Results for ' 03G30'

8 found
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  1.  38
    Topological representation of geometric theories.Henrik Forssell - 2012 - Mathematical Logic Quarterly 58 (6):380-393.
    Using Butz and Moerdijk's topological groupoid representation of a topos with enough points, a ‘syntax-semantics’ duality for geometric theories is constructed. The emphasis is on a logical presentation, starting with a description of the semantic topological groupoid of models and isomorphisms of a theory. It is then shown how to extract a theory from equivariant sheaves on a topological groupoid in such a way that the result is a contravariant adjunction between theories and groupoids, the restriction of which is a (...)
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  2.  45
    Hilbert’s varepsilon -operator in intuitionistic type theories.John L. Bell - 1993 - Mathematical Logic Quarterly 39 (1):323--337.
    We investigate Hilbert’s varepsilon -calculus in the context of intuitionistic type theories, that is, within certain systems of intuitionistic higher-order logic. We determine the additional deductive strength conferred on an intuitionistic type theory by the adjunction of closed varepsilon -terms. We extend the usual topos semantics for type theories to the varepsilon -operator and prove a completeness theorem. The paper also contains a discussion of the concept of “partially defined‘ varepsilon -term. MSC: 03B15, 03B20, 03G30.
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  3.  20
    Syntax and Semantics of the Logic.Carsten Butz - 1997 - Notre Dame Journal of Formal Logic 38 (3):374-384.
    In this paper we study the logic , which is first-order logic extended by quantification over functions (but not over relations). We give the syntax of the logic as well as the semantics in Heyting categories with exponentials. Embedding the generic model of a theory into a Grothendieck topos yields completeness of with respect to models in Grothendieck toposes, which can be sharpened to completeness with respect to Heyting-valued models. The logic is the strongest for which Heyting-valued completeness is known. (...)
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  4.  11
    Syntax and Semantics of the Logic $\mathcal{L}^\lambda_{\omega\omega}$.Carsten Butz - 1997 - Notre Dame Journal of Formal Logic 38 (3):374-384.
    In this paper we study the logic $\mathcal{L}^\lambda_{\omega\omega}$, which is first-order logic extended by quantification over functions (but not over relations). We give the syntax of the logic as well as the semantics in Heyting categories with exponentials. Embedding the generic model of a theory into a Grothendieck topos yields completeness of $\mathcal{L}^\lambda_{\omega\omega}$ with respect to models in Grothendieck toposes, which can be sharpened to completeness with respect to Heyting-valued models. The logic $\mathcal{L}^\lambda_{\omega\omega}$ is the strongest for which Heyting-valued completeness (...)
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  5.  8
    Syntax and Semantics of the Logic $\mathcal{L}^\lambda_{\omega\omega}$.Carsten Butz - 1997 - Notre Dame Journal of Formal Logic 38 (3):374-384.
    In this paper we study the logic $\mathcal{L}^\lambda_{\omega\omega}$, which is first-order logic extended by quantification over functions . We give the syntax of the logic as well as the semantics in Heyting categories with exponentials. Embedding the generic model of a theory into a Grothendieck topos yields completeness of $\mathcal{L}^\lambda_{\omega\omega}$ with respect to models in Grothendieck toposes, which can be sharpened to completeness with respect to Heyting-valued models. The logic $\mathcal{L}^\lambda_{\omega\omega}$ is the strongest for which Heyting-valued completeness is known. Finally, (...)
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  6.  28
    Isomorphic formulae in classical propositional logic.Kosta Došen & Zoran Petrić - 2012 - Mathematical Logic Quarterly 58 (1):5-17.
    Isomorphism between formulae is defined with respect to categories formalizing equality of deductions in classical propositional logic and in the multiplicative fragment of classical linear propositional logic caught by proof nets. This equality is motivated by generality of deductions. Characterizations are given for pairs of isomorphic formulae, which lead to decision procedures for this isomorphism.
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  7.  18
    Models of Martin-Löf Type Theory From Algebraic Weak Factorisation Systems.Nicola Gambino & Marco Federico Larrea - 2023 - Journal of Symbolic Logic 88 (1):242-289.
    We introduce type-theoretic algebraic weak factorisation systems and show how they give rise to homotopy-theoretic models of Martin-Löf type theory. This is done by showing that the comprehension category associated with a type-theoretic algebraic weak factorisation system satisfies the assumptions necessary to apply a right adjoint method for splitting comprehension categories. We then provide methods for constructing several examples of type-theoretic algebraic weak factorisation systems, encompassing the existing groupoid and cubical sets models, as well as new models based on normal (...)
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  8.  82
    On Gabbay's Proof of the Craig Interpolation Theorem for Intuitionistic Predicate Logic.Michael Makkai - 1995 - Notre Dame Journal of Formal Logic 36 (3):364-381.
    Using the framework of categorical logic, this paper analyzes and streamlines Gabbay's semantical proof of the Craig interpolation theorem for intuitionistic predicate logic. In the process, an apparently new and interesting fact about the relation of coherent and intuitionistic logic is found.
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