## Value Minimization in Circumscription

### C. Baral, A. Gabaldon and A. Provetti

## 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.