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Indexed Categories and Bottom-Up Semantics of Logic Programs

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Logic for Programming, Artificial Intelligence, and Reasoning (LPAR 2001)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2250))

Abstract

We propose a categorical framework which formalizes and extends the syntax, operational semantics and declarative model theory of a broad range of logic programming languages. A program is interpreted in an indexed category in such a way that the base category contains all the possible states which can occur during the execution of the program (such as global constraints or type information), while each fiber encodes the logic at each state.

We define appropriate notions of categorical resolution and models, and we prove the related correctness and completeness properties.

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Author information

Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Universitá di Udine, via delle Scienze, 206, Udine, Italy

    Gianluca Amato

  2. Mathematics Department, Wesleyan University, 265 Church St., Middletown, CT, USA

    James Lipton

Authors
  1. Gianluca Amato
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  2. James Lipton
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Editor information

Editors and Affiliations

  1. Department of Software, Technical University of Catalonia, Jordi Girona 1, 08034, Barcelona, Spain

    Robert Nieuwenhuis

  2. Department of Computer Science, University of Manchester, Kilburn Building, Oxford Road, M13 9PL, Manchester, UK

    Andrei Voronkov

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© 2001 Springer-Verlag Berlin Heidelberg

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Amato, G., Lipton, J. (2001). Indexed Categories and Bottom-Up Semantics of Logic Programs. In: Nieuwenhuis, R., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2001. Lecture Notes in Computer Science(), vol 2250. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45653-8_30

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  • DOI: https://doi.org/10.1007/3-540-45653-8_30

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42957-9

  • Online ISBN: 978-3-540-45653-7

  • eBook Packages: Springer Book Archive

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