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Conjunctive Reasoning on Fuzzy Taxonomies with Order-Sorted Feature Logic
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We present an extended version of the CEDAR taxonomic reasoner for large ontologies. This new version provides fuller support for TBox reasoning, checking consistency, and retrieving instances. The CEDAR system is based upon the OSF formalism. It is implemented on an entirely new architecture which includes several optimization techniques. We define a bidirectional mapping between OSF graph structures and the Resource Description Framework (RDF) allowing a translation from OSF queries into SPARQL for retrieving instances from an RDF triplestore. We carried out comparative performance evaluation experiments using CEDAR
as well as well-known Semantic Web reasoners (such as FaCT++, Pellet, HermiT, TrOWL, and RacerPro) on very large public ontologies. For the same queries on the same ontologies, the results achieved by CEDAR were compared to those obtained by all the other reasoners. The results of experiments show that CEDAR consistently performs on a par with the fastest systems for concept classification, and several
orders of magnitude more efficiently in terms of response time for Boolean query answering over attributed concepts, as well as for ABox triplestore querying. The latter result is irrespective of the triplestore management used because the CEDAR reasoner uses its knowledge to optimize SPARQL queries before submitting them to the triplestore.
In this article, we address the question of how efficiently Semantic Web (SW) reasoners perform in processing (classifying and querying) taxonomies of enormous size and whether it is possible to improve on existing implementations. We use a bit-vector encoding technique to implement taxonomic concept classification and Boolean-query answering. We describe the technique we have used, which achieves high performance, and discuss implementation issues. We compare the performance of our implementation with those of the best existing SW reasoning systems over several very large taxonomies under the exact same conditions for so-called TBox reasoning. The results show that our system is among the best for concept classification and several orders-of-magnitude more efficient in terms of response time for query answering. We present these results in detail and comment them. We also discuss pragmatic issues such as cycle detection and decoding.
We consider the notion of fuzzy lattice introduced by Chon (Korean J. Math 17 (2009), No. 4, 361-374), and define the operations of product and collapsed sum on bounded fuzzy lattice analogous to the classical theory. Also, we prove that the product and collapsed sum on bounded fuzzy lattices are fuzzy posets and, consequently, bounded fuzzy lattices.
Current developments within the information technology industry are creating new opportunities for traditional information suppliers such as Ordnance Sur- vey. In particular the ability to electronically trade information creates oppor- tunities to increase the use of Ordnance Survey's topographic information in ways that can be go beyond the delivery of such data in the form of a map. The future development of a semantic web may create new business opportuni- ties particularly for the mobile connected user who may access Ordnance Sur- vey information through an application without ever realising it. More general- ly the ability to semantically translate between one information source and oth- ers may reduce both the time and cost of services better enabling joined-up gov- ernment and industry. In response to these challenges Ordnance Survey has em- barked upon research to investigate the development of a topographic ontology to underpin our data and to investigate how it may be used to support interoper- ation with other information sources and information based services. This pa- per describes our thoughts and experiences on the development of an ontology using the Web Ontology Language (OWL DL).
This paper provides a survey to and a comparison of state-of-the-art Semantic Web reasoners that succeed in classifying large ontologies expressed in the tractable OWL 2 EL profile. Reasoners are characterized along several dimensions: The first dimension comprises underlying reasoning characteristics, such as the employed reasoning method and its correctness as well as the expressivity and worst-case computational complexity of its supported language and whether the reasoner supports incremental classification, rules, justifications for inconsistent concepts and ABox reasoning tasks. The second dimension is practical usability: whether the reasoner implements the OWL API and can be used via OWLlink, whether it is available as Protégé plugin, on which platforms it runs, whether its source is open or closed and which license it comes with. The last dimension contains performance indicators that can be evaluated empirically, such as classification, concept satisfiability, subsumption checking and consistency checking performance as well as required heap space and practical correctness, which is determined by comparing the computed concept hierarchies with each other. For the very large ontology SNOMED CT, which is released both in stated and inferred form, we test whether the computed concept hierarchies are correct by comparing them to the inferred form of the official distribution. The reasoners are categorized along the defined characteristics and benchmarked against well-known biomedical ontologies. The main conclusion from this study is that reasoners vary significantly with regard to all included characteristics, and therefore a critical assessment and evaluation of requirements is needed before selecting a reasoner for a real-life application.
Lattice operations such as greatest lower bound (GLB), least upper bound (LUB), and relative complementation (BUTNOT) are becoming more and more important in programming languages supporting object inheritance. We present a general technique for the efficient implementation of such operations based on an encoding method. The effect of the encoding is to plunge the given ordering into a boolean lattice of binary words, leading to an almost constant time complexity of the lattice operations. A first method is described based on a transitive closure approach. Then, a more space-efficient method minimizing code-word length is described. Finally, a powerful grouping technique called modulation is presented which drastically reduces code space while keeping all three lattice operations highly efficient. This technique takes into account idiosyncrasies of the topology of the poset being encoded which are quite likely to occur in practice. All methods are formally justified. We see this work a...
LIFE (Logic, Inheritance, Functions, Equations) is an experimental programming language proposing to integrate three orthogonal programming paradigms proven useful for symbolic computation. From the programmer's standpoint, it may be perceived as a language taking after logic programming, functional programming, and object-oriented programming. From a formal perspective, it may be seen as an instance (or rather, a composition of three instances) of a Constraint Logic Programming scheme due to Hoehfeld and Smolka refining that of Jaffar and Lassez.
We start with an informal overview demonstrating LIFE as a programming language, illustrating how its primitives offer rather unusual, and perhaps (pleasantly) startling, conveniences. The second part is a formal account of LIFE's object unification seen as constraint-solving over specific domains. We build on work by Smolka and Rounds to develop type-theoretic, logical, and algebraic renditions of a calculus of order-sorted feature approximations.
Thesis (Ph. D.)--University of Pennsylvania, 1984. Includes bibliographical references (p. 174-182) and index. Includes index.
We characterize a fuzzy partial order relation using its level set, find sufficient conditions for the image of a fuzzy partial order relation to be a fuzzy partial order relation, and find sufficient conditions for the inverse image of a fuzzy partial order relation to be a fuzzy partial order relation. Also we define a fuzzy lattice as fuzzy relations, characterize a fuzzy lattice using its level set, show that a fuzzy totally ordered set is a distributive fuzzy lattice, and show that the direct product of two fuzzy lattices is a fuzzy lattice.
I will provide an overview of many of the use cases that we looked at to apply OWL ABox reasoning in the real world. The fields we covered included (a) healthcare, and life sciences where the plethora of ontologies might be seen as providing a strong use case for OWL reasoning, (b) information retrieval over unstructured text, (c) master data management, which involves reasoning over product and consumer data incorporated from multiple data sources within an enterprise. In each case, we ran into a series of bottlenecks including incorrect modeling of constructs in the ontology, inherent difficulties in scaling OWL reasoning to real world requirements, needing formalisms outside that of OWL, and needing techniques to semi-automate the construction of ontologies. At least in the use cases we had seen, there is a need for performing TBox OWL reasoning over expressive ontologies, but most realistic uses of ABox reasoning have to be relatively simple in terms of expressivity, for practical reasons.
Fuzzy Sets and Systems. Theory and Applications.; ser. Mathematics in Science and Engineering
- D Dubois
- H Prade