Quantitative Disjunctive Logic Programming: semantics and computation

Authors:
Cristinel Mateis
Affiliations:
Institut für Informationssysteme 184/2, Technical University of Vienna, Favoritenstrasse 9‐11, A‐1040 Wien, Austria E‐mail: mateis@dbai.tuwien.ac.at
Venue:
AI Communications
Year:
2000

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Abstract

A new knowledge representation language, called QDLP, which extends DLP to deal with uncertain values is introduced. Each (quantitative) rule is assigned a certainty degree interval (a subinterval of [0,1]). The propagation of uncertainty information from the premises to the conclusion of a quantitative rule is achieved by means of triangular norms (T‐norms). Different T‐norms induce different semantics for one given quantitative program. In this sense, QDLP is parameterized and each choice of a T‐norm induces a different QDLP language. Each T‐norm is eligible for events with determinate relationships (e.g., independence, exclusiveness) between them. Since there are infinitely many T‐norms, it turns out that there is a family of infinitely many QDLP languages. This family is carefully studied and the set of QDLP languages which generalize traditional DLP is precisely singled out. Algorithms for computing the minimal models of quantitative programs are proposed.