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

arXiv: https://arxiv.org/abs/1803.01571 · HTML: https://mlsanity.com/paper/1803.01571/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Mar 2018.

## Built on by (most cited first, 1 of 1)

- [Morpho-logic from a Topos Perspective: Application to symbolic AI](https://mlsanity.com/paper/2303.04895/) (2023)

## Abstract (arXiv)

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.