Extending Defeasibility for Propositional Standpoint Logics

2025-07-14

AI Summary

This paper addresses the limitation of propositional stance logic in expressing multi-level defeasibility. We propose Defeasible Propositional Stance Logic (DPL), the first stance logic incorporating defeasible necessity and possibility operators, enabling nonmonotonic reasoning at three levels: entailment relations, stance modalities, and stance-sharpening statements. Methodologically, DPL integrates conditional defeasibility, stance modal operators, and a stance-refinement mechanism, yielding a sound and complete tableaux calculus grounded in preference-based semantics. Theoretical contributions include: (i) a sound and complete deductive system for DPL; and (ii) a proof that its decision problem is PSpace-complete. This work establishes the first logically expressive and computationally tractable framework for dynamic, revisable reasoning in stance modeling.

Technology Category

• Knowledge Representation and Reasoning: Nonmonotonic Reasoning
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

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 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.

Problem

• Extends defeasible propositional standpoint logic framework
• Integrates defeasible conditionals and necessity concepts
• Develops sound tableaux calculus with PSpace complexity

Innovation

• Integrates defeasible conditionals into standpoint logic
• Introduces preferential semantics for extended language
• Proposes sound and complete PSpace tableaux calculus