Completeness results for intuitionistic and modal logic in a categorical setting

Annals of Pure and Applied Logic 72 (1):25-101 (1995)
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Abstract

Versions and extensions of intuitionistic and modal logic involving biHeyting and bimodal operators, the axiom of constant domains and Barcan's formula, are formulated as structured categories. Representation theorems for the resulting concepts are proved. Essentially stronger versions, requiring new methods of proof, of known completeness theorems are consequences. A new type of completeness result, with a topos theoretic character, is given for theories satisfying a condition considered by Lawvere . The completeness theorems are used to conclude results asserting that certain logics are conservatively interpretable in others

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Citations of this work

On logics with coimplication.Frank Wolter - 1998 - Journal of Philosophical Logic 27 (4):353-387.
Category theory.Jean-Pierre Marquis - 2008 - Stanford Encyclopedia of Philosophy.
Modes of Adjointness.M. Menni & C. Smith - 2013 - Journal of Philosophical Logic (2-3):1-27.

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References found in this work

A completeness theorem in modal logic.Saul Kripke - 1959 - Journal of Symbolic Logic 24 (1):1-14.
Semantical Analysis of Modal Logic I. Normal Propositional Calculi.Saul A. Kripke - 1963 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 9 (5‐6):67-96.
The Algebra of Topology.J. C. C. Mckinsey & Alfred Tarski - 1944 - Annals of Mathematics, Second Series 45:141-191.

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