Multi-dimensional description logics

In this paper, we construct a new concept description language intended for representing dynamic and intensional knowledge. 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 contain both local (i. e. , state-dependent) and global (i. e. , state-independent) concepts, roles and ob­ jects. All this provides us with the most com­ plete and natural means for reflecting the dy­ namic and intensional behaviour of application domains. We construct a satisfiability check­ ing (mosaic-type) algorithm for this language (based on 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 com­ mon knowledge operator for 2 agents.

Authors

• Frank Wolter
• Michael Zakharyaschev

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