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Finding Tractable Formulas in NNF

  • Edgar Altamirano
  • Gonçal Escalada-Imaz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1861)

Abstract

Many applications in Computer Science require to represent knowledge and to reason with non normal form formulas. However, most of the advances in tractable reasoning are applied only to CNF formulas. In this paper, we extend tractability to several classes of non normal formulas which are of high practical interest. Thus, we first define three non normal Horn-like classes of formulas F 1F 2 ∧... ∧F n where each F i is constituted by a disjunction of two optional terms F i = NNF i -C i +: the first one is in Negation Normal Form (NNF) composed exclusively with negative literals and the second one is a conjunction of positive propositions. These formulas codify the same problems that the Horn formulas but with significantly, even exponentially, less propositional symbols. Second, we define sound and refutational complete inference rule sets for each class. Our third contribution consists in the design of a sound, complete and strictly linear running time algorithm for each class. As a result, the time required by our linear algorithms running on the defined non normal Horn-like formulas can be exponentially less than that required by the existing linear Horn-SAT algorithms.

Keywords

Inference Rule Conjunctive Normal Form Horn Clause Unit Clause Empty Clause 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Edgar Altamirano
    • 1
  • Gonçal Escalada-Imaz
    • 1
  1. 1.Artificial Intelligence Research Institute (IIIA)Spanish Scientific Research Council (CSIC)Bellaterra, BarcelonaSpain

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