Abstract
The National Knowledge Infrastructure (NKI) is a multi-domain knowledge base. The classical type theory is no longer appropriate to describe every kind of object in multi-domains, such as artifacts, natural or micro objects. Three different kinds of type theories are defined: the classical, atomic and pseudo type theories; in the classical type theory, two new type constructors are defined: setm and ∨, to describe the types of sets of all the elements of the types and unions of two sets of different types, respectively. The structures and categories in the type theory are defined, and the sub-structures and homomorphic structures are used to describe the part-of relations that give the algebraic specifications for the natural objects and the part-of relations between the natural objects, micro objects and artifacts.
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References
Andrews P. An Introduction to Mathematical Logic and Type Theory: to truth through proof. Applied Logic Series 27. Dordrecht: Kluwer Academic Publishers, 2002
Hindley J R. Basic Simple Type Theory. Cambridge University Press, 1997
Pierce B C. Types and Programming Languages. MIT Press, 2002
Astesiano E, Bidoit M, Kirchner H, et al. CASL: The common algebraic specification language. Theoretical Computer Science, 2002, 286(2): 153–196
McGuinness D. Ontologies come of age. In: Fensel D, et al, eds. The Semantic Web: Why, What, and How. MIT Press 2002
Gómez-Pérez A, Corcho O. Ontology language for the semantic web. IEEE Intelligent Systems, 2002, 54–60
Cao C, Feng Q Z, Gao Y, et al. Progress in the development of National Knowledge Infrastructure. Journal of Computer Science and Technology, 2002(17): 1–16
Gu F, Cao C, Sui Y, et al. Domain-specific ontology of botany. Journal of Computer Science and Technology, 2004(19): 238–248
Margolis E, Laurence S. Concepts: Core Readings. MIT Press, 1999
Sowa J F. Knowledge Representation: Logical, Philosophical, and Computational Foundations. Brooks Cole Publishing Co., 2000
Baader F, Calvanese D, McGuinness D L, et al, eds. The Description Logic Handbook. Cambridge University Press, 2002
Simons P. Parts: A Study in Ontology. Oxford: Clarendon Press, 1987
Varzi A C. Basic problems of mereotopology. In: Guarino N, ed. Formal Ontology in Information Systems. Amsterdam: IOS Press, 1998: 29–38
Winston M E, Chaffin R, and Hermann D. A taxonomy of part-whole relations. Cognitive Science, 1987(11): 417–444
van Eijck J, Unger C. Computational Semantics with Functional Programming, Chapters 1-6, http://homepages. cwi.nl/jve/cs/cs.pdf
Rajasekaran P. Computational semantics and type theory and its influence on semantic web and related applications-An introduction. Essay M S, LSDIS Lab, Computer Science Department, University of Georgia, Athens, 2004
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Zhang, X., Zhang, Z. & Sui, Y. Types, structures and theories in NKI. Front. Comput. Sci. China 2, 451–459 (2008). https://doi.org/10.1007/s11704-008-0032-9
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DOI: https://doi.org/10.1007/s11704-008-0032-9