Truthmakers, Incompatibility, and Modality

Abstract

This paper introduces a new framework, based on the notion of compatibility space, obtained by adding a primitive incompatibility relation to a state space in the sense of Fine. The key idea inspiring the framework is to modify Fine's truthmaker semantics by taking the notion of incompatibility as primitive, and use it to define other notions. We discuss some interesting features of the framework and explore its advantages over the standard framework of state spaces. We review some applications of the framework, including proofs of soundness and completeness theorems for a number of logics, one way to use compatibility states to mirror Kripke frames, and an exploration of a way to use the new framework to provide truthmaking clauses for modal formulas.