Notre Dame Journal of Formal Logic

The Expressive Unary Truth Functions of n-valued Logic

Stephen Pollard

Source: Notre Dame J. Formal Logic Volume 46, Number 1 (2005), 93-105.

Abstract

The expressive truth functions of two-valued logic have all been identified. This paper begins the task of identifying the expressive truth functions of n-valued logic by characterizing the unary ones. These functions have distinctive algebraic, semantic, and closure-theoretic properties.

Primary Subjects: 03B50
Secondary Subjects: 03B22
Keywords: expressive logics; many-valued logics; closure spaces
Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.ndjfl/1107220676
Digital Object Identifier: doi:10.1305/ndjfl/1107220676
Mathematical Reviews number (MathSciNet): MR2131549
Zentralblatt MATH identifier: 02186753

References

[1] Beall, J. C. , and B. C. van Fraassen, Possibilities and Paradox, Oxford University Press, Oxford, 2003.
[2] \global\editortrue Gabbay, D. M. , and H. Wansing, editors, What Is Negation?, vol. 13 of Applied Logic Series, Kluwer Academic Publishers, Dordrecht, 1999.
Mathematical Reviews (MathSciNet): MR2001f:03015
Zentralblatt MATH: 0957.00012
[3] Martin, N. M. , and S. Pollard, Closure Spaces and Logic, vol. 369 of Mathematics and its Applications, Kluwer Academic Publishers Group, Dordrecht, 1996.
Mathematical Reviews (MathSciNet): MR97m:03022
Zentralblatt MATH: 0855.54001
[4] Pollard, S., "The expressive truth conditions of two-valued logic", Notre Dame Journal of Formal Logic, vol. 43 (2002), pp. 221--30.
Mathematical Reviews (MathSciNet): MR2034747
Digital Object Identifier: doi:10.1305/ndjfl/1074396307
Project Euclid: euclid.ndjfl/1074396307
[5] Pollard, S. , and N. M. Martin, "Contractions of closure systems", Notre Dame Journal of Formal Logic, vol. 35 (1994), pp. 108--15.
Mathematical Reviews (MathSciNet): MR95m:03019
Zentralblatt MATH: 0804.06004
Digital Object Identifier: doi:10.1305/ndjfl/1040609298
Project Euclid: euclid.ndjfl/1040609298
[6] Pollard, S. , and N. M. Martin, "Closed bases and closure logic", The Monist, vol. 79 (1996), pp. 117--27.
[7] Rasiowa, H., An Algebraic Approach to Nonclassical Logics, vol. 78 of Studies in Logic and the Foundations of Mathematics, North-Holland Publishing Co., Amsterdam, 1974.
Mathematical Reviews (MathSciNet): MR56:5285
Zentralblatt MATH: 0299.02069
[8] van Fraassen, B. C., Formal Semantics and Logic, Macmillan, New York, 1971.
Zentralblatt MATH: 0253.02002
[9] Weaver, G., "Compactness theorems for finitely-many-valued sentential logics", Studia Logica, vol. 37 (1978), pp. 413--16.
Mathematical Reviews (MathSciNet): MR80h:03037
Zentralblatt MATH: 0415.03018
[10] Wójcicki, R., Theory of Logical Calculi: Basic Theory of Consequence Operations, vol. 199 of Synthese Library, Kluwer Academic Publishers Group, Dordrecht, 1988.
Mathematical Reviews (MathSciNet): MR90j:03001
Zentralblatt MATH: 0682.03001
[11] Woodruff, P. W., "On compactness in many-valued logic. I", Notre Dame Journal of Formal Logic, vol. 14 (1973), pp. 405--7.
Mathematical Reviews (MathSciNet): MR48:8199
Zentralblatt MATH: 0245.02022
Project Euclid: euclid.ndjfl/1093891009

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