Multi-Dimensional Description Logics

Abstract

In this paper, we construct a new concept description language intended for representing dynamic and intensional knowledg e. The most important feature distinguishing this language from its predecessors in the literature is that it allows applications of modal operators to all kinds of syntactic terms: concepts, roles and formulas. Moreover, the language may co ntain both local (i.e., state-dependent) and global (i.e., state-independent) concepts, roles and objects. All this provides us with the most complete and natural means for reflecting the dynamic and intensional behaviour of application domains. We construct a satisfiability checking (mosaic-type) algorithm for this language (based on A.CC) in (i) arbitrary multimodal frames, (ii) frames with universal accessibility relations (for knowledge) and (iii) frames with transitive, symmetrical and euclidean relations (for beliefs). On the other hand, it is shown that the satisfaction problem becomes undecidable if the underlying frames are arbitrary linear orders or the language contains the common knowledge operator for n ?: 2 agents.