Work

An Algebraic Notion of Conditional Independence, and Its Application to Knowledge Representation

Year: 2025

Type: conference-paper

Abstract: Conditional independence is a crucial concept supporting adequate modelling and efficient reasoning in probabilistics. In knowledge representation, the idea of conditional independence has also been introduced for specific formalisms, such as propositional logic and belief revision. In this paper, the notion of conditional independence is studied in the algebraic framework of approximation fixpoint theory. This gives a language-independent account of conditional independence that can be straightforwardly applied to any logic with fixpoint semantics. It is shown how this notion allows to reduce global reasoning to parallel instances of local reasoning, leading to fixed-parameter tractability results. Furthermore, relations to existing notions of conditional independence are discussed and the framework is applied to normal logic programming.

Source: Proceedings of the AAAI Conference on Artificial Intelligence

DOI: 10.1609/aaai.v39i14.33641

Author: Jesse Heyninck

Institutions: University of Cape Town, Open University of the Netherlands

Language: English

Topic: Logic, Reasoning, and Knowledge

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

Funder: Nederlandse Organisatie voor Wetenschappelijk Onderzoek

Award: LogicLM: Combining Logic Programs with Language Model