Extending Defeasibility for Propositional Standpoint Logics

TL;DR

This paper extends propositional standpoint logic by incorporating defeasibility, enabling nuanced reasoning about beliefs and modalities, with a sound, complete tableaux calculus and PSpace complexity analysis.

Contribution

It introduces a defeasible version of propositional standpoint logic with a new semantics and a sound, complete tableaux calculus, advancing reasoning capabilities in this domain.

Findings

Developed a preferential semantics for the extended logic

Proposed a tableaux calculus that is sound and complete

Established the computational complexity as PSpace

Abstract

In this paper, we introduce a new defeasible version of propositional standpoint logic by integrating Kraus et al.'s defeasible conditionals, Britz and Varzinczak's notions of defeasible necessity and distinct possibility, along with Leisegang et al.'s approach to defeasibility into the standpoint logics of G\'omez \'Alvarez and Rudolph. The resulting logical framework allows for the expression of defeasibility on the level of implications, standpoint modal operators, and standpoint-sharpening statements. We provide a preferential semantics for this extended language and propose a tableaux calculus, which is shown to be sound and complete with respect to preferential entailment. We also establish the computational complexity of the tableaux procedure to be in PSpace.