Some logics of belief and disbelief

TL;DR

This paper introduces four new logics that explicitly incorporate disbelief into knowledge representation, enhancing expressivity and addressing various motivations like belief contraction and negation.

Contribution

It presents four novel logics of disbelief with soundness and completeness proofs, expanding the tools for belief change and knowledge representation.

Findings

Four logics of disbelief are defined and analyzed.

Soundness and completeness results are provided for each logic.

The logics are compared in terms of applicability and utility.

Abstract

The introduction of explicit notions of rejection, or disbelief, into logics for knowledge representation can be justified in a number of ways. Motivations range from the need for versions of negation weaker than classical negation, to the explicit recording of classic belief contraction operations in the area of belief change, and the additional levels of expressivity obtained from an extended version of belief change which includes disbelief contraction. In this paper we present four logics of disbelief which address some or all of these intuitions. Soundness and completeness results are supplied and the logics are compared with respect to applicability and utility.