Background
The semantics of disjunctive logic programs is based on minimal models
which make atoms appearing in a disjunctive program false by default.
In many cases, this is highly desirable, but certain problems become
awkward to formalize if all atoms are blindly subject to minimization.
Parallel circumscription enables the use of varying and
fixed atoms in addition to those minimized which eases
the task of knowledge presentation in many cases.
The idea is that the atoms in P= An extended notation Circ(Π,P_1>...>P_k,V,F) is introduced to represent the prioritized circumscription of disjunctive program Π which includes the parallel circumscription of Π as its special case, that is, when k=1. The idea is that atoms in P_1 are falsified with the highest priority, those in P_2 with the next highest priority, and so on. We say that models of Circ(Π,P_1>...>P_k,V,F) are the ⟨P_1>...>P_k,V,F⟩-minimal models of positive program Π. Lifschitz [Lifschitz, 1985] shows that a prioritized circumscription Circ(Π,P_1>...>P_k,V,F) corresponds to a conjunction
The translator
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