The Semantics of Potential Intentions

The SharedPlans theory provides an axiomatic framework of collaborative plans based on four types of intentional attitudes. However, there still lacks an adequate semantics for the ‘potential intention’ operators. In this paper, we give a formal semantics to potential intentions, and examine models that can validate various relations between beliefs, intentions, and potential intentions. Introduction Philosophers have long struggled over how best to characterize the concept of intention (Searle 1983; Bratman 1987), which is intimately connected with means-ends reasoning. Normal modal logics have been employed to define possible-worlds semantics for intentions (Cohen & Levesque 1990; Rao & Georgeff 1995). Konolige & Pollack (1993) provide a representationalist theory of intention, using cognitive structures to directly represent intentions and the means-ends relationship among intentions. Singh & Asher (1993) give a theory of intentions based on Discourse Representation Theory. Existing solutions have been extended to investigate intentions involving groups and cooperations (Grosz & Sidner 1990; Singh 1993; Herzig & Longin 2002). The SharedPlans theory (Grosz & Kraus 1996) provides an axiomatic framework of collaborative plans based on four types of intentional attitudes. Operators Int.To and Int.Th represent intentions that have been adopted by an agent, while Pot.Int.To and Pot.Int.Th represent potential intentions—intentions that an agent would like to adopt, but to which it is not yet committed. Int.To and Pot.Int.To apply to actions while Int.Th and Pot.Int.Th apply to propositions. However, Grosz & Kraus only informally characterized what it means for an agent to have a potential intention. There still lacks an adequate semantics for the ‘potential intention’ operators. Our aim in this paper is to present a formal semantics of potential intentions and investigate the relationships of potential intentions with agent beliefs and normal intentions. Desire is a potential influencer of conduct while intention is a conduct-controlling pro-attitude (Bratman 1990). From such a sense, potential intentions are agent desires. Copyright c © 2005, American Association for Artificial Intelligence (www.aaai.org). All rights reserved. Desires play an important role in determining goals and intentions that stand for the consistent worlds an agent is striving for (Cohen & Levesque 1990). The notion of ‘potential intentions’ differs from the concepts of ‘goal’ and ‘want’ as appeared in the literature. Goals are chosen desires (Cohen & Levesque 1990). Thus, one major difference between potential intentions and goals is that an agent cannot hold incompatible goals but can hold incompatible potential intentions. Potential intentions as used in the SharedPlans theory are also different from the ‘want’ attitude proposed by Sadek (1992). want(A, p) abbreviates Bel(A, p) ∨ Int(A,Bel(A, p)). Thus, an agent wants what it believes. This is quite different from potential intentions. The paper is organized as follows. We introduce the motivations in Sec. 2. We then give the formal language (Sec. 3), model (Sec. 4), and semantics (Sec. 5), and examine models (Sec. 6) that can validate various relations between beliefs, intentions, and potential intentions.