Base-extension semantics for modal logic

Logic Journal of the IGPL (forthcoming)
  Copy   BIBTEX

Abstract

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.

Other Versions

No versions found

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 101,960

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Analytics

Added to PP
2024-03-03

Downloads
30 (#764,992)

6 months
9 (#531,649)

Historical graph of downloads
How can I increase my downloads?

Author Profiles

David Pym
University College London
Timo Eckhardt
University College London

Citations of this work

No citations found.

Add more citations

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.
Modal Logic.Patrick Blackburn, Maarten de Rijke & Yde Venema - 2001 - Studia Logica 76 (1):142-148.
Articulating Reasons: An Introduction to Inferentialism.Robert Brandom - 2002 - Philosophical Quarterly 52 (206):123-125.

View all 16 references / Add more references