By Franz Baader, Ian Horrocks, Ulrike Sattler (auth.), PD Dr. Steffen Staab, Professor Dr. Rudi Studer (eds.)
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Hence, classes may have methods defined on them and may be instances of other classes which serve as a kind of metaclass. Furthermore, variables are permitted at all positions in an isa- or subclass-F-atom. , ROL [L99]), F-Iogic permits that an object is an instance of several classes that are incomparable by the subclass relationship. Analogously, a class may have several incomparable direct superclasses. Thus, the subclass relationship specifies a partial order on the set of classes, so that the class hierarchy may be considered as a directed acyclic (but not reflexive) graph with the classes as its nodes.
Franz Baader, Sebastian Brandt, and Ralf Küsters. Matching under side conditions in description 10gics. In Bernhard Nebel, editor, Proc. o/the 17th Int. Joint Conf on Artificiallntelligence (IJCAI 2001), pages 213-218, Seattle, Washington, 2001. Morgan Kaufmann. 1 Description Logics 23 6. Franz Baader, Martin Buchheit, and Bemhard Hollunder. Cardinality restrictions on concepts. ArtificialIntelligence, 88(1-2): 195-213, 1996. 7. Franz Baader, Hans-Jürgen Bürckert, Bemhard Hollunder, Wemer Nutt, and Jörg H.
In fact, ExpTIME-hardness can be shown by an easy adaptation of the ExpTIME-hardness proof for satisfiability in propositional dynamic logic . t. role hierarchies is indeed decidable within exponential time. In the remainder of this section, we sketch a tableau-based decision procedure for this problem. This procedure, which is described in more detail in , runs in worstcase nondeterministic double exponential time. 13 However, according to the current state of the art, this procedures is more practical than the EXpTIME automata-based procedure in .