92,583 research outputs found

    Subsumption Algorithms for Some Attributive Concept Description Languages

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    This paper investigates subsumption algorithms for logic-based knowledge representation languages of the KL-ONE family. We amalgamate the attributive concept description language ALC, that contains value restrictions, intersections, unions and complements with number restrictions, role hierarchies (to model the KL-ONE’s roleset differentiation), and Feature Logic, respectively. We show that deciding consistency and subsumption of ALC extended with number restrictions and ALC extended with role hierarchies is PSPACE-complete. Furthermore, for all these languages we give subsumption algorithms

    Practical Reasoning for Very Expressive Description Logics

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    Description Logics (DLs) are a family of knowledge representation formalisms mainly characterised by constructors to build complex concepts and roles from atomic ones. Expressive role constructors are important in many applications, but can be computationally problematical. We present an algorithm that decides satisfiability of the DL ALC extended with transitive and inverse roles and functional restrictions with respect to general concept inclusion axioms and role hierarchies; early experiments indicate that this algorithm is well-suited for implementation. Additionally, we show that ALC extended with just transitive and inverse roles is still in PSPACE. We investigate the limits of decidability for this family of DLs, showing that relaxing the constraints placed on the kinds of roles used in number restrictions leads to the undecidability of all inference problems. Finally, we describe a number of optimisation techniques that are crucial in obtaining implementations of the decision procedures, which, despite the worst-case complexity of the problem, exhibit good performance with real-life problems

    Reasoning with Very Expressive Fuzzy Description Logics

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    It is widely recognized today that the management of imprecision and vagueness will yield more intelligent and realistic knowledge-based applications. Description Logics (DLs) are a family of knowledge representation languages that have gained considerable attention the last decade, mainly due to their decidability and the existence of empirically high performance of reasoning algorithms. In this paper, we extend the well known fuzzy ALC DL to the fuzzy SHIN DL, which extends the fuzzy ALC DL with transitive role axioms (S), inverse roles (I), role hierarchies (H) and number restrictions (N). We illustrate why transitive role axioms are difficult to handle in the presence of fuzzy interpretations and how to handle them properly. Then we extend these results by adding role hierarchies and finally number restrictions. The main contributions of the paper are the decidability proof of the fuzzy DL languages fuzzy-SI and fuzzy-SHIN, as well as decision procedures for the knowledge base satisfiability problem of the fuzzy-SI and fuzzy-SHIN

    A Description Logic with Transitive and Converse Roles, Role Hierarchies and Qualifying Number Restrictions

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    As widely argued [HG97; Sat96], transitive roles play an important role in the adequate representation of aggregated objects: they allow these objects to be described by referring to their parts without specifying a level of decomposition. In [HG97], the Description Logic (DL) ALCHR+ is presented, which extends ALC with transitive roles and a role hierarchy. It is argued in [Sat98] that ALCHR+ is well-suited to the representation of aggregated objects in applications that require various part-whole relations to be distinguished, some of which are transitive. However, ALCHR+ allows neither the description of parts by means of the whole to which they belong, or vice versa. To overcome this limitation, we present the DL SHI which allows the use of, for example, has part as well as is part of. To achieve this, ALCHR+ was extended with inverse roles. It could be argued that, instead of defining yet another DL, one could make use of the results presented in [DL96] and use ALC extended with role expressions which include transitive closure and inverse operators. The reason for not proceeding like this is the fact that transitive roles can be implemented more efficiently than the transitive closure of roles (see [HG97]), although they lead to the same complexity class (ExpTime-hard) when added, together with role hierarchies, to ALC. Furthermore, it is still an open question whether the transitive closure of roles together with inverse roles necessitates the use of the cut rule [DM98], and this rule leads to an algorithm with very bad behaviour. We will present an algorithm for SHI without such a rule. Furthermore, we enrich the language with functional restrictions and, finally, with qualifying number restrictions. We give sound and complete decision proceduresfor the resulting logics that are derived from the initial algorithm for SHI. The structure of this report is as follows: In Section 2, we introduce the DL SI and present a tableaux algorithm for satisfiability (and subsumption) of SI-concepts—in another report [HST98] we prove that this algorithm can be refined to run in polynomial space. In Section 3 we add role hierarchies to SI and show how the algorithm can be modified to handle this extension appropriately. Please note that this logic, namely SHI, allows for the internalisation of general concept inclusion axioms, one of the most general form of terminological axioms. In Section 4 we augment SHI with functional restrictions and, using the so-called pairwise-blocking technique, the algorithm can be adapted to this extension as well. Finally, in Section 5, we show that standard techniques for handling qualifying number restrictions [HB91;BBH96] together with the techniques described in previous sections can be used to decide satisfiability and subsumption for SHIQ, namely ALC extended with transitive and inverse roles, role hierarchies, and qualifying number restrictions. Although Section 5 heavily depends on the previous sections, we have made it self-contained, i.e. it contains all necessary definitions and proofs from scratch, for a better readability. Building on the previous sections, Section 6 presents an algorithm that decides the satisfiability of SHIQ-ABoxes

