Dunn Semantics for Contra-Classical Logics

TL;DR

This paper demonstrates that many contra-classical logics can be understood as variants of FDE through modifications of truth or falsity conditions, with Dunn semantics clarifying the source of their contra-classicality.

Contribution

It provides a systematic analysis of how Dunn semantics explains contra-classical logics as variants of FDE by modifying evaluation conditions.

Findings

Contra-classical logics can be derived from FDE by modifying truth or falsity conditions.

Dunn semantics clarifies the source of contra-classicality in these logics.

A detailed analysis of evaluation condition modifications is provided.

Abstract

In this paper I show, with a rich and systematized diet of examples, that many contra-classical logics can be presented as variants of FDE, obtained by modifying at least one of the truth or falsity conditions of some connective. Then I argue that using Dunn semantics provides a clear understanding of the source of contra-classicality, namely, connectives that have either the classical truth or the classical falsity condition of another connective. This requires a fine-grained analysis of the sorts of modifications that can be made to an evaluation condition, analysis which I offer here as well.