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Deriving Focused Lattice Calculi

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Rewriting Techniques and Applications (RTA 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2378))

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Abstract

We derive rewrite-based ordered resolution calculi for semilattices, distributive lattices and boolean lattices. Using ordered resolution as a metaprocedure, theory axioms are first transformed into independent bases. Focused inference rules are then extracted from inference patterns in refutations. The derivation is guided by mathematical and procedural background knowledge, in particular by ordered chaining calculi for quasiorderings (forgetting the lattice structure), by ordered resolution (forgetting the clause structure) and by Knuth-Bendix completion for non-symmetric transitive relations (forgetting both structures). Conversely, all three calculi are derived and proven complete in a transparent and generic way as special cases of the lattice calculi.

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Authors and Affiliations

  1. Institut für Informatik, Universität Augsburg, Universitätsstr. 14, D-86135, Augsburg, Germany

    Georg Struth

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  1. Georg Struth
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Editor information

Editors and Affiliations

  1. LIFL Bâtiment M3, Université de Lille 1, Cité Scientifique, 59655, Villeneuve d’Ascq cedex, France

    Sophie Tison

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© 2002 Springer-Verlag Berlin Heidelberg

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Struth, G. (2002). Deriving Focused Lattice Calculi. In: Tison, S. (eds) Rewriting Techniques and Applications. RTA 2002. Lecture Notes in Computer Science, vol 2378. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45610-4_7

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  • DOI: https://doi.org/10.1007/3-540-45610-4_7

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43916-5

  • Online ISBN: 978-3-540-45610-0

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