Defeasible Modalities

TL;DR

This paper introduces a new family of modal logics that incorporate defeasibility into modal notions like actions and obligations by enriching possible worlds semantics with preferences, along with a sound and complete tableau calculus.

Contribution

It extends standard modal logic with defeasible modalities using preferential semantics and provides a formal tableau calculus for reasoning within this framework.

Findings

The proposed modal logics effectively model defeasible modalities.

A sound and complete tableau calculus is developed for these logics.

The approach offers an elegant way to formalize defeasibility in modal contexts.

Abstract

Nonmonotonic logics are usually characterized by the presence of some notion of 'conditional' that fails monotonicity. Research on nonmonotonic logics is therefore largely concerned with the defeasibility of argument forms and the associated normality (or abnormality) of its constituents. In contrast, defeasible modes of inference aim to formalize the defeasible aspects of modal notions such as actions, obligations and knowledge. In this work we enrich the standard possible worlds semantics with a preference ordering on worlds in Kripke models. The resulting family of modal logics allow for the elegant expression of defeasible modalities. We also propose a tableau calculus which is sound and complete with respect to our preferential semantics.