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BELIEF REVISION, PROBABILISM, AND LOGIC CHOICE

Published online by Cambridge University Press:  09 September 2014

EDWIN MARES*
Affiliation:
Victoria University of Wellington
*
*PHILOSOPHY PROGRAMME AND CENTRE FOR LOGIC LANGUAGE, AND COMPUTATION VICTORIA UNIVERSITY OF WELLINGTON WELLINGTON, NEW ZEALAND, 6140 E-mail: Edwin.Mares@vuw.ac.nz

Abstract

This paper presents a probabilist paraconsistent theory of belief revision. This theory is based on a very general theory of probability, that fits with a wide range of classical and nonclassical logics. The theory incorporates a version of Jeffrey conditionalisation as its method of updating. A Dutch book argument is given, and the theory is applied to the problem of choosing a logical system.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2014 

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References

BIBLIOGRAPHY

Allwein, G., & Dunn, J. M. (1993). Kripke models for linear logic. The Journal of Symbolic Logic, 58, 514545.Google Scholar
Belnap, N. (1977). A useful 4-valued logic. In Dunn, J. M., and Epstein, G., editors. Modern Uses of Many-Valued Logic, Dordrecht: Reidel, pp. 837.Google Scholar
Brady, R. (2006). Universal Logic. Stanford: CSLI.Google Scholar
Buchak, L. (2013). Risk and Rationality. Oxford: Oxford University Press.Google Scholar
Dunn, J. M. (1968). Natural versus formal languages. In American Philosophical Association meeting presented at the joint APA-ASL symposium, New York, Dec. 27, unpublished.Google Scholar
Dunn, J. M. (1976). Intuitive semantics for first-degree entailments and “coupled trees”. Philosophical Studies, 29, 149168.Google Scholar
Fine, K. (1974). Models for entailment. Journal of Philosophical Logic, 3, 347372.Google Scholar
Girard, J-Y. (1998). Light linear logic. Information and Computation, 14, 175204.Google Scholar
Goldblatt, R. (1993). The Mathematics of Modality. Stanford: CSLI.Google Scholar
Goldblatt, R. (2011). Quantifiers, Propositions, and Identity: Admissible Semantics for Quantified Modal and Substructural Logics. Cambridge: Cambridge University Press.Google Scholar
Kyburg, H. (1970). Conjunctivitis. In Swain, M., editor. Induction, Acceptance, and Rational Belief, Dordrecht: Reidel, pp. 5582.Google Scholar
Mares, E. (1997). Paraconsistent probability theory and paraconsistent bayesianism. Logique et Analyse, 160, 375384.Google Scholar
Mares, E. (2000). Even dialetheists should hate contradictions. Australasian Journal of Philosophy, 78, 503–316.CrossRefGoogle Scholar
Mares, E. (2002). A paraconsistent theory of belief revision. Erkenntnis, 56, 229246.Google Scholar
Mares, E. (2004). Relevant Logic: A Philosophical Interpretation. Cambridge: Cambridge University Press.Google Scholar
Mares, E. (2014). Liars, lotteries, and prefaces: Two paraconsistent accounts of theory change. In Hansson, S. O., editor. David Makinson on Classical Methods for Non-Classical Problems, Dordrecht: Springer Verlag, pp. 119141.CrossRefGoogle Scholar
Mares, E., & Goldblatt, R. (2006). An alternative semantics for quantified relevant logic. The Journal of Symbolic Logic, 71, 163187.Google Scholar
Ono, H. (1993). Semantics for substructural logics. In Došen, K., and Schröder-Heister, P., editors. Substructural Logic, Oxford: Oxford University Press, pp. 259291.CrossRefGoogle Scholar
Paoli, F. (2002). Substructural Logics: A Primer. Dordrecht: Springer.Google Scholar
Paoli, F., & Restall, G. (2005). The geometry of non-distributive logics. The Journal of Symbolic Logic, 70, 11081126.Google Scholar
Paris, J. B. (2001). A note on the Dutch book method. In Proceedings of the second International Symposium on imprecise Probabilities and their Applications, ISIPTA, Ithaca, NY: Shaker, pp. 301306.Google Scholar
Popper, K. (1959). Logic of Scientific Discovery. London: Hutchinson.CrossRefGoogle Scholar
Priest, G. (2006). In Contradiction (second edition). Oxford: Oxford University Press.Google Scholar
Priest, G. (2008). An Introduction to Non-classical Logic: From If to Is. Cambridge: Cambridge University Press.Google Scholar
Ramsey, F. P. (1931). Foundations of Mathematics and Other Logical Essays. London: K. Paul, Trench, Trubner and Company.Google Scholar
Rényi, A. (1970). Foundations of Probability. San Francisco: Holden-Day.Google Scholar
Routley, R., & Meyer, R. K. (1972a). Semantics for entailment II. Journal of Philosophical Logic, 1, 5373.CrossRefGoogle Scholar
Routley, R., & Meyer, R. K. (1972b). Semantics for entailment III. Journal of Philosophical Logic, 1, 192208.Google Scholar
Routley, R., & Meyer, R. K. (1973). Semantics for entailment. In Leblanc, H., editor. Truth, Syntax, and Modality, Amsterdam: North Holland, pp. 199243.CrossRefGoogle Scholar
Smith, N. J. J. (forthcoming). Vagueness, uncertainty, and degrees of belief – two kinds of indeterminacy, one kind of credence. Erkenntnis, Available from Springer Link: DOI: 10.1007/s10670-013-9588-3.Google Scholar
Weatherson, B. (2003). From classical to constructive probability. Notre Dame Journal of Formal Logic, 44, 111123.Google Scholar
Williams, J. R. G. (2012). Generalized probabilism: Dutch books and accuracy domination. Journal of Philosophical Logic, 41, 811840.CrossRefGoogle Scholar