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A five-valued logic and a system
Keywords:
Many-Valued Logics, Foundations of Computing Science, Knowledge Representation, Philosophy of Computer Science, Deductive Systems, EpistemologyAbstract
The present article introduces a five-valued logic and a deductive system. Here, the logic presented is a relevant fragment of the @-logic, which is also a space-time logic. These five values correspond to the following semantics: unknown, possibly known but consistent, false, true, and inconsistent. The present logic and the PLAIN programming language are two results of the same intuitions and from the same philosophical view. Finally, as well as the purposes of PLAIN, the logic ought to be used to support (mobile) agents systems in some manner, besides general purposes.
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References
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[2] A. R. Anderson and N. D. Belnap Junior. Entailment: The Logic of Relevance and Necessity, volume 1. Princeton University Press, 1975.
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[5] R. Bull. Logic and Reality: essays on the legacy of Arthur Prior, chapter Logics without Contraction I, pages 317–336. Oxford University Press, 1996.
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[2] A. R. Anderson and N. D. Belnap Junior. Entailment: The Logic of Relevance and Necessity, volume 1. Princeton University Press, 1975.
[3] D. Batens, C. Mortensen, G. Priest, and J.-P. V. Bendegem, editors. Frontiers of Paraconsistent Logic, volume 8 of Studies in Logic and Computation. Research Studies Press Ltd, 2000.
[4] N. D. Belnap Junior. A useful four-valued logic. In J. M. Dunn and G. Epstein, editors, Proceedings of the Fifth International Symposium on Multiple-Valued Logic, Modern Uses of Multiple-Valued Logic, pages 8– 37. Indiana University, D Reidel Publishing Company, 1975.
[5] R. Bull. Logic and Reality: essays on the legacy of Arthur Prior, chapter Logics without Contraction I, pages 317–336. Oxford University Press, 1996.
[6] M. Bunder. Logic and Reality: essays on the legacy of Arthur Prior, chapter Logics without Contraction II, pages 337–349. Oxford University Press, 1996.
[7] J. M. Dunn. Handbook of Philosophical Logic, volume III: Alternatives to Classical Logic of Synthese library; v. 166, chapter Relevance Logic and Entailment, pages 117–224. Kluwer Academic Publisher, 1986.
[8] U. Ferreira. The plain www page. URL http://www.ufba.br/˜plain, 1996–2003.
[9] M. Fitting. Handbook of Logic in Artifi cial Intelligence and Logic Programming, volume 1: Logical Foundations, chapter Basic Modal Logic, pages 365– 448. Oxford University Press, 1993.
[10] A. Fuhrmann. An Essay on Contraction. Studies in Logic, Language and Information. CSLI Publications and FoLLI, 1997.
[11] D. M. Gabbay. Labelled Deductive Systems, volume 1 of Oxford Logic Guides 33. Oxford University Press, 1996.
[12] J.-Y. Girard, P. Taylor, and Y. Lafont. Proofs and Types. Cambridge University Press, 1993.
[13] A. Gupta and N. Belnap Junior. The Revision Theory of Truth, chapter 2 Fixed Points: Some Basic Facts, page 43. The MIT Press, 1993.
[14] S. Negri and J. V. Plato. Structural Proof Theory. Cambridge University Press, 2001.
[15] S. Read. Relevant Logic: a philosophical examination of inference, Brasil Blackwell, 1988.
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Published
2004-10-01
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[1]
“A five-valued logic and a system”, JCS&T, vol. 4, no. 03, pp. p. 134–140, Oct. 2004, Accessed: Jan. 14, 2026. [Online]. Available: https://journal.info.unlp.edu.ar/JCST/article/view/891
