Four-valued logics of indicative conditionals

TL;DR

This paper explores extending three-valued indicative conditional logics by adding a new truth-value, using twist constructions to develop and represent these new four-valued logics.

Contribution

It introduces a novel four-valued logic framework for indicative conditionals based on twist constructions, expanding existing three-valued models.

Findings

Develops four-valued logic models for indicative conditionals

Provides algebraic semantics using twist constructions

Proves representation theorems for the new logics

Abstract

We detail some ways in which the study of three-valued logics of indicative conditionals can be extended by further adding a new truth-value. Our approach heavily relies on twist constructions, which have been already used in the literature in order to provide algebraic semantics in the three-valued case. Here we follow the inverse path: we first specify how these twist constructions, expanded with the new truth-value, induce new logics and then we prove the corresponding twist representation results.