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DOI: 10.4230/LIPIcs.FSCD.2020.30

Constraint Solving over Multiple Similarity Relations

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

Published in: LIPIcs, Volume 167, 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)

Abstract

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.

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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)

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@InProceedings{dundua_et_al:LIPIcs.FSCD.2020.30,
  author =	{Dundua, Besik and Kutsia, Temur and Marin, Mircea and Pau, Cleopatra},
  title =	{{Constraint Solving over Multiple Similarity Relations}},
  booktitle =	{5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)},
  pages =	{30:1--30:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-155-9},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{167},
  editor =	{Ariola, Zena M.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2020.30},
  URN =		{urn:nbn:de:0030-drops-123522},
  doi =		{10.4230/LIPIcs.FSCD.2020.30},
  annote =	{Keywords: Fuzzy relations, similarity, constraint solving}
}

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DOI: 10.4230/LIPIcs.RTA.2010.193

Order-Sorted Unification with Regular Expression Sorts

Authors: Temur Kutsia and Mircea Marin

Published in: LIPIcs, Volume 6, Proceedings of the 21st International Conference on Rewriting Techniques and Applications (2010)

Abstract

We extend first-order order-sorted unification by permitting regular expression sorts for variables and in the domains of function symbols. The set of basic sorts is finite. The obtained signature corresponds to a finite bottom-up hedge automaton. The unification problem in such a theory generalizes some known unification problems. Its unification type is infinitary. We give a complete unification procedure and prove decidability.

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Temur Kutsia and Mircea Marin. Order-Sorted Unification with Regular Expression Sorts. In Proceedings of the 21st International Conference on Rewriting Techniques and Applications. Leibniz International Proceedings in Informatics (LIPIcs), Volume 6, pp. 193-208, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{kutsia_et_al:LIPIcs.RTA.2010.193,
  author =	{Kutsia, Temur and Marin, Mircea},
  title =	{{Order-Sorted Unification with Regular Expression Sorts}},
  booktitle =	{Proceedings of the 21st International Conference on Rewriting Techniques and Applications},
  pages =	{193--208},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-18-7},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{6},
  editor =	{Lynch, Christopher},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.RTA.2010.193},
  URN =		{urn:nbn:de:0030-drops-26537},
  doi =		{10.4230/LIPIcs.RTA.2010.193},
  annote =	{Keywords: Unification, sorts, regular expression}
}

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Documents authored by Marin, Mircea

Constraint Solving over Multiple Similarity Relations

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Order-Sorted Unification with Regular Expression Sorts

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