    Consequence-based Reasoning for Description Logics with Disjunction, Inverse Roles, Number Restrictions, and Nominals

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    We present a consequence-based calculus for concept subsumption and classification in the description logic ALCHOIQ, which extends ALC with role hierarchies, inverse roles, number restrictions, and nominals. By using standard transformations, our calculus extends to SROIQ, which covers all of OWL 2 DL except for datatypes. A key feature of our calculus is its pay-as-you-go behaviour: unlike existing algorithms, our calculus is worst-case optimal for all the well-known proper fragments of ALCHOIQ, albeit not for the full logic

    Selectional Restrictions in HPSG

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    Selectional restrictions are semantic sortal constraints imposed on the participants of linguistic constructions to capture contextually-dependent constraints on interpretation. Despite their limitations, selectional restrictions have proven very useful in natural language applications, where they have been used frequently in word sense disambiguation, syntactic disambiguation, and anaphora resolution. Given their practical value, we explore two methods to incorporate selectional restrictions in the HPSG theory, assuming that the reader is familiar with HPSG. The first method employs HPSG's Background feature and a constraint-satisfaction component pipe-lined after the parser. The second method uses subsorts of referential indices, and blocks readings that violate selectional restrictions during parsing. While theoretically less satisfactory, we have found the second method particularly useful in the development of practical systems

    SNOMED CT standard ontology based on the ontology for general medical science

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    Background: Systematized Nomenclature of Medicine—Clinical Terms (SNOMED CT, hereafter abbreviated SCT) is acomprehensive medical terminology used for standardizing the storage, retrieval, and exchange of electronic healthdata. Some efforts have been made to capture the contents of SCT as Web Ontology Language (OWL), but theseefforts have been hampered by the size and complexity of SCT. Method: Our proposal here is to develop an upper-level ontology and to use it as the basis for defining the termsin SCT in a way that will support quality assurance of SCT, for example, by allowing consistency checks ofdefinitions and the identification and elimination of redundancies in the SCT vocabulary. Our proposed upper-levelSCT ontology (SCTO) is based on the Ontology for General Medical Science (OGMS). Results: The SCTO is implemented in OWL 2, to support automatic inference and consistency checking. Theapproach will allow integration of SCT data with data annotated using Open Biomedical Ontologies (OBO) Foundryontologies, since the use of OGMS will ensure consistency with the Basic Formal Ontology, which is the top-levelontology of the OBO Foundry. Currently, the SCTO contains 304 classes, 28 properties, 2400 axioms, and 1555annotations. It is publicly available through the bioportal athttp://bioportal.bioontology.org/ontologies/SCTO/. Conclusion: The resulting ontology can enhance the semantics of clinical decision support systems and semanticinteroperability among distributed electronic health records. In addition, the populated ontology can be used forthe automation of mobile health applications
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