Title: Next Steps for Description Logics of Minimal Knowledge and Negation as Failure.
Abstract: The more DLs are being used in applications such as the Semantic Web [2], biology, and the clinical sciences, the more certain expressive weaknesses are commented upon. A recurring set of these comments is due to the fact that only few DLs and even fewer DL reasoners support forms of defeasible reasoning. For example, Rector describes in [12, 16] how useful statements such as “the heart of a human is normally located on the left hand side of the body” could be for the clinical sciences, and OWL design patterns have been developed to work around the lack of such statements. Various combinations of DLs with nonmonotonic formalisms have been investigated so far. DL-MKNF, the combination of DLs with minimal knowledge and negation as failure (MKNF) [9] is introduced in [4]. DL-MKNF extends DLs with two modal operators and is considered to be a unified framework for nonmonotonic extensions of DLs since various nonmonotonic logics can be embedded into MKNF [9]; these include default logic [13] and autoepistemic logic [10]. The combination of DLs with default logic was introduced [1], implemented in Pellet [7], and its translation into DL-MKNF was explained in [4]. The combination of DLs with circumscription [3] provides a powerful and flexible alternative way for nonmonotonic reasoning in DLs since its entailment relation is parametrized with a set of concepts to be circumscribed. Hence we can pick different modes of defeasibility without changing our knowledge base. Decidablity and complexity are known for various DLs with circumscription [3], but no calculus or implementation is known. The integration of DLs with logic programming (LP) using MKNF [11] is closely related to DL-MKNF. They differ in expressive power since LP rules can make use of arbitrarily connected variables, yet these variables are all quantified in the same way. In contrast, DL-MKNF allows modal operators appearing in existential and universal restrictions. An exact comparison of this relationship is part of our future work. A tableau algorithm for the combination of the basic DL ALC [15] with MKNF (ALCKNF ) has been described in [4]. As mentioned in [4], ALCKNF can capture certain kinds of defaults and integrity constraints (ICs). For example, our example default regarding the location of the heart in humans can be formalised
Publication Year: 2008
Publication Date: 2008-01-01
Language: en
Type: article
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Cited By Count: 36
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