleene probability theory Andrey Kolmogorov ... Functional programming Some descriptions may have been derived in part from Princeton University WordNet or Wikipedia Last update: December 19, 2007

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McFLY Title page Categorical logic Categorical logic is a branch of category theory within mathematics , adjacent to mathematical logic but in fact more notable for its connections to theoretical computer science . In broad terms, it is a theory about the transition from a type theory , understood to be within an intuitionistic logic or constructive mathematics setting, to a category , by means of a translation that respects both the syntax and the intended computational meaning of type-theoretic constructions. The subject has been recognisable in these terms since about 1970, when the needs of domain theory started to call on category theory. The earlier history is relatively complex, and contains some ironies. Categorical logic originated within sheaf theory , as a suitable version of Kripke semantics one can say with hindsight, and emerged as a theory with a character of its own only in shedding the necessary connection with sheaves. This can be traced in a number of stages, from 1960 onwards: the formulation of the Grothendieck topos , and then of the elementary topos , giving rise first to topos theory . Topos theory, as would now be understood, is the intuitionistic replacement for

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var skin = 'monobook';var stylepath = '/wiki/skins'; Categorical logic From ExampleProblems.com Jump to: navigation search Categorical logic is a branch of category theory within mathematics , adjacent to mathematical logic but in fact more notable for its connections to theoretical computer science . In broad terms, it is a theory about the transition from a type theory , understood to be within an intuitionistic logic or constructive mathematics setting, to a category , by means of a translation that respects both the syntax and the intended computational meaning of type-theoretic constructions. The subject has been recognisable in these terms since about , when the needs of domain theory started to call on category theory. The earlier history is relatively complex, and contains some ironies. Categorical logic originated within sheaf theory , as a suitable version of Kripke semantics one can say with hindsight, and emerged as a theory with a character of its own only in shedding the necessary connection with sheaves. This can be traced in a number of stages, from onwards: the formulation of the Grothendieck topos , and then of the elementary topos , giving rise first to topos theory . Topos theory, as would now be understood, is the intuitionistic replacement for

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Welcome to the MedLibrary.org Wikipedia Supplement on Categorical logic Please Click to Return to Front Page We subscribe to the HONcode principles. Verify here Web medlibrary.org Categorical logic This MedLibrary.org supplementary page on Categorical logic is provided directly from the open source Wikipedia as a service to our readers. Please see the note below on authorship of this content, as well as the Wikipedia usage guidelines. To search for other content from our encyclopedia supplement, please use the form below: Related Sponsors Categorical logic is a branch of category theory within mathematics , adjacent to mathematical logic but in fact more notable for its connections to theoretical computer science . In broad terms, categorical logic represents both syntax and semantics by a category , and an interpretation by a functor. The categorical framework provides a rich conceptual background for logical and type-theoretic constructions. The subject has been recognisable in these terms since around Categorical logic originated with Bill Lawvere 's Functorial Semantics of Algebraic Theories (1963), and

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US states Yellow Pages Explore Categories/Topics Auto ... Feedback NEWS UPDATES Categorical logic is a branch of category theory within mathematics , adjacent to mathematical logic but in fact more notable for its connections to theoretical computer science . In broad terms, categorical logic represents both syntax and semantics by a category , and an interpretation by a functor. The categorical framework provides a rich conceptual background for logical and type-theoretic constructions. The subject has been recognisable in these terms since around Grothendieck topos , introduced in algebraic topology as a generalised space, as a generalisation of the category of Sets, (Quantifiers and Sheaves (1970)). With Myles Tierney, Lawvere then developed the notion of elementary topos , thus establishing the fruitful field of topos theory , which provides a unified categorical treatment of the syntax and semantics of higher-order predicate logic. The resulting logic is formally intuitionistic. Andre Joyal is credited, in the term Kripke-Joyal semantics, with the observation that the sheaf models for predicate logic, provided by topos theory, generalise Kripke semantics . Joyal and others applied these models to study higher-order concepts such as the real numbers in the intuitionistic setting.

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Main Page Alphabetical index addBookmark('Bookmark'); English Encyclopedia Categorical logic From Wikipedia, the free encyclopedia. Categorical logic is a branch of category theory within mathematics , adjacent to mathematical logic but in fact more notable for its connections to theoretical computer science . In broad terms, it is a theory about the transition from a type theory , understood to be within an intuitionistic logic or constructive mathematics setting, to a category , by means of a translation that respects both the syntax and the intended computational meaning of type-theoretic constructions. The subject has been recognisable in these terms since about , when the needs of domain theory started to call on category theory. The earlier history is relatively complex, and contains some ironies. Categorical logic originated within sheaf theory , as a suitable version of Kripke semantics one can say with hindsight, and emerged as a theory with a character of its own only in shedding the necessary connection with sheaves. This can be traced in a number of stages, from onwards: the formulation of the Grothendieck topos , and then of the elementary topos , giving rise first to topos theory . Topos theory, as would now be understood, is the intuitionistic replacement for

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@import "portal2.css"; Hol.eu : Categorical logic A European Direct Navigation Website learn more Categorical logic Categorical logic is a branch of category theory within mathematics , adjacent to mathematical logic but in fact more notable for its connections to theoretical computer science . In broad terms, categorical logic represents both syntax and semantics by a category , and an interpretation by a functor. The categorical framework provides a rich conceptual background for logical and type-theoretic constructions. The subject has been recognisable in these terms since around 1970. Categorical logic originated with Bill Lawvere's Functorial Semantics of Algebraic Theories (1963), and Elementary Theory of the Category of Sets (1964). Lawvere recognised the Grothendieck topos , introduced in algebraic topology as a generalised space, as a generalisation of the category of Sets, (Quantifiers and Sheaves (1970)). With Myles Tierney, Lawvere then developed the notion of elementary topos , thus establishing the fruitful field of topos theory , which provides a unified categorical treatment of the syntax and semantics of higher-order predicate logic. The resulting logic is formally intuitionistic. Andre Joyal is credited, in the term Kripke-Joyal semantics, with the observation that the sheaf models for predicate logic, provided by topos theory, generalise

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