We give a new logic of intention where (contrarily to Cohen&Levesque's approach) intention is a primitive modal operator having a non-normal possible worlds semantics. We then highlight the relation between intention and belief by a set of axioms. In our logic we formulate principles of cooperation allowing an agent to infer new intentions from his beliefs about other agents' intentions. Finally, building on results of linguistic pragmatics, we show that our cooperation principles allow to infer the effects of a yes-no question ``Does A hold?'' from that of an associated assertive ``I have the intention to know whether A''. In the same manner requests can be inferred, which form another important subclass of directives. It is the aim of this work to obtain a minimal logic that can be mechanized in a simple way.