vix.ing · top · new · best · stats · spec

Paraconsistency, resolution and relevance

2019/06/08 by Michał Walicki, Michal Walicki, Walicki, Michal +2
Computer Science · Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Logic (math.LO) #Logic in Computer Science (cs.LO) #Logic, Reasoning, and Knowledge #Multi-Agent Systems and Negotiation #Semantic Web and Ontologies #cs.LO #math.LO

paper · pdf · doi:10.48550/arxiv.1906.03476

arxiv created 2019/06/08 · openalex publication_date 2019/06/08 · arxiv updated 2019/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Digraphs provide an alternative syntax for propositional logic, with digraph kernels corresponding to classical models. Semikernels generalize kernels and we identify a subset of well-behaved semikernels that provides nontrivial models for inconsistent theories, specializing to the classical semantics for the consistent ones. Direct (instead of refutational) reasoning with classical resolution is sound and complete for this semantics, when augmented with a specific weakening which, in particular, excludes Ex Falso. Dropping all forms of weakening yields reasoning which also avoids typical fallacies of relevance.

Citations

Related