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Semantics and expressiveness of disjunctive ordered logic

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Abstract

The paper proposes a knowledge representation language which extends logic programming with disjunction, inheritance, true negation and modularization. The resulting language is called Disjunctive Ordered Logic (\(\mathcal{D}\mathcal{O}\mathcal{L}\) for short). A model‐theoretic semantics for \(\mathcal{D}\mathcal{O}\mathcal{L}\) is given, and it is shown to extend the stable model semantics of disjunctive logic programs. A number of examples show the suitability of \(\mathcal{D}\mathcal{O}\mathcal{L}\) for knowledge representation and commonsense reasoning. Among other things, the proposed language appears to be a powerful tool for the description of diagnostic processes which are based on stepwise refinements. The complexity and the expressiveness of the language are carefully analyzed. The analysis pays particular attention to the relative power and complexity of inheritance, negation and disjunction. An interesting result in this course concerns the role played by inheritance. Indeed, our results show that inheritance does not increase at all the complexity of any fragment of the language, while it does increase the expressive power of some \(\mathcal{D}\mathcal{O}\mathcal{L}\) fragments.

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Authors and Affiliations

  1. DIMET, Università di Reggio Calabria, I‐89100, Reggio Calabria, Italy

    Francesco Buccafurri

  2. Information Systems Department, Vienna University of Technology, Paniglgasse 16, A‐1040, Vienna, Austria

    Nicola Leone

  3. Dipartimento di Matematica, U, niversità della Calabria, I‐87030, Rende, Italy

    Pasquale Rullo

Authors
  1. Francesco Buccafurri
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  2. Nicola Leone
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  3. Pasquale Rullo
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Buccafurri, F., Leone, N. & Rullo, P. Semantics and expressiveness of disjunctive ordered logic. Annals of Mathematics and Artificial Intelligence 25, 311–337 (1999). https://doi.org/10.1023/A:1018986207453

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