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

TL;DR

This paper introduces a new framework for abductive reasoning in arbitrary satisfaction-based logics using retraction, expanding previous propositional logic approaches and enabling broader applicability.

Contribution

It develops a generalized retraction-based framework for abductive reasoning applicable to various satisfaction systems, extending prior propositional logic methods.

Findings

Framework successfully defines abductive operators in multiple logics

Retraction properties are weaker, allowing more flexible abduction operators

Application to several logics demonstrates versatility

Abstract

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.