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Characterizing the Semantics of Terminological Cycles in ALN using Finite Automata

R. Küsters

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 fixed-point semantics, namely, greatest and least fixed-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 automata theoretic characterizations of these semantics. More precisely, the already existing results for FL0 are extended to the language ALN, which additionally allows for primitive negation and number-restric\-tions. Unlike FL0, 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 FL0 to ALN. This distinguishes ALN from the very expressive languages with fixed-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.