Abstract
Since the last decade the wide spread language for expressing ontologies relies on Description Logics (DLs). However, most of the versions syntactically anchor their modeling primitives on classical logic and require additional theories (i.e., first-order logic, ...) for simultaneously supporting (i) the introduction of constant values (e.g., for individuals) (ii) the limitation of expressiveness for decidability and (iii) the introduction of variables for reasoning with rules. In this paper we show that the introduction of a type theoretical formalism that relies both on a constructive logic and on a typed lambda calculus is able to go beyond these aspects in a single theory. In particular we will show that a number of logical choices (constructive logic, predicative universes for data types, impredicative universe for logic, ...) about the theory will lead to an highly expressive theory which allows for the production of conceptually clean and semantically unambiguous ontologies.
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References
Jacobs, B.: Categorical Logic and Type Theory. Studies in Logic and the Foundations of Mathematics. Elsevier (1999)
Bittner, T., Donnelly, M.: Computational ontologies of parthood, componenthood, and containment. In: Procs. of the Nineteenth International Joint Conference on Artificial Intelligence, pp. 382–387 (2005)
Burstall, R., Goguen, J.: The Semantics of Clear, a Specification Language. In: Bjorner, D. (ed.) Abstract Software Specifications. LNCS, vol. 86, pp. 292–332. Springer, Heidelberg (1980)
Coquand, T., Huet, G.: The calculus of constructions. Information and Computation 76(2–3), 95–120 (1988)
Dapoigny, R., Barlatier, P.: Towards Ontological Correctness of Part-whole Relations with Dependent Types. In: Procs. of the Sixth International Conference, FOIS 2010, pp. 45–58 (2010)
Dapoigny, R., Barlatier, P.: Modeling Contexts with Dependent Types. Fundamenta Informaticae 104(4), 293–327 (2010)
Gangemi, A., Guarino, N., Masolo, C., Oltramari, A., Schneider, L.: Sweetening ontologies with DOLCE. In: Gómez-Pérez, A., Benjamins, V.R. (eds.) EKAW 2002. LNCS (LNAI), vol. 2473, pp. 166–181. Springer, Heidelberg (2002)
Guarino, N.: The Ontological Level. In: Philosophy and the Cognitive Sciences, pp. 443–456. Holder-Pichler-Tempsky (1994)
Guizzardi, G.: The Role of Foundational Ontology for Conceptual Modeling and Domain Ontology Representation. In: 7th International Baltic Conference on Databases and Information Systems, Keynote Paper (2006)
Hoekstra, R., Liem, J., Bredeweg, B., Breuker, J.: Requirements for Representing Situations. In: OWLED (2006)
Luo, Z.: Computation and Reasoning, vol. 11. Oxford Science Publications (1994)
Masolo, C., Borgo, S., Gangemi, A., Guarino, N., Oltramari, A.: Ontology Library. WonderWeb Deliverable D18 (ver.1.0, 31-12-2003) (2003)
Masolo, C.: Understanding Ontological Levels. In: Procs. of the Twelfth International Conference on the Principles of Knowledge Representation and Reasoning (KR 2010), pp. 258–268. AAAI Press (2010)
Reus, B., Streicher, T.: Verifying Properties of Module Construction in Type Theory. In: Borzyszkowski, A.M., Sokolowski, S. (eds.) MFCS 1993. LNCS, vol. 711, pp. 660–670. Springer, Heidelberg (1993)
Smith, B., Rosse, C.: The Role of Foundational Relations in the Alignment of Biomedical Ontologies. In: Procs. of MEDINFO 2004, pp. 444–449 (2004)
Werner, B.: On the strength of proof-irrelevant type theories. Logical Methods in Computer Science 4(3) (2008)
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Dapoigny, R., Barlatier, P. (2011). Using a Dependently-Typed Language for Expressing Ontologies. In: Xiong, H., Lee, W.B. (eds) Knowledge Science, Engineering and Management. KSEM 2011. Lecture Notes in Computer Science(), vol 7091. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25975-3_23
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DOI: https://doi.org/10.1007/978-3-642-25975-3_23
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