SEMANTICS OF DISJUNCTIVE LOGIC PROGRAMS AND DEDUCTIVE DATABASES

Recently the author introduced the so called stationary semantics which extends the well-founded semantics of normal logic programs to the class of all disjunctive logic programs and deductive databases. The stationary semantics also extends the perfect model semantics defined earlier for stratified disjunctive databases. As a result, the stationary semantics is the only currently known semantics which extends both semantics and is defined for all disjunctive databases. However, the original definition of stationary semantics was given in terms of 3-valued models and 3-valued theories and therefore seemed to require non-standard, 3-valued logic. In this paper we show, however, that the stationary semantics can be equivalently defined in terms of classical, 2- valued logic, without any reference to 3-valued models. As a byproduct we obtain a simpler and more natural description of the stationary semantics. For every disjunctive database P we define the so called stationary expansions of P and we show that among all such expansions there is always the smallest one called the stationary completion STAT(P) of P, which, like Clark's Predicate Completion of P, is a first order extension of P providing the appropriate meaning or semantics for the database. We also show that the stationary semantics can be equivalently defined as the iterated minimal model semantics and as the kast fixed point of a minimal model operator.