Minimal knowledge problem: A new approach (Q1329374)

The paper introduces a new logic of minimal knowledge, which falls into the general scheme of Shoham's preference semantics. It is argued that this logic overcomes some of the limitations of earlier formalisms, and can be viewed as a generalization of default and autoepistemic logics. It is also shown that the logic of minimal knowledge is a special case of McDermott and Doyle's nonmonotonic modal logic, which makes it possible to use standard modal logic techniques in proving the results introduced in the paper. The main result is a new specification of the general minimal knowledge paradigm, represented by means of a class of knowledge- belief models. Given a class of such models of a theory \(I\) describing initial assumptions, it is possible to specify a subclass by defining the notion of maximality, which is different from the notion used by \textit{J. Halpern} and \textit{Y. Moses} [Logics and models of concurrent systems, Proc. NATO Adv. Study Inst., La Colle-su-Loup/France 1984, NATO ASI Sér., Sér. F 13, 459-476 (1985; Zbl 0581.68067)]. The approach presented in the paper yields two minimal knowledge-belief logics: one bimodal, and one with a single modality. This allows to vary domains, and thus to model the situation when the agent is not aware of all of the objects existing in the world. The obtained formalisms are nonmonotonic because they model a nonmonotonic reasoning. The relationship between the proposed logics and other nonmonotonic formalisms is also considered.