Paraconsistent disjunctive deductive databases

The author develops a theory of disjunctive logic programming, with negations allowed to appear both in the head of a clause and in the body. As such programs can easily contain inconsistent information (with respect to the intuitions of two-valued logic), this means that the formalism allows reasoning about systems that are intuitively inconsistent but yet have models (in nonclassical model theory). Such an ability is important because inconsistencies may occur very easily during the design and development of deductive databases and/or expert systems. The author also develops a theory of disjunctive deductive databases that (perhaps) contain inconsistent information. The author shows how to associate, with any such database, an operator that maps multivalued-model states to multivalued-model states. It is shown that this operator has a least fixed point which is identical to the set of all variable-free disjunctions that are provable from the database under consideration. A procedure to answer queries to such databases is devised. Soundness and completeness results are proved. The techniques introduced are fairly general. However, the results are applicable to databases that are quantitative in nature