Disjunctive Programs
In a disjunctive rule, the head may be the disjunction of several atoms:
(the semicolon is viewed as alternative notation for disjunction ). Traditional rules correspond to, and constraints to . To extend the stable model semantics to disjunctive programs, we first define that in the absence of negation ( in each rule) the stable models of a program are its minimal models. The definition of the reduct for disjunctive programs remains the same as before. A set of atoms is a stable model of if is a stable model of the reduct of relative to .
For example, the set is a stable model of the disjunctive program
because it is one of two minimal models of the reduct
The program above has one more stable model, .
As in the case of traditional programs, each element of any stable model of a disjunctive program is a head atom of, in the sense that it occurs in the head of one of the rules of . As in the traditional case, the stable models of a disjunctive program are minimal and form an antichain. Testing whether a finite disjunctive program has a stable model is -complete .
Read more about this topic: Stable Model Semantics
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