An Algorithm to Compute Minimal Models in Prioritized Circumscription by 0-1 Integer Programming

Abstract

The purpose of this paper is to propose an algorithm that computes all the minimal models in propositional prioritized circumscription by 0-1 integer linear programming. An algorithm for non-prioritized circumscription based on integer linear programming has been proposed by Bell et al. We extend their method to handle prioritized circumscription. A set of formulas is transformed into a set of linear inequality constraints and the objective function is determined by priority over minimized propositions. Our algorithm works as follows. We firstly compute a minimal model by optimizing the objective function under the given constraints. Then, we add a set of new constraints which prevents from choosing models that is not smaller than the previous minimal model and we iterate this process until any models are derived from the constraints.