Explanatory relations in arbitrary logics based on satisfaction systems, cutting and retraction
This work addresses the problem of generalizing abductive reasoning across various logics for researchers in formal logic and AI, though it appears incremental as it builds on prior concepts with weaker requirements.
The paper introduces a new framework for defining abductive reasoning operators using retraction in arbitrary logics based on satisfaction systems, extending previous work on propositional logics by requiring weaker properties for retraction to enable a larger set of suitable operators for different logics.
The aim of this paper is to introduce a new framework for defining abductive reasoning operators based on a notion of retraction in arbitrary logics defined as satisfaction systems. We show how this framework leads to the design of explanatory relations satisfying properties of abductive reasoning, and discuss its application to several logics. This extends previous work on propositional logics where retraction was defined as a morphological erosion. Here weaker properties are required for retraction, leading to a larger set of suitable operators for abduction for different logics.