Curb Your Theory! A Circumspective Approach for Inclusive Interpretation of Disjunctive Information

We introduce curbing, a new nonmonotonic technique of commonsense reasoning that is based on model minimality but unlike circumscription treats disjunction inclusively. A finitely axiomatized first-order theory T is transformed to a formula Curb(T) whose set of models is defined as the smallest collection of models which contains all minimal models of T and which is closed under formation of minimal upper bounds with respect to inclusion. We first give an intuitive definition of Curb in third-order logic and then show how Curb can be equivalently expressed in second-order logic. We study the complexity of inferencing from a curbed propositional theory and present a PSPACE algorithm for this problem. Finally, we address different possibilities to approximate the curb of a theory.