Domenico Cantone, Marianna Nicolosi-Asmundo, Daniele Francesco Santamaria
DMI-UNICT
Abstract
The Semantic Web is a vision of the World Wide Web arisen to improve the Web infrastructure so to make it appropriate for integrating information on the Web and to permit smart applications to perform to their potential. Its basic contribution to a smarter Web consists in the Resource Description Framework (RDF) data model, representing the distributed Web of Data as a graph whose nodes and edges, labelled with appropriate IRIs, respectively denote resources and relationships between them. To reason on such data, however, formal descriptions of application domains, also called ontologies, are needed. For such purpose, the Semantic Web provides the RDF Schema language (RDFS) and the Web Ontology Language (OWL), that are languages for knowledge representation that permit to infer implicit information from the one stated explicitly and based on description logics [1].
Recently, it turned out that there exists a natural translation function between languages for the Semantic Web and some fragments of elementary set theory. Thus, decidability results of Computable Set Theory [3, 10, 12]. have been used for knowledge representation and reasoning, in particular, in the context of description logics and rule languages for the Semantic Web. In particular, the decidable four-level stratified set theoretic fragment 
, involving variables of four sorts, pair terms, and a restricted form of quantification over variables of the first three sorts [4] has been used in [5] to represent the expressive description logic 
. Such logic has been analyzed in [6, 7] to study decidability and feasibility of its reasoning problems. In [8] a C++ reasoner has been implemented to reason on ontologies expressible in the . As already mentioned such logic is quite expressive as it can represent real world ontologies such as ArcheOntology [11] and OntoCeramic [9], for the classification of archaeological finds and ArchivioMuseoFabbrica [2], concerning the renovation of the Monastery of San Nicola l’Arena in Catania by the architect Giancarlo De Carlo.
References:
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2. C. Cantale, D. Cantone, M. Nicolosi-Asmundo, and D.F. Santamaria. Distant Reading Through Ontologies: The Case Study of Catania’s Benedictines Monastery. JIS.it, 8,3 (September 2017).
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4. D. Cantone and M. Nicolosi Asmundo. On the satisfiability problem for a 4-level quantified syllogistic and some applications to modal logic. Fundamenta Informaticae, 124(4):427–448, 2013.
5. D. Cantone, M. Nicolosi-Asmundo, and D. F. Santamaria. Conjunctive query answering via a fragment of set theory. In Proc. of ICTCS 2016, Lecce, September 7-9, CEUR-WS Vol. 1720, pp. 23–35, 2016.
6. D. Cantone, M. Nicolosi-Asmundo, and D. F. Santamaria. A set-theoretic approach to ABox reasoning services. In Costantini S., Franconi E., Van Woensel W., Kontchakov R., Sadri F., Roman D. Rules and Reasoning. RuleML+RR 2017., Lecture Notes in Computer Science, vol 10364. Springer, 2017.
7. D. Cantone, M. Nicolosi-Asmundo, and D. F. Santamaria. An optimized KE-tableau-based system for reasoning in the description logic . Submitted.
8. D. Cantone, M. Nicolosi-Asmundo, and D. F. Santamaria. A set-based reasoner for the description logic . Submitted.
9. D. Cantone, M. Nicolosi-Asmundo, D. F. Santamaria, and F. Trapani. Ontoceramic: an OWL ontology for ceramics classification. In Proc. of CILC 2015, CEUR-WS, vol. 1459, pp. 122-127, Genova, July 1-3, 2015.
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