Filter Preferential Entailment for the Logic of Action in Almost Continuous Worlds

Abstract

Mechanical systems, of the kinds which are of interest for qualitative reasoning, are characterized by a set of real-valued parameters, each of which is a piecewise continuous function of real-valued time. A temporal logic is introduced which allows the description of parameters, both in their continuous intervals and around their breakpoints, and which also allows the description of actions being performed in sequence or in parallel. If axioms are given which characterize physical laws, conditions and effects of actions, and observations or goals at specific points in time, one wishes to identify sets of actions ("plans") which account for the observations or obtain the goals. The paper proposes preference criteria which should determine the model set for such axioms. It is shown that conventional preferential entailment is not sufficient. A modified condition, filter preferential entailment is defined where preference conditions and axiom satisfaction conditions are interleaved.