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On stratified disjunctive programs

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Abstract

We address the problem of a consistent fixpoint semantics for general disjunctive programs restricted to stratifiable programs which do not recurse through negative literals. We apply the nonmonotonic fixpoint theory developed by Apt, Blair and Walker to a closure operatorT c and develop a fixpoint semantics for stratified disjunctive programs. We also provide an iterative definition for negation, called the Generalized Closed World Assumption for Stratified programs (GCWAS), and show that our semantics captures this definition. We develop a model-theoretic semantics for stratified disjunctive programs and show that the least state characterized by the fixpoint semantics corresponds to a stable-state defined in a manner similar to the stable-models of Gelfond and Lifschitz. We also discuss a weaker stratification semantics for general disjunctive programs based on the Weak Generalized Closed World Assumption.

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References

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Authors and Affiliations

  1. Department of Computer Science and Institute for Advanced Computer Studies, University of Maryland, 20742, College Park, MD, USA

    Arcot Rajasekar & Jack Minker

Authors
  1. Arcot Rajasekar
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  2. Jack Minker
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Rajasekar, A., Minker, J. On stratified disjunctive programs. Ann Math Artif Intell 1, 339–357 (1990). https://doi.org/10.1007/BF01531083

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