A Modal Logic for Beliefs and Pro Attitudes

Kaile Su, Abdul Sattar, Han Lin, Mark Reynolds

Abstract: Agents' pro attitudes such as goals, intentions, desires, wishes, and judgements of satisfactoriness play an important role in how agents act rationally. To provide a natural and satisfying formalization of these attitudes is a longstanding problem in the community of agent theory. Most of existing modal logic approaches are based on Kripke structures and have to face the so-called side-effect problem. This paper presents a new modal logic formalizing agents' pro attitudes, based on neighborhood models. There are three distinguishing features of this logic. Firstly, this logic naturally satisfies Bratman's requirements for agents' beliefs and pro attitudes, as well as some interesting properties that have not been discussed before. Secondly, we give a sound and complete axiom system for characterizing all the valid properties of beliefs and pro attitudes. We introduce for the first time the notion of linear neighborhood frame for obtaining the semantic model, and this brings a new member to the family of non-normal modal logics. Finally, we argue that the present logic satisfies an important requirement proposed from the viewpoint of computation, that is, computational grounding, which means that properties in this logic can be given an interpretation in terms of some concrete computational model. Indeed, the presented neighborhood frame can be naturally derived from probabilistic programming with utilities.