Heinrich Wansing

In this paper non-normal worlds semantics is presented as a basic, general, and unifying approach to epistemic logic. The semantical framework of non-normal worlds is compared to the model theories of several logics for knowledge and belief that were recently developed in Artificial Intelligence (AI). It is shown that every model for implicit and explicit belief (Levesque), for awareness, general awareness, and local reasoning (Fagin and Halpern), and for awareness and principles (van der Hoek and Meyer) induces a non-normal worlds model validating precisely the same formulas (of the language in question).

Since it is desirable to be able to talk about rational agents forming attitudes toward their concrete agency, we suggest an introduction of doxastic, volitional, and intentional modalities into the multi-agent logic of deliberatively seeing to it that, dstit logic. These modalities are borrowed from the well-known BDI (belief-desire-intention) logic. We change the semantics of the belief and desire operators from a relational one to a monotonic neighbourhood semantic in order to handle ascriptions of conflicting but not inconsistent beliefs and desires as being satisfiable. The proposed bdi-stit logic is defined with respect to branching time frames, and it is shown that this logic is a generalization of a bdi logic based on branching time possible worlds frames (but without temporal operators) and dstit logic. The new bdi-stit logic generalizes bdi and dstit logic in the sense that for any model of bdi or dstit logic, there is an equivalent bdi-stit model