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International Conference on Logic Programming and Nonmonotonic Reasoning

LPNMR 1997: Logic Programming And Nonmonotonic Reasoning pp 309–323Cite as

Programs with universally quantified embedded implications

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1265))

Abstract

We suggest to consider the class of logic programs with the new nonmonotonic operator which we call universally quantified embedded implication. By such implications we mean formulas of the form ∀x 1⋯∀x l(P 1 & ⋯ & Pm → Q1 & ⋯ & Qn). The main subject of the paper is lifting notions and theorems, related to normal logic programs, to programs with universally quantified embedded implications. For this class of programs we define the standard model semantics for stratified programs, the stable model semantics, the well-founded semantics. We show that main properties of above semantics for normal logic programs hold as well for programs with implications. Besides, we investigate the possibilities of reducing programs with implications to normal logic programs. Finally we define a calculus corresponding to SLDNF-calculus [9] and prove theorem of its soundness.

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Authors and Affiliations

  1. Department of Mathematics, Irkutsk State University, K.Marks st., 1, 664003, Irkutsk, Russia

    Vyacheslav Petukhin

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  1. Vyacheslav Petukhin
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Jürgen Dix Ulrich Furbach Anil Nerode

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© 1997 Springer-Verlag Berlin Heidelberg

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Petukhin, V. (1997). Programs with universally quantified embedded implications. In: Dix, J., Furbach, U., Nerode, A. (eds) Logic Programming And Nonmonotonic Reasoning. LPNMR 1997. Lecture Notes in Computer Science, vol 1265. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63255-7_23

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  • DOI: https://doi.org/10.1007/3-540-63255-7_23

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63255-9

  • Online ISBN: 978-3-540-69249-2

  • eBook Packages: Springer Book Archive

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