Specification of Nonmonotonic Reasonong

Two levels of description of nonmonotonic reasoning are distinguished. For these levels semantical formalizations are given. The first level is defined semantically by the notion of belief state frame, the second level by the notion of reasoning frame. We introduce two specification languages to describe nonmonotonic reasoning at each of the levels: (1) a specification language for level 1, with formal semantics based on belief state frames, (2) a fragment of infinitary temporal logic as a general specification language for level 2, with formal semantics based on reasoning frames. In our framework every level 2 description can be abstracted to level 1, and for every level 1 description there are level 2 descriptions which are a specialization of it.