2024/01/24 by Timo Eckhardt, Eckhardt, Timo, David Pym +1 · 1 citation
Computer Science · #Advanced Algebra and Logic #FOS: Computer and information sciences #FOS: Mathematics #Logic (math.LO) #Logic in Computer Science (cs.LO) #Logic, Reasoning, and Knowledge #Semantic Web and Ontologies
paper · pdf · doi:10.48550/arxiv.2401.13597
openalex publication_date 2024/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.