Justification logics with counterfactual and relevant conditionals

TL;DR

This paper introduces new conditional justification logics that integrate counterfactuals, providing formal semantics and applications to philosophical problems like knowledge analysis and counterexamples such as Gettier cases.

Contribution

It develops a novel family of conditional justification logics with relational semantics, tableau proof systems, and formalizations of philosophical counterfactual conditions.

Findings

Introduced conditional justification logics with relational semantics

Developed a tableau system and proved completeness

Formalized Nozick's counterfactual conditions within the logic

Abstract

The purpose of this paper is to introduce justification logics based on conditional logics. We introduce a new family of logics, called conditional justification logics, which incorporates a counterfactual conditional in its language. For the semantics, we offer relational models that merge the selection-function semantics of conditional logics with the relational semantics of justification logics. As an application, we formalize Nozick's counterfactual conditions in his analysis of knowledge and investigate their connection to Aumann's concepts of knowledge. Additionally, we explore Gettier's counterexamples to the justified true belief analysis, as well as McGinn's counterexamples to Nozick's analysis of knowledge. Furthermore, we introduce a justification logic that includes a relevant counterfactual conditional and we demonstrate the variable-sharing property for this conditional. We also develop a tableau system for this logic and establish its completeness with respect to Routley relational models. Finally, we formalize Nozick's counterfactual conditions using this relevant counterfactual conditional and represent the sheep in the field example of Chisholm within this logic.