Abstract
For many years vagueness understood as a deficiency of meaning has been the subject of investigations and many authors are engaged in this research. The present paper is an attempt to show that problems concerning semantics of vague concepts may find their proper foundation in the theory of rough sets originated by Pawlak (1982). We give a formal framework to what is considered to be different ways of making vague concepts precise and we describe semantics within this framework. Following the idea accepted by many logicians that reasoning in a language containing expressions representing vague concepts requires a special logic, we present a kind of modal logic suitable for deductions in the presence of vagueness.
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References
Black, M., 1937, Vagueness, Philosophy of Science, 4:427–455.
Black, M., 1963, Reasoning with Loose Concepts, Dialogue, 2:1–12.
Fine, K., 1975, Vagueness, Truth and Logic, Synthese, 30:265–300.
Goguen, J. A., 1969, The Logic of Inexact Concepts, Synthese, 19:325–373.
Kubiński, T., 1958, Nazwy nieostre (Vague Terms), Studia Logica, 7:115–179, in Polish.
Lakoff, G., 1973, Hedges: A Study in Meaning Criteria and the Logic of Fuzzy Concepts, Journal of Philosophical Logic, 2:458–508.
Lewis, D., 1970, General Semantics, Synthese, 22:18–67.
Mehlberg, H., 1956, “The Reach of Science,” Toronto University Press, Toronto.
Orłowska, E., 1983, “Representation of Vague Information,” ICS PAS Reports 503, Warsaw.
Pawlak, Z., 1981, “Classification of Objects by Means of Attributes,” ICS PAS Reports 429, Warsaw.
Pawlak, Z., 1982, Rough Sets, International Journal of Computer and Information Sciences, 11:341–350.
Peacocke, Ch., 1981, Are Vague Predicates Incoherent?, Synthese, 46:121–141.
Przełȩcki, M., 1980, Set Theory as an Ontology for Semantics, in: “Proceedings of the 4th International Wittgenstein Symposium,” R. Haller and W. Grassl, eds., Hölder-Pichler-Tempsky, Vienna.
Rolf, B., 1980, A Theory of Vagueness, Journal of Philosophical Logic, 9:315–325.
Russell, B., 1923, Vagueness, Australasian Journal of Philosophy, 1:84–92.
Sanford, D., 1976, Competing Semantics of Vagueness: Many Values Versus Super-Truth, Synthese, 33:195–210.
Van Fraassen, B. C., 1966, Singular Terms, Truth-Value Gaps, and Free Logic, Journal of Philosophy, 63:481–495.
Van Fraassen, B. C., 1968, Presupposition, Implication and Self-Reference, Journal of Philosophy, 65:136–152.
Vopenka, P., 1979, “Mathematics in the Alternative Set Theory,” Taubner-Texte zur Mathematik, Leipzig.
Vopenka, P., and Hajek, P., 1972, “The Theory of Semisets,” North-Holland, Amsterdam.
Wright, C., 1975, On the Coherence of Vague Predicates, Synthese, 30:325–365.
Zadeh, L. A., 1965, Fuzzy Sets, Information and Control, 8:338–353.
Zadeh, L. A., 1975, Fuzzy Logic and Approximate Reasoning, Synthese, 30:407–428.
Zakowski, W., 1983, Approximations in the Space (U, IT), Demonstratio Mathematicae, 16:761–769.
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Orłowska, E. (1985). Semantics of Vague Concepts. In: Dorn, G., Weingartner, P. (eds) Foundations of Logic and Linguistics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-0548-2_20
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DOI: https://doi.org/10.1007/978-1-4899-0548-2_20
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