From belief change to modality: Epistemic semantics for modal and conditional logic

Abstract

This paper sets out to extend the epistemic semantics presented in Dahl (2023) to modal and conditional logics. To do so, I extend the notion of belief expansion systems, inspired by the AGM-model of belief change, to include belief revision , and use the resulting structures as models for both conditional and modal logic. In the first case, this applies the well-known approach to conditionals initiated by Gärdenfors (1978), but in a weaker setting which doesn’t assume an underlying logic. As such, we get semantics for both classical conditional logic and the intuitionistic conditionals studied by Weiss (2019). For modal logics, I use the condition that $$\Box \varphi$$ is accepted if and only if $$\varphi$$ is accepted under every belief revision. As a result of this system of semantics, we get soundness and completeness theorems for both classical and non-classical systems of modal and conditional logic on the basis of a single type of structure. Finally, I briefly discuss how models based on belief change can still be thought to explain the semantics of objective modal claims.