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Kurt Gödel Colloquium on Computational Logic and Proof Theory

KGC 1997: Computational Logic and Proof Theory pp 203–218Cite as

Comparing computational representations of Herbrand models

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1289))

Abstract

Finding computationally valuable representations of models of predicate logic formulas is an important issue in the field of automated theorem proving, e.g. for automated model building or semantic resolution. In this article we treat the problem of representing single models independently of building them and discuss the power of different mechanisms for this purpose. We start with investigating context-free languages for representing single Herbrand models. We show their computational feasibility and prove their expressive power to be exactly the finite models. We show an equivalence with “ground atoms and ground equations” concluding equal expressive power. Finally we indicate how various other well known techniques could be used for representing essentially infinite models (i.e. models of not finitely controllable formulas), thus motivating our interest in relating model properties with syntactical properties of corresponding Herbrand models and in investigating connections between formal language theory, term schematizations and automated model building.

This work was partially supported by the Austrian Science Foundation under FWF grant P11624-MAT.

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Authors and Affiliations

  1. Institut für Informationssysteme, Abteilung für Wissensbasierte Systeme, Technische Universität Wien, Treitlstr. 3/E184-3, A-1040, Wien, Austria, Europe

    Robert Matzinger

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  1. Robert Matzinger
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Georg Gottlob Alexander Leitsch Daniele Mundici

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© 1997 Springer-Verlag Berlin Heidelberg

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Matzinger, R. (1997). Comparing computational representations of Herbrand models. In: Gottlob, G., Leitsch, A., Mundici, D. (eds) Computational Logic and Proof Theory. KGC 1997. Lecture Notes in Computer Science, vol 1289. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63385-5_44

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  • DOI: https://doi.org/10.1007/3-540-63385-5_44

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63385-3

  • Online ISBN: 978-3-540-69806-7

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