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Literal Projection for First-Order Logic

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Logics in Artificial Intelligence (JELIA 2008)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5293))

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Abstract

The computation of literal projection generalizes predicate quantifier elimination by permitting, so to speak, quantifying upon an arbitrary sets of ground literals, instead of just (all ground literals with) a given predicate symbol. Literal projection allows, for example, to express predicate quantification upon a predicate just in positive or negative polarity. Occurrences of the predicate in literals with the complementary polarity are then considered as unquantified predicate symbols. We present a formalization of literal projection and related concepts, such as literal forgetting, for first-order logic with a Herbrand semantics, which makes these notions easy to access, since they are expressed there by means of straightforward relationships between sets of literals. With this formalization, we show properties of literal projection which hold for formulas that are free of certain links, pairs of literals with complementary instances, each in a different conjunct of a conjunction, both in the scope of a universal first-order quantifier, or one in a subformula and the other in its context formula. These properties can justify the application of methods that construct formulas without such links to the computation of literal projection. Some tableau methods and direct methods for second-order quantifier elimination can be understood in this way.

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Author information

Authors and Affiliations

  1. Universität Koblenz-Landau,  

    Christoph Wernhard

Authors
  1. Christoph Wernhard
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Editors and Affiliations

  1. Department of Computer Science, TU Dresden, Germany

    Steffen Hölldobler

  2. Institut für Theoretische Informatik, TU Dresden, Germany

    Carsten Lutz

  3. Institute of Philosophy, Dresden University of Technology, Dresden, Germany

    Heinrich Wansing

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Wernhard, C. (2008). Literal Projection for First-Order Logic. In: Hölldobler, S., Lutz, C., Wansing, H. (eds) Logics in Artificial Intelligence. JELIA 2008. Lecture Notes in Computer Science(), vol 5293. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87803-2_32

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  • DOI: https://doi.org/10.1007/978-3-540-87803-2_32

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-87802-5

  • Online ISBN: 978-3-540-87803-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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