Indicative Conditionals and Dynamic Epistemic Logic

TL;DR

This paper explores the intersection of formal semantics and dynamic epistemic logic, introducing new logical tools and axiomatizations for indicative conditionals and epistemic modals, and proving decidability results.

Contribution

It provides a complete axiomatization for a semantic consequence relation and introduces a new dynamic operator based on Kolodny and MacFarlane's semantics.

Findings

A simple, complete axiomatization for Yalcin's semantic consequence relation.

Introduction of a new dynamic operator for indicative conditionals.

Decidability of the logic with epistemic modals and indicative conditionals.

Abstract

Recent ideas about epistemic modals and indicative conditionals in formal semantics have significant overlap with ideas in modal logic and dynamic epistemic logic. The purpose of this paper is to show how greater interaction between formal semantics and dynamic epistemic logic in this area can be of mutual benefit. In one direction, we show how concepts and tools from modal logic and dynamic epistemic logic can be used to give a simple, complete axiomatization of Yalcin's [16] semantic consequence relation for a language with epistemic modals and indicative conditionals. In the other direction, the formal semantics for indicative conditionals due to Kolodny and MacFarlane [9] gives rise to a new dynamic operator that is very natural from the point of view of dynamic epistemic logic, allowing succinct expression of dependence (as in dependence logic) or supervenience statements. We prove decidability for the logic with epistemic modals and Kolodny and MacFarlane's indicative conditional via a full and faithful computable translation from their logic to the modal logic K45.