Morphologic for knowledge dynamics: revision, fusion, abduction

TL;DR

This paper introduces algebraic morphological operators within propositional logic to model knowledge dynamics tasks like revision, fusion, and abduction, providing intuitive, well-behaved, and computationally feasible methods.

Contribution

It develops a semantic, algebraic framework using morphological operations for knowledge dynamics, offering new operators for revision, fusion, and abduction in propositional logic.

Findings

Operators are semantically intuitive and well-behaved.

Methods are computationally tractable.

Examples demonstrate effective knowledge modeling.

Abstract

Several tasks in artificial intelligence require to be able to find models about knowledge dynamics. They include belief revision, fusion and belief merging, and abduction. In this paper we exploit the algebraic framework of mathematical morphology in the context of propositional logic, and define operations such as dilation or erosion of a set of formulas. We derive concrete operators, based on a semantic approach, that have an intuitive interpretation and that are formally well behaved, to perform revision, fusion and abduction. Computation and tractability are addressed, and simple examples illustrate the typical results that can be obtained.