Extending Defeasibility for Propositional Standpoint Logics
This work addresses a theoretical gap in formal logic for AI and knowledge representation, but it is incremental as it builds on prior defeasibility and standpoint logic approaches.
The paper tackles the problem of incorporating defeasibility into propositional standpoint logics by integrating existing defeasible conditionals and notions, resulting in a new logical framework with a preferential semantics, sound and complete tableaux calculus, and computational complexity in PSpace.
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 Gómez Álvarez 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.