Abstract

Minimization in circumscription has focussed on minimizing the extent of a set of predicates (with or without priorities among them), or of a formula. Although functions and other constants may be left varying during circumscription, no earlier formalism to the best of our knowledge minimized functions. In this paper we introduce and motivate the notion of {\em value minimizing} a function in circumscription. Intuitively, value minimizing a function consists in choosing those models where the value of the function is minimal relative to an ordering on its range. We first give the formulation of value minimization of a single function based on a syntactic transformation and then give a formulation in model theoretic terms. We then discuss value minimization of a set of functions with and without priorities. We show how Lifschitz's Nested Abnormality Theories can be used to express value minimization, and discuss the prospect of its use for knowledge representation, particularly in formalizing reasoning about actions.