On the Relation Between Approximation Fixpoint Theory and Justification Theory

Research output: Chapter in Book/Report/Conference proceedingConference paper

2 Citations (Scopus)
79 Downloads (Pure)

Abstract

Approximation Fixpoint Theory (AFT) and Justification Theory (JT) are two frameworks to unify logical formalisms. AFT studies semantics in terms of fixpoints of lattice operators, and JT in terms of so-called justifications, which are explanations of why certain facts do or do not hold in a model. While the approaches differ, the frameworks were designed with similar goals in mind, namely to study the different semantics that arise in (mainly) non-monotonic logics. The first contribution of our current paper is to provide a formal link between the two frameworks. To be precise, we show that every justification frame induces an approximator and that this mapping from JT to AFT preserves all major semantics. The second contribution exploits this correspondence to extend JT with a novel class of semantics, namely ultimate semantics: we formally show that ultimate semantics can be obtained in JT by a syntactic transformation on the justification frame, essentially performing some sort of resolution on the rules.

Original languageEnglish
Title of host publicationProceedings of the 30th International Joint Conference on Artificial Intelligence, IJCAI 2021
EditorsZhi-Hua Zhou
PublisherIJCAI
Pages1973-1980
Number of pages8
ISBN (Electronic) 978-0-9992411-9-6
ISBN (Print) 978-0-9992411-9-6
DOIs
Publication statusPublished - 2021
Event30th International Joint Conference on Artificial Intelligence (IJCAI-21): IJCAI-21 - Canada, Montreal, Canada
Duration: 21 Aug 202126 Aug 2021
https://ijcai-21.org/

Publication series

NameIJCAI International Joint Conference on Artificial Intelligence
ISSN (Print)1045-0823

Conference

Conference30th International Joint Conference on Artificial Intelligence (IJCAI-21)
Abbreviated titleIJCAI 2021
CountryCanada
CityMontreal
Period21/08/2126/08/21
Internet address

Fingerprint

Dive into the research topics of 'On the Relation Between Approximation Fixpoint Theory and Justification Theory'. Together they form a unique fingerprint.

Cite this