Value Minimization in Circumscription

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 most circumscription formalisms allow varying of functions and other constants, no formalism to the best of our knowledge minimized functions. In this paper we introduce and motivate the notion of value minimizing a function in circumscription. In value minimizing we do not minimize the extent of the function; rather we minimize the value of the function. We show how Lifschitz's nested abnormality theories can be used to do value minimization.