Extending Disjunctive Logic Programming by T-norms

This paper proposes a new knowledge representation language, called QDLP, which extends DLP to deal with uncertain values. A certainty degree interval (a subinterval of [0; 1]) is assigned to each (quantitative) rule. Triangular norms (T -norms) are employed to define calculi for propagating uncertainty information from the premises to the conclusion of a quantitative rule. Negation is considered and the concept of stable model is extended to QDLP. 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. Finally, the complexity of the main decisional problems arising in the context of QDLP (i.e., Model Checking, Stable Model Checking, Consistency, and Brave Reasoning) is analyzed. It is shown that the complexity of the relevant fragments of QDLP coincides exactly with the complexity of DLP. That is, reasoning with uncertain values is more general and not harder than reasoning with boolean values.