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    Department of Computer Science, Rutgers University

    An Intuitionistic Interpretation of Finite and Infinite Failure

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    In this paper, we propose an intuitionistic semantics for negation-as-failure in logic programs. The basic idea is to work with the completion of the program, not in classical logic, but in intuitionistic (or, more precisely, minimal) logic. Moreover, we consider two forms of completion: (1) first-order predicate completion, as defined by Clark, which is related to SLDNF resolution; and (2) second-order completion, using circumscription. Specifically, given any program R, we write a sentence in second-order intuitionistic logic, called the partial intuitionistic circumscription axiom, and we declare this sentence to be the "meaning" of R. We then show that our semantics -- called the PIC semantics -- agrees with the perfect model semantics in the case of a locally stratified program. For nonstratified programs, we show that the PIC semantics is strictly stronger than the (3-valued) wellfounded semantics. We also show a more complex relationship to the (2-valued) stable model semantics....

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    New Full text for this article was not available? Send a request to the author(s).
    Title : An Intuitionistic Interpretation of Finite and Infinite Failure
    Abstract : In this paper, we propose an intuitionistic semantics for negation-as-failure in logic programs. The basic idea is to work with the completion of the program, not in classical logic, but in intuitionistic (or, more precisely, minimal) logic. Moreover, we consider two forms of completion: (1) first-order predicate completion, as defined by Clark, which is related to SLDNF resolution; and (2) second-order completion, using circumscription. Specifically, given any program R, we write a sentence in second-order intuitionistic logic, called the partial intuitionistic circumscription axiom, and we declare this sentence to be the "meaning" of R. We then show that our semantics -- called the PIC semantics -- agrees with the perfect model semantics in the case of a locally stratified program. For nonstratified programs, we show that the PIC semantics is strictly stronger than the (3-valued) wellfounded semantics. We also show a more complex relationship to the (2-valued) stable model semantics....
    Subject : unspecified
    Area : Computer Science
    Language : English
    Affiliations : 
    Url : http://www.cse.unsw.edu.au/~meyden/research/lpnmr93.ps
    Doi : 10.1.1.34.6975

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