Abstract.
In this paper, I: (1) argue that the issue of intensionality is of great importance for formalization of conceptual structures, (2) show that this issue is underestimated in contemporary formalizations of conceptual structures, and (3)–as a remedy to this discrepancy–introduce an intensional language for formalization of conceptual structures. The language has a syntax similar to the description logic \({\cal ALC}\) with the exception that an additional equivalence relation is introduced. The purpose of this relation is to enable formalization of intensional equivalence of concepts. The intensional semantics is defined by a novel algebraic semantics which basically is an algebraic generalization of the well-known extensional semantics.
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References
Anthony Anderson, C.: General intensional logic. In: Gabbay, D., Guenthner, F. (eds.) Handbook of Philosophical Logic, vol. II, pp. 355–385. D. Reidel Publishing Company, Dordrecht (1984)
Audi, R. (ed.): The Cambridge Dictionary of Philosophy, 2nd edn. Cambridge University Press, Cambridge (1999)
Baader, F., Calvanese, D., McGuinness, D., Nardi, D., Patel-Schneider, P. (eds.): The Description Logic Handbook. Cambridge University Press, Cambridge (2003)
Baader, F., Nutt, W.: Basic description logics. In: Baader, F., et al. (eds.) [3], pp. 47–100
Bealer, G.: Quality and Concept. Clarendon Press, Oxford (1982)
Bealer, G., Mönnich, U.: Property theories. In: Gabbay, D., Guenthner, F. (eds.) Handbook of Philosophical Logic, vol. IV, pp. 133–251. D. Reidel Publishing Company (1989)
Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic. Cambridge University Press, Cambridge (2001)
Boman, M., Bubenko Jr., J.A., Johannesson, P., Wangler, B.: Conceptual Modelling. Prentice Hall, Englewood Cliffs (1997)
Brink, C., Britz, K., Schmidt, R.A.: Peirce algebras. Formal Aspects of Computing 6, 339–358 (1994)
Brink, C., Schmidt, R.: Subsumption computed algebraically. Comput. Math. Appl. 23, 329–342 (1992); Special Issue on semantic networks in Artificial Intelligence
Carnap, R.: Meaning and Necessity, 2nd edn. The University of Chicago Press (1956)
Church, A.: A formulation of the logic of sense and denotation. In: Henle, P., Kallen, H.M., Langer, S.K. (eds.) Structure, Method, and Meaning: Essays in Honor of Henry M. Scheffer. Liberal Arts Press, New York (1951)
Davey, B.A., Priestley, H.A.: Introduction to Lattices and Order. Cambridge University Press, Cambridge (1990)
Frege, G.: On sense and meaning. In: McGuinness, B. (ed.) Gottlob Frege—Collected Papers on Mathematics, Logic, and Philosophy, pp. 157–177. Basil Blackwell Publisher, Malden (1984); Originally published under the title Über Sinn und Bedeutung in Zeitschrift für Philosophie und philosophische Kritik 100, , pp. 25–50 (1892); Translated by Max Black
Genesereth, M.R., Fikes, R.E.: Knowledge Interchange Format, Version 3.0 Reference Manual. Technical Report Logic-92-1, Computer Science Department, Stanford University, Stanford, CA, USA (June 1992)
Genesereth, M.R.: Knowledge interchange format. In: Allen, J.F., Fikes, R., Sandewall, E. (eds.) KR 1991: Principles of Knowledge Representation and Reasoning, pp. 599–600. Morgan Kaufmann, San Francisco (1991)
Grätzer, G.: Universal Algebra, 2nd edn. Springer, New York (1979) (First edition 1968)
Jónsson, B., Tarski, A.: Boolean algebras with operators, Part I. Amer. J. Math. 73, 891–939 (1951)
McCarthy, J.: First order theories of individual concepts and propositions. First published in Machine Intelligence 9 (1979), Revised version from http://wwwformal.stanford.edu/jmc/
Menzel, C.: A Complete, Type-free “Second-order” Logic and Its Philosophical Foundations. CSLI (1986)
Montague, R.: Formal Philosophy: Selected Papers of Richard Montague. Yale University Press, New Haven (1974); Edited with an introduction by R.H. Thomason
Ogden, C.K., Richards, I.A.: The Meaning of Meaning. Routledge & Kegan Paul, London (1923)
Schmidt-Schauß, M., Smolka, G.: Attributive concept descriptions with complements. Artificial Intelligence 48(1), 1–26 (1991)
Sowa, J.F.: Knowledge Representation: logical, philosophical and computational foundations. Brooks/Cole, Monterey (2000)
Swoyer, C.: Complex predicates and logics for properties and relations. Journal of Philosophical Logic 27(3), 295–325 (1998)
Welty, C., Guarino, N.: Supporting ontological analysis of taxonomic relationships. Data & Knowledge Engineering 39, 51–74 (2001)
Woods, W.A.: Understanding subsumption and taxonomy: A framework for progress. In: Sowa, J.F. (ed.) Principles of Semantics Networks, pp. 45–94. Morgan Kaufmann, San Francisco (1991)
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Oldager, N. (2003). Intensional Formalization of Conceptual Structures. In: Ganter, B., de Moor, A., Lex, W. (eds) Conceptual Structures for Knowledge Creation and Communication. ICCS 2003. Lecture Notes in Computer Science(), vol 2746. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45091-7_5
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DOI: https://doi.org/10.1007/978-3-540-45091-7_5
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