Constraint Solving over Multiple Similarity Relations

Authors Besik Dundua, Temur Kutsia, Mircea Marin, Cleopatra Pau

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Besik Dundua
  • FBT, International Black Sea University, Tbilisi, Georgia
  • VIAM, Ivane Javakhishvili Tbilisi State University, Georgia
Temur Kutsia
  • Johannes Kepler University, Research Institute for Symbolic Computation, Linz, Austria
Mircea Marin
  • West University of Timişoara, Romania
Cleopatra Pau
  • Johannes Kepler University, Research Institute for Symbolic Computation, Linz, Austria

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Besik Dundua, Temur Kutsia, Mircea Marin, and Cleopatra Pau. Constraint Solving over Multiple Similarity Relations. In 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 167, pp. 30:1-30:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Logic
  • Computing methodologies → Symbolic and algebraic manipulation
  • Theory of computation → Semantics and reasoning
  • Fuzzy relations
  • similarity
  • constraint solving


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