Characterizing the Semantics of Terminological Cycles in ALN Using Finite Automata

The representation of terminological knowledge may naturally lead to terminological cycles. In addition to descriptive semantics , the meaning of cyclic terminologies can also be captured by xed-point semantics, namely, greatest and least xed-point semantics. To gain a more profound understanding of these semantics and to obtain inference algorithms as well as complexity results for inconsistency, subsumption, and related inference tasks, this paper provides au-tomata theoretic characterizations of these semantics. More precisely, the already existing results for FL 0 are extended to the language ALN, which additionally allows for primitive negation and number-restrictions. Unlike FL 0 , the language ALN allows to express inconsistent concepts, which makes non-trivial extensions of the characterizations and algorithms necessary. Nevertheless , the complexity of reasoning does not increase when going from FL 0 to ALN. This distinguishes ALN from the very expressive languages with xed-point operators proposed in the literature. It will be shown, however, that cyclic ALN-terminologies are expressive enough to capture schemas in certain semantic data models.