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1. CiteULike: Tag Categorical_logic [1 Article]
Recent papers classified by the tag Categorical_logic. posted to modal_logic kripke _file _copy Categorical_logic by adrian_pigors on 200712-13
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##### 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
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2. Categorical Logic - Wikipedia, The Free Encyclopedia
Retrieved from http//en.wikipedia.org/wiki/Categorical_logic . Categories Logic stubs Systems of formal logic Theoretical computer science
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##### Categorical logic
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 KripkeÃ¢ÂÂJoyal semantics, with the observation that the sheaf models for predicate logic, provided by topos theory, generalise

3. Category:Categorical Logic - Indopedia, The Indological Knowledgebase
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5. Categorical Logic
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6. Definitions
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##### 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.
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• Categorical logic, Categorical semantics

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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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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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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:
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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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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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

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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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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

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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 KripkeÃ¢ÂÂ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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'Categorical logic' is a branch of category theory within mathematics , adjacent to

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48. Categorical Logic [Definition]
This page defines Categorical logic, as well as providing detailed articles on topics related to Categorical logic.
http://www.wikimirror.com/Categorical_logic
 Categorical logic information on Wikimirror.com Read below for information on Categorical logic Search Categorical logic is a branch of category theory Category theory is a mathematical theory that deals in an abstract way with mathematical structures and relationships between them. It is half-jokingly known as "generalized abstract nonsense". The use of this phrase does not mean that mathematicians consider category theory to be fuzzy or non-rigorous, merely that a small minority consider it too abstract to be useful or interesting.... [click for more] within mathematics Mathematics is commonly defined as the study of patterns of structure, change, and space; more informally, one might say it is the study of "figures and numbers". Mathematical knowledge is constantly growing, through research and application, but mathematics itself is not usually considered a natural science. One reason is that mathematical knowledge is revised and updated in a different way; though arguably founded on experiment in some manner, it is not comparable to the natural sciences in this respect. ... [click for more] , adjacent to mathematical logic Mathematical logic is a discipline within mathematics, studying formal systems in relation to the way they encode intuitive concepts of proof and computation as part of the foundations of mathematics....

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51. Category:Categorical Logic
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##### Articles in category "Categorical logic"
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52. The Pedia - Categorical Logic
Categories category theory category Logic stubs Systems of formal logic Theoretical computer science Categorical logic
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Logic stubs

Systems of formal logic
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Categorical logic
##### Summary Of: Categorical logic
categorical logic represents both syntax and semantics by a... Another route to categorical logic would therefore have been through Kolmogorov...
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53. Categorical Logic
Cambridge University Press, Cambridge, UK, 1997. Reprinted with corrections, 2000. Retrieved from en.wikipedia.org/wiki/Categorical_logic. Contents
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