2026-07-22T12:57:16Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:12352 2024-03-06T10:50:02Z ddc:004 open_access

Constraint Solving over Multiple Similarity Relations Dundua, Besik Kutsia, Temur Marin, Mircea Pau, Cleopatra Fuzzy relations similarity constraint solving Similarity relations are reflexive, symmetric, and transitive fuzzy relations. They help to make approximate inferences, replacing the notion of equality. Similarity-based unification has been quite intensively investigated, as a core computational method for approximate reasoning and declarative programming. In this paper we consider solving constraints over several similarity relations, instead of a single one. Multiple similarities pose challenges to constraint solving, since we can not rely on the transitivity property anymore. Existing methods for unification with fuzzy proximity relations (reflexive, symmetric, non-transitive relations) do not provide a solution that would adequately reflect particularities of dealing with multiple similarities. To address this problem, we develop a constraint solving algorithm for multiple similarity relations, prove its termination, soundness, and completeness properties, and discuss applications. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Besik Dundua and Temur Kutsia and Mircea Marin and Cleopatra Pau 2020 Is Part Of LIPIcs, Volume 167, 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.FSCD.2020.30 urn:nbn:de:0030-drops-123522 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2020.30 eng https://creativecommons.org/licenses/by/3.0/legalcode