By Ralf Küsters
Description logics (DLs) are used to symbolize based wisdom. Inference companies trying out consistency of data bases and computing subconcept/superconcept hierarchies are the most characteristic of DL structures. extensive learn over the past fifteen years has ended in hugely optimized platforms that permit to cause approximately wisdom bases successfully. although, purposes frequently require extra non-standard inferences to help either the development and the upkeep of information bases, hence making the inference strategies back incomplete.
This e-book, that's a revised model of the author's PhD thesis, constitutes an important step to fill this hole via delivering a good formal beginning of the main trendy non-standard inferences. The descriptions given contain designated definitions, whole algorithms and thorough complexity research. With its strong starting place, the publication additionally serves as a foundation for destiny research.
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Description logics (DLs) are used to symbolize based wisdom. Inference companies checking out consistency of information bases and computing subconcept/superconcept hierarchies are the most characteristic of DL platforms. extensive study over the past fifteen years has resulted in hugely optimized structures that permit to cause approximately wisdom bases successfully.
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Since it is not possible to construct a model I that shows that Eex (and thus, Cex ¬Dex ), is satisﬁable, the tableau-algorithm returns ‘yes’ indicating that Cex Dex holds. 4 Decision Algorithms 31 Comparing Structural and Tableau-Based Algorithms. The main feature of structural subsumption algorithms is that concept descriptions are turned into normal forms. 1). Intuitively speaking, their common property is that they are ﬁnite representations of the set of all implications that can be drawn from the original concept descriptions.
In particular, the three problems mentioned above, namely, dealing with unsatisﬁable subexpressions and certain same-as equalities (like ε ↓ spouse ◦ spouse) as well as the impact of the diﬀerent semantics for attributes are settled. 1). This algorithm can deal with descriptions that contain unsatisﬁable subexpressions and arbitrary same-as equalities. The algorithm also shows that in ALN S the lcs always exists and that for two concepts it can be computed in polynomial-time. For sequences of concept descriptions, however, the lcs may grow exponentially in the size of the sequence and there exists an exponential-time algorithm for computing it.
Finally, the last section discusses some novel inferences proposed in the literature but not further investigated in the present book. K¨ usters: Non-Standard Inferences in Description Logics, LNAI 2100, pp. 33–72, 2001. c Springer-Verlag Berlin Heidelberg 2001 34 3. 1). 2. The last two subsections give an overview of known and new theoretical results on these inferences. All technical details are postponed to Chapter 5 in order to concentrate on the results themselves. 1 Deﬁnition of LCS and MSC In what follows, let L denote some DL.