Explanatory relations in arbitrary logics based on satisfaction systems,\n cutting and retraction

2018/03/05 by Marc Aiguier, Aiguier, Marc, Jamal Atif +5
Computer Science · #Advanced Algebra and Logic #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #Logic, Reasoning, and Knowledge #Semantic Web and Ontologies

paper · pdf · doi:10.48550/arxiv.1803.01571

openalex publication_date 2018/03/05 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

The aim of this paper is to introduce a new framework for defining abductive\nreasoning operators based on a notion of retraction in arbitrary logics defined\nas satisfaction systems. We show how this framework leads to the design of\nexplanatory relations satisfying properties of abductive reasoning, and discuss\nits application to several logics. This extends previous work on propositional\nlogics where retraction was defined as a morphological erosion. Here weaker\nproperties are required for retraction, leading to a larger set of suitable\noperators for abduction for different logics.\n

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