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COMPLETENESS OF SECOND-ORDER PROPOSITIONAL S4 AND H IN TOPOLOGICAL SEMANTICS

Published online by Cambridge University Press:  27 September 2018

PHILIP KREMER
PHILIP KREMER*
Affiliation:
Department of Philosophy, University of Toronto
*
*DEPARTMENT OF PHILOSOPHY UNIVERSITY OF TORONTO TORONTO, ON M5S 3H7, CANADA E-mail: kremer@utsc.utoronto.ca
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Abstract

We add propositional quantifiers to the propositional modal logic S4 and to the propositional intuitionistic logic H, introducing axiom schemes that are the natural analogs to axiom schemes typically used for first-order quantifiers in classical and intuitionistic logic. We show that the resulting logics are sound and complete for a topological semantics extending, in a natural way, the topological semantics for S4 and for H.

Keywords

03B4503B20second-order propositional logicmodal logicintuitionistic logictopological semantics
Type
Research Article
Information
The Review of Symbolic Logic , Volume 11 , Issue 3 , September 2018 , pp. 507 - 518
Copyright
Copyright © Association for Symbolic Logic 2018 

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