Partial Implication Semantics for Desirable Propositions

Motivational attitudes play an important role in investigations into intelligent agents. One of the key problems of representing and reasoning about motivational attitudes is which propositions are the desirable ones. The answer based on classical logic is that the propositions that logically imply the goal are desirable and the others are not. We argue that this criterion is inadequate for the incomplete knowledge about environments for an agent. In this paper, we present a simple and intuitive semantics---partial implication---for the characterization of desirable propositions. In this semantics, Proposition P is a desirable one with respect to a given goal Q if and only if P is “useful” and “harmless” to Q in any situation. Partial implication is an extension of classical implication. We investigate some fundamental properties of partial implication and discuss some of the potential applications.