An Extension of Regularity Conditions for Complex Role Inclusion Axioms
نویسنده
چکیده
The description logic (DL) SROIQ [1] provides a logical foundation for the new version of the web ontology language OWL 2. In comparison to the DL SHOIN which underpins the first version of OWL, SROIQ provides several new constructors for classes and axioms. One of the new powerful features of SROIQ are so-called complex role inclusion axioms (RIAs) which allow for expressing implications between role chains and roles R1 · · ·Rn v R. It is wellknown that unrestricted usage of such axioms can easily lead to undecidability for modal and description logics [2–5], with a notable exception of the DL EL [6]. Therefore certain syntactic restrictions are imposed on RIAs in SROIQ to regain decidability. Specifically, the restrictions ensure that RIAs R1 · · ·Rn v R when viewed as production rules for context-free grammars R → R1 . . . Rn induce a regular language. In fact, the tableau-based reasoning procedure for SROIQ [1] does not use the syntactic restrictions directly, but takes as an input the resulting non-deterministic finite automata for RIAs. This means that it is possible to use exactly the same procedure for any set of RIAs for which the corresponding regular automata can be constructed. Unfortunately, the syntactic restrictions on RIAs in SROIQ are not satisfied in all cases when the language induced by the RIAs is regular. In fact, it is not possible to come up with such a most general syntactic restriction since, given a context-free grammar, it is in general not possible to determine whether it defines a regular language (see, e.g., [7]). In this paper we analyse several common use cases of RIAs which correspond to regular languages but cannot be expressed within SROIQ. We then propose an extension of the syntactic restrictions for RIAs, which can capture such cases. Our restrictions have several nice properties, which could allow for their seamless integration into future revisions of OWL:
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An Extension of Complex Role Inclusion Axioms in the Description Logic SROIQ
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