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DYNAMIC NEGATION AND NEGATIVE INFORMATION

Published online by Cambridge University Press:  01 March 2009

SEBASTIAN SEQUOIAH-GRAYSON
SEBASTIAN SEQUOIAH-GRAYSON*
Affiliation:
Centre for Logic and Analytical Philosophy, University of Leuven, IEG, Computing Laboratory, University of Oxford, and GPI, University of Hertfordshire
*
*GPI, UNIVERSITY OF HERTFORDSHIRE, DEPARTMENT OF PHILOSOPHY, HATFIELD, AL10 9AB., E-mail:[email protected]
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Abstract

This essay proposes a procedural interpretation of negative information in terms of split negation as procedural prohibition. Information frames and models are introduced, with negation defined as the implication of bottom, 0. A method for extracting the procedures prohibited by complex formulas is outlined, and the relationship between types of prohibited procedures is identified. Definitions of negation types in terms of the implication of 0 on an informational interpretation have been criticized. This criticism turns on the definitions creating a purportedly unnatural asymmetry between positive and negative information. It is demonstrated below that a strong asymmetry between positive and negative information is in fact the case. As such, an asymmetry between positive and negative information is natural, and something that we should want an informational interpretation of negation to preserve.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 2 , Issue 1 , March 2009 , pp. 233 - 248
Copyright
Copyright © Association for Symbolic Logic 2009

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References

BIBLIOGRAPHY

Abrusci, V. M., & Ruet, P. (2000). Non-commutative logic, I: The multiplicative fragment. Annals of Pure and Applied Logic, 29–64.Google Scholar
Dosen, K. (1993). A historical introduction to substructural logics. In Schroeder-Heister, P., and Dosen, K., editors. Substructural Logics, Studies in Logic and Computation No. 2. Oxford, UK: Oxford Science Publications, Clarendon Press, 101, pp. 1–30.Google Scholar
Dretske, F. (1981). Knowledge and the Flow of Information. Cambridge, MA: MIT Press, Reprinted in Stanford, CA: CSLI, 1999.Google Scholar
Dunn, J. M. (1993). Partial gaggles applied to logics with restricted structural rules. In Schroeder-Heister, P., and Dosen, K., editors. Substructural Logics, Studies in Logic and Computation No. 2. Oxford, UK: Oxford Science Publications, Clarendon Press, pp. 63–108.CrossRefGoogle Scholar
Dunn, J. M. (1994). Star and perp: Two treatments of negation. In Tomberlin, J. E., editor. Philosophical Perspectives, Atascadero, CA: Ridgeview Publishing Company, Vol. 7. pp. 331–357.Google Scholar
Dunn, J. M. (1996). Generalised ortho negation. In Wansing, H., editor. Negation: A Notion in Focus. Berlin, Germany: Walter de Gruyter, pp. 3–26.CrossRefGoogle Scholar
Floridi, L. (2004). Outline of a theory of strongly semantic information. Minds and Machines, 14, 192–221.CrossRefGoogle Scholar
Girard, J.-Y. (1987). Linear logic. Theoretical Computer Science, 50, 1–101.CrossRefGoogle Scholar
Grzegorczyk, A. (1964). A philosophically plausible interpretation of intuitionistic logic. Indagnationes Mathematicae, 26, 596–601.Google Scholar
Gurevich, Y. (1977). Intuitionistic logic with strong negation. Studia Logica, 36, 49–59.CrossRefGoogle Scholar
Kripke, S. A. (1965). Semantical analysis of intuitionistic logic I. In Crossley, J., and Dummett, M., editors. Formal Systems and Recursive Functions. Amsterdam, The Netherlands: North-Holland, pp. 92–129.CrossRefGoogle Scholar
Mares, E. (2009). General information in relevant logic, forthcoming in synthese, section: Knowledge, rationality, and action. In Floridi, L., and Sequoiah-Grayson, S., editors. The Philosophy of Information and Logic, Synthese, 167, 343–362KRA. Proceedings of PIL-07, The First Workshop on the Philosophy of Information and Logic, University of Oxford, November 3–4, 2007.Google Scholar
Paoli, F. (2002). Substructural Logics: A Primer. Dordrecht, The Netherlands: Springer.CrossRefGoogle Scholar
Sequoiah-Grayson, S. (2007). The metaphilosophy of information. Minds and Machines, 17, 331–344.CrossRefGoogle Scholar
Sequoiah-Grayson, S. (2009). A positive information logic for inferential information, forthcoming in Synthese, section: Knowledge, rationality, and action. In Floridi, L., and Sequoiah-Grayson, S., editors. The Philosophy of Information and Logic, Synthese, 167, 409–431KRA. Proceedings of PIL-07, The First Workshop on the Philosophy of Information and Logic, University of Oxford, November 3–4, 2007.Google Scholar
Wansing, H. (1993). The Logic of Information Structures. Lecture Notes in Artificial Intelligence No. 681, Subseries of Lecture Notes in Computer Science. Berlin, Germany: Springer-Verlag.CrossRefGoogle Scholar