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Inference for Annotated Logics over Distributive Lattices

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Foundations of Intelligent Systems (ISMIS 2002)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2366))

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Abstract

The inference rule ℧-resolution was introduced in [18] as a technique for developing an SLD-style query answering procedure for the logic programming subset of annotated logic. This paper explores the properties of ℧-resolution in the general theorem proving setting. In that setting, it is shown to be complete and to admit a linear restriction. Thus ℧-resolution is amenable to depth-first control strategies that require little memory. An ordering restriction is also described and shown to be complete, providing a promising saturation-based procedure for annotated logic. The inference rule essentially requires that the lattice of truth values be ordinary. Earlier investigations left open the question of whether all distributive lattices are ordinary; this is answered in the affirmative here.

This research was supported in part by the National Science Foundation under grant CCR-9731893.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, Emory University Atlanta, GA, 30322, USA

    James J. Lu

  2. Department of Computer Science, State University of New York, Albany, NY, 12222, USA

    Neil V. Murray

  3. Department of Mathematics, Dalhousie University Halifax, Nova Scotia, B3H 3J5, Canada

    Heydar Radjavi

  4. Department of Mathematics, University of New Haven, West Haven, CT, 06516, USA

    Erik Rosenthal

  5. Department of Mathematics, University of Toronto, Toronto, Ontario, M5S 3G3, Canada

    Peter Rosenthal

Authors
  1. James J. Lu
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  2. Neil V. Murray
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  3. Heydar Radjavi
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  4. Erik Rosenthal
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  5. Peter Rosenthal
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Editor information

Editors and Affiliations

  1. UFR d’Informatique, Université Claude Bernard Lyon I, 8, boulevard Niels Bohr, 69622, Villeurbanne Cedex, France

    Mohand-Saïd Hacid

  2. Dept. of Computer Science College of IT, University of North Carolina, Charlotte, NC, 28223, USA

    Zbigniew W. Raś

  3. Băt. L. Equipe de Recherche en Ingénierie des Connaissances, Université Lumière Lyon 2, 5, avenue Pierre Mendes-France, 69676, Bron Cedex, France

    Djamel A. Zighed

  4. LRI, Université Paris Sud, Băt. 490, 91405, Orsay Cedex, France

    Yves Kodratoff

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© 2002 Springer-Verlag Berlin Heidelberg

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Lu, J.J., Murray, N.V., Radjavi, H., Rosenthal, E., Rosenthal, P. (2002). Inference for Annotated Logics over Distributive Lattices. In: Hacid, MS., Raś, Z.W., Zighed, D.A., Kodratoff, Y. (eds) Foundations of Intelligent Systems. ISMIS 2002. Lecture Notes in Computer Science(), vol 2366. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48050-1_32

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  • DOI: https://doi.org/10.1007/3-540-48050-1_32

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  • Print ISBN: 978-3-540-43785-7

  • Online ISBN: 978-3-540-48050-1

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