Combining Closed World Assumptions with Stable Negation

We study the semantics of disjunctive logic programs that simultaneously contain multiple kinds of default negations. We introduce operators notG, notW, and notSTB in the language of logic programs to represent the Generalized Closed World Assumption, the Weak Generalized Closed World Assumption, and the stable negation, respectively. The notion of stratification involving different kinds of negations is defined and the meaning of stratified programs with multiple negations is described. The class of stratified programs is extended to the class of quasi-stratified programs and the semantics of the latest class is studied.