NDLI: Complexities of Horn Description Logics

Content Provider	ACM Digital Library
Author	Krötzsch, Markus Rudolph, Sebastian Hitzler, Pascal
Copyright Year	2013
Abstract	Description logics (DLs) have become a prominent paradigm for representing knowledge in a variety of application areas, partly due to their ability to achieve a favourable balance between expressivity of the logic and performance of reasoning. Horn description logics are obtained, roughly speaking, by disallowing all forms of disjunctions. They have attracted attention since their (worst-case) data complexities are in general lower than those of their non-Horn counterparts, which makes them attractive for reasoning with large sets of instance data (ABoxes). It is therefore natural to ask whether Horn DLs also provide advantages for schema (TBox) reasoning, that is, whether they also feature lower combined complexities. This article settles this question for a variety of Horn DLs. An example of a tractable Horn logic is the DL underlying the ontology language OWL RL, which we characterize as the Horn fragment of the description logic $\textit{SROIQ}$ without existential quantifiers. If existential quantifiers are allowed, however, many Horn DLs become intractable. We find that $Horn-\textit{ALC}$ already has the same worst-case complexity as $\textit{ALC},$ that is, ExpTime, but we also identify various DLs for which reasoning is PSpace-complete. As a side effect, we derive simplified syntactic definitions of Horn DLs for which we exploit suitable normal form transformations.
Starting Page	1
Ending Page	36
Page Count	36
File Format	PDF
ISSN	15293785
e-ISSN	1557945X
DOI	10.1145/2422085.2422087
Volume Number	14
Issue Number	1
Journal	ACM Transactions on Computational Logic (TOCL)
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2013-02-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Description logics Horn logic Computational complexity
Content Type	Text
Resource Type	Article
Subject	Theoretical Computer Science Logic Computational Mathematics Computer Science

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