A Context for Belief Revision: Forward Chaining - Normal Nonmonotonic Rule Systems

A number of nonmonotonic reasoning formalism have been introduced to model the set of beliefs of an agent. For example, Reiter [Rei80] introduced default logic where the set of beliefs of an agent reasoning with incomplete information corresponded to a extension of a default theory < D,W >. In the realm of logic programming, the stable models of a general logic program as introduced by Gelfond and Lifschitz [GL88] can be used to model the set of beliefs of an agent. Similarly, extensions of truth maintenance systems as defined by Doyle [Doy79] and De Kleer [dK86], with subsequent contributions of Reinfrank, Dressler, and Brewka [RDB89] can be used to model the set of beliefs of an agent. We introduced nonmonotonic rule systems as a non-logical generalization of all essential features of default theories, truth maintenance systems, and logic programs so that theorems applying to all could be proven once and for all, see [MNR90] and [MNR92c].