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International Workshop on Computer Science Logic

CSL 1994: Computer Science Logic pp 264–278Cite as

Reasoning and rewriting with set-relations I: Ground completeness

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 933))

Abstract

The paper investigates reasoning with set-relations: intersection, inclusion and identity of 1-element sets. A language is introduced which, interpreted in a multi-algebraic semantics, allows one to specify such relations. An inference system is given and shown sound and refutationally ground-complete for a particular proof strategy which selects only maximal literals from the premise clauses. Each of the introduced set-relations satisfies only two among the three properties of the equivalence relations — we study rewriting with such non-equivalence relations and point out differences from the equational case. As a corollary of the main ground-completeness theorem we obtain ground-completeness of the introduced rewriting technique.

Both authors gratefully acknowledge the financial support received from the Norwegian Research Council.

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Author information

Authors and Affiliations

  1. Department of Mathematical Logic, Institute of Mathematics and Informatics, Vilnius, Lithuania

    Valentinas Kriaučiukas

  2. Deptartment of Informatics, University of Bergen, Norway

    Michał Walicki

Authors
  1. Valentinas Kriaučiukas
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  2. Michał Walicki
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Editor information

Leszek Pacholski Jerzy Tiuryn

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© 1995 Springer-Verlag Berlin Heidelberg

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Kriaučiukas, V., Walicki, M. (1995). Reasoning and rewriting with set-relations I: Ground completeness. In: Pacholski, L., Tiuryn, J. (eds) Computer Science Logic. CSL 1994. Lecture Notes in Computer Science, vol 933. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0022262

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  • DOI: https://doi.org/10.1007/BFb0022262

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60017-6

  • Online ISBN: 978-3-540-49404-1

  • eBook Packages: Springer Book Archive

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