Twin-subset semantic model for intention

Intention, an indispensable cognition attribute of agent, plays an important role in agent's rational behavior. There is a lot of research on formalization of cognitive state that include intentions of the agents in a multi-agent system. These theories are based on normal modal logic, interpret intention as unary normal modal operator in Kripke semantics, and hence suffer from the harmful logical omniscience and side-effect problems. These have not been eliminated satisfactorily as yet. In this paper, we interpret intention as unary non-normal modal operator and introduce novel possible world semantics for intention, called the twin-subset semantics. It describes the intentions of agent in a possible world w with two subsets of W, where W is the set of all possible worlds which an agent can be in, and allows us to embody essential cognitive features of intention and the relations between belief and intention. Compared with classical normal or non-normal modal logics, not only does it avoid the logical omniscience and side-effect problems but also the classical semantics of logical connectives are still valid; and moreover, it improves the true-false subset semantics, which were introduced by us previously, and overcomes its serious drawbacks.