Weak Kleene Logic and Topic-Sensitive Logics

Abstract

This paper makes first steps toward a systematic investigation of how pertinence to topic contributes to determine deductively valid reasoning along with preservation of designated values. I start from the interpretation of Weak Kleene Logic WKL as a reasoning tool that preserves truth and topic pertinence, which is offered by Jc Beall. I keep Beall’s motivations and I argue that WKL cannot meet them in a satisfying way. In light of this, I propose an informal definition of a topic-sensitive logic and I proceed to turn it into a formal one by deploying the topic-algebraic framework from the Topic-Sensitive Intentional Modalities project by Francesco Berto. I apply the framework in order to define semantically a ‘classical topic-sensitive logic’ CTSL that meets Beall’s motivations and proves topic-sensitive. Then, I prove results that connect CTSL and any possible topic-sensitive logic to the tradition of containment logics and provide a unification tool for a wide range of recent proposals in philosophical logic. A topic-theoretical interpretation of WKL is then offered without prejudice to the fact that the logic is not topic-sensitive. Finally, the paper discusses some conceptual issues and research perspectives.