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Logical inference and polyhedral projection

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Computer Science Logic (CSL 1991)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 626))

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Abstract

We explore connections between polyhedral projection and inference in propositional logic. We formulate the problem of drawing all inferences that contain a restricted set of atoms (i.e., all inferences that pertain to a given question) as a logical projection problem. We show that polyhedral projection partially solves this problem and in particular derives precisely those inferences that can be obtained by a certain form of unit resolution. We prove that this unit resolution algorithm is exponential in the number of atoms in the restricted set but is polynomial in the problem size when this number of fixed. We also survey a number of new satisfiability algorithms that have been suggested by the polyhedral interpretation of propositional logic.

Supported in part by the Air Force Office of Scientific Research, Grant number AFOSR-91-0287.

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Authors and Affiliations

  1. GSIA, Carnegie Mellon University, 15213, Pittsburgh, PA, USA

    J. N. Hooker

  2. Matematisk Institut, Åarhus Universitet, DK-8000, Åarhus C, Denmark

    J. N. Hooker

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  1. J. N. Hooker
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Egon Börger Gerhard Jäger Hans Kleine Büning Michael M. Richter

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© 1992 Springer-Verlag Berlin Heidelberg

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Hooker, J.N. (1992). Logical inference and polyhedral projection. In: Börger, E., Jäger, G., Kleine Büning, H., Richter, M.M. (eds) Computer Science Logic. CSL 1991. Lecture Notes in Computer Science, vol 626. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023767

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  • DOI: https://doi.org/10.1007/BFb0023767

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55789-0

  • Online ISBN: 978-3-540-47285-8

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