Capturing Parallel Circumscription with Disjunctive Logic Programs

The stable model semantics of disjunctive logic programs is based on classical models which are minimal with respect to subset inclusion. As a consequence, every atom appearing in a disjunctive program is false by default. This is sometimes undesirable from the knowledge representation point of view and a more refined control of minimization is called for. Such features are already present in Lifschitz’s parallel circumscription where certain atoms are allowed to vary or to have fixed values while all other atoms are minimized. In this paper, it is formally shown that the expressive power of minimal models is properly increased in the presence of varying atoms. In spite of this, we show how parallel circumscription can be embedded into disjunctive logic programming in a relatively systematic fashion using a linear and faithful, but non-modular translation. This enables the conscious use of varying atoms in disjunctive logic programs — leading to more elegant and concise problem representations in various domains.