In this paper we present a weak and a strong intuitionistie calculus for query answering in Description Logics (DL). Given the standard modeltheoretic semantics for DL, a complete query-answering calculus has to perform complex ease analyses to cope with implicit disjunctions stemming from some of the concept-forming operators in DL. To avoid this complexity we propose an intuitionistie approach to query answering based on the Sequent-Calculusstyle axiomatization of DL we have developed in [20] and [21]. By taking into account only the intuitionistie inference schemata of this axiomatization, we obtain a strong intuitionistie query-answering calculus. An additional restriction to reasoning about explicit objects allows a further simplification of the proof theory and yields a weak intuitionistic calculus. We prove completeness of these calculi wrt axiomatic semantics based on the Intuitionistie Sequent Calculus. For the weak calculus we also give a least fixed point semantics as known from Deductive Databases and Logic Programming.
CITATION STYLE
Royer, V., & Quantz, J. J. (1994). On intuitionistie query answering in description bases. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 814 LNAI, pp. 326–340). Springer Verlag. https://doi.org/10.1007/3-540-58156-1_23
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