Generalized Epstein semantics for Parry systems

TL;DR

This paper introduces a generalized set-assignment semantics based on Epstein's framework, enabling a formal characterization of Parry's logic of analytic implication and its recent variants.

Contribution

It extends Epstein semantics to include dual algebras for extensional and intensional values, providing a novel set-assignment semantics for Parry systems.

Findings

Developed a generalized Epstein semantics for Parry systems

Provided Hilbert-style axiomatizations and completeness proofs

Established a set-assignment semantics for Parry's logic

Abstract

In this paper I introduce a generalized version of Richard Epstein's set-assignment semantics ([Epstein, 1990]). As a case study, I consider how this framework can be used to characterize William Parry's logic of analytic implication and some of its recent variations proposed by [Ferguson, 2023a]. In generalized Epstein semantics the parallel use of two algebras, one for extensional and the other for intensional values, allows to account for various forms of content sharing between formulae, which motivates the choice to investigate Parry systems. Hilbert-style axiomatizations and completeness proofs will be presented for all the considered calculi, in particular as main result I provide a set-assignment semantics for Parry's logic.