Stable Model Semantics - Stable Models of A Set of Propositional Formulas

Stable Models of A Set of Propositional Formulas

Rules, and even disjunctive rules, have a rather special syntactic form, in comparison with arbitrary propositional formulas. Each disjunctive rule is essentially an implication such that its antecedent (the body of the rule) is a conjunction of literals, and its consequent (head) is a disjunction of atoms. David Pearce and Paolo Ferraris showed how to extend the definition of a stable model to sets of arbitrary propositional formulas. This generalization has applications to answer set programming.

Pearce's formulation looks very different from the original definition of a stable model. Instead of reducts, it refers to equilibrium logic -- a system of nonmonotonic logic based on Kripke models. Ferraris's formulation, on the other hand, is based on reducts, although the process of constructing the reduct that it uses differs from the one described above. The two approaches to defining stable models for sets of propositional formulas are equivalent to each other.