Base-extension Semantics for Modal Logic

In proof-theoretic semantics, meaning is based on inference. It may seen as the mathematical expression of the inferentialist interpretation of logic. Much recent work has focused on base-extension semantics, in which the validity of formulas is given by an inductive definition generated by provabil...

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Bibliographic Details
Published inarXiv.org
Main Authors Eckhardt, Timo, Pym, David J
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 12.02.2024
Subjects
Logic
Semantics
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Summary:In proof-theoretic semantics, meaning is based on inference. It may seen as the mathematical expression of the inferentialist interpretation of logic. Much recent work has focused on base-extension semantics, in which the validity of formulas is given by an inductive definition generated by provability in a `base' of atomic rules. Base-extension semantics for classical and intuitionistic propositional logic have been explored by several authors. In this paper, we develop base-extension semantics for the classical propositional modal systems K, KT , K4, and S4, with \(\square\) as the primary modal operator. We establish appropriate soundness and completeness theorems and establish the duality between \(\square\) and a natural presentation of \(\lozenge\). We also show that our semantics is in its current form not complete with respect to euclidean modal logics. Our formulation makes essential use of relational structures on bases.
ISSN:2331-8422