A Correspondence Theory for Terminological Logics: Preliminary Report (1991) [215 citations — 0 self]
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author = {Klaus Schild},
title = {A Correspondence Theory for Terminological Logics: Preliminary Report},
booktitle = {In Proc. of IJCAI-91},
year = {1991},
pages = {466--471}
}
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Abstract:
We show that the terminological logic ALC comprising Boolean operations on concepts and value restrictions is a notational variant of the propositional modal logic K (m) . To demonstrate the utility of the correspondence, we give two of its immediate by-products. Namely, we axiomatize ALC and give a simple proof that subsumption in ALC is PSPACE-complete, replacing the original six-page one. Furthermore, we consider an extension of ALC additionally containing both the identity role and the composition, union, transitive-reflexive closure, range restriction, and inverse of roles. It turns out that this language, called T SL, is a notational variant of the propositional dynamic logic converse- PDL. Using this correspondence, we prove that it suffices to consider finite T SL-models, show that T SL-subsumption is decidable, and obtain an axiomatization of T SL. By discovering that features correspond to deterministic programs in dynamic logic, we show that adding them to T SL preserves...
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