Abstract
I present two measures of information for both consistentand inconsistent sets of sentences in a finite language ofpropositional logic. The measures of information are based onmeasures of inconsistency developed in Knight (2002).Relative information measures are then provided corresponding to thetwo information measures.
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References
de Finetti, B., 1931, “Sul significato soggettivo dell probabilitá,” Fundamenta Mathematicae 17, 298–329.
Dunn, J.M., 1976, “Intuitive semantics for first-degree entailments and ‘coupled trees',” Philosophical Studies 29, 149–168.
Hintikka, J., 1970, “On semantic information,” pp. 3–27 in Information and Inference, J. Hintikka and P. Suppes, eds., Dordrecht: D. Reidel.
Jaynes, E.T., 1957, “Information theory and statistical mechanics,” Physical Review 106, 620–630.
Kemeny, J.G., 1953, “A logical measure function,” Journal of Symbolic Logic 18, 289–308.
Kincaid, D.R. and Cheney, E.W., 1996, Numerical Analysis: Mathematics of Scientific Computing, 2nd edition, Pacific Grove: Brooks/Cole.
Knight, K.M., 2002, “Measuring inconsistency,” Journal of Philosophical Logic 31, 77–98.
Lozinskii, E.L., 1994a, “Information and evidence in logic systems,” Journal of Experimental and Theoretical Artificial Intelligence 6, 163–193.
Lozinskii, E.L., 1994b, “Resolving contradictions: A plausible semantics for inconsistent systems,” Journal of Automated Reasoning 12, 1–31.
Paris, J.B., 1994, The Uncertain Reasoner's Companion: A Mathematical Perspective, Cambridge Tracts in Theoretical Computer Science, No. 39, Cambridge: Cambridge University Press.
Paris, J.B., 1999, “Common sense and maximum entropy,” Synthese 117, 75–93.
Paris, J.B., 2001, “A note on the Dutch Book method,” pp. 301–306 in Proceedings of the Second International Symposium on Imprecise Probabilities and their Applications, G. de Cooman, T. L. Fine, and T. Seidenfeld, eds., Ithaca, NY: Cornell University.
Paris, J.B. and Vencovská, A., 1998, “Proof systems for probabilistic uncertain reasoning,” Journal of Symbolic Logic 63(3), 1007–1039.
Priest, G., 1979, “Logic of paradox,” Journal of Philosophical Logic 8, 219–241.
Rawls, J., 1971, A Theory of Justice, Cambridge: Belknap.
Rescher, N. and Manor, R., 1970, “On inference from inconsistent premisses,” Theory and Decision 1, 179–217.
Roberts, L., 2000, “Maybe, maybe not: Probabilistic semantics for two paraconsistent logics,” pp. 233–254 in Frontiers of Paraconsistent Logics, D. Batens, C. Mortensen, G. Priest, and J.-P. van Bendegem, eds., Studies in Logic and Computation, Vol. 8, Baldock: Research Studies Press.
Shannon, C.E. and Weaver, W., 1949, The Mathematical Theory of Communication, Chicago, IL: University of Illinois Press.
Shore, J.E. and Johnson, R.W., 1980, “Axiomatic derivation of the principle of maximum entropy and the principle of minimum crossentropy,” IEEE Transactions on Information Theory IT–26, 26–37.
Suppes, P., 1966, “Probabilistic inference and the concept of total evidence,” pp. 49–65 in Aspects of Inductive Logic, J. Hintikka and P. Suppes, eds., Amsterdam: North-Holland.
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Knight, K.M. Two Information Measures for Inconsistent Sets. Journal of Logic, Language and Information 12, 227–248 (2003). https://doi.org/10.1023/A:1022351919320
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DOI: https://doi.org/10.1023/A:1022351919320