A note on entropy of logic
DOI:
https://doi.org/10.2298/YJOR151025011BKeywords:
many-valued propositional logics, Lindenbaum-Tarski algebra, partition, entropyAbstract
We propose an entropy based classification of propositional calculi. Our method can be applied to finite–valued propositional logics and then, extended asymptotically to infinite–valued logics. In this paper we consider a classification depending on the number of truth values of a logic and not on the number of its designated values. Furthermore, we believe that almost the same approach can be useful in classification of finite algebras.References
Belnap, N. D., ”A useful four–valued logic”, in J–M. Dunn, G. Epstein (eds.), Modern Uses of Multiple–Valued Logic, D. Reidel, Dordrecht, 1977, 5–37.
Boričić, M., ”On entropy of a logical system”, Journal of Multiple–Valued Logic and Soft Computing, 21 (5–6) (2013) 439–452.
Boričić, M., ”On entropy of a propositional logic”, Bulletin of Symbolic Logic, 20 (2) (2014) 225, Abstract, Logic Colloquium, 2013.
Hosoi, T., ”On intermediate logics”, Journal of the Faculty of Science, University of Tokyo, section I, 14 (1967) 293–312, and 16 (1969) 1–12. (Review by C. G. McKay, J. Symbolic Logic 36 (1971) 329).
Jonquière, A., ”Note sur la série n=1 Σ x_n ns”, Bulletin de la Société Mathématique de France, 17 (1889) 142-152.
Kleene, S. C., ”On notation for ordinal numbers”, Journal of Symbolic Logic, 3 (1938) 150–155.
Kleene, S. C., Introduction to Metamathematics, North-Holland, Amsterdam, 1952.
Lukasiewicz, J., ”O logice trójwartościowej”, Ruch filozoficzny 5 (1920) 170-171. (English translation: ”On three-valued logic”, in: L. Borkowski (ed.), J. Lukasiewicz, Selected Works, North-Holland, Amsterdam, 1970, 87-88.)
Lukasiewicz, J., Tarski, A., ”Untersuchungen über den Aussagenkalkül”, Comptes Rendus des Séances de la Société des Sciences et des Lettres de Varsovie, Classe III 23 (1930) 30-50. (Translated in: S. R. Givant and R. N. McKenzie (eds.) A. Tarski, Collected Papers, Vol. 1, Birkhäuser, Bazel, 1986, 321–343.)
McKay, C. G., ”On finite logics”, Indagationes Mathematicae, 70 (1967) 363-365. (Review by T. Umezawa, J. Symbolic Logic, 36 (1971) 330.)
Nishimura, I., ”On formulas of one variable in intuitionistic propositional calculus”, Journal of Symbolic Logic, 25 (1960) 327–331.
Priest, G., An Introduction to Non–Classical Logic, Cambridge University Press, New York, 2001. (Second edition 2008.)
Shepp, L., and Olkin, I., ”Entropy of the sum of independent Bernoulli random variables and of the multinomial distribution”, in: J. Gani V. K. Rohatgi (eds.) Contributions to Probability, Academic Press, New York, 1981, 201–206.
Wajsberg, M., ”Aksjomatyzacja trójwartściowego računa zdán”, Comptes Rendus des Séances de la Société des Sciences et des Lettres de Varsovie, Cl. III 23 (1931) 126-145. (English translation: ”Axiomatization of the three-valued propositional calculus”, 13-29, in: S.J. Surma (ed.), Mordechaj Wajsberg. Logical Works, Polish Academy of Sciences, Ossolineum, Wroclaw 1977.)
Downloads
Published
Issue
Section
License
Copyright (c) 2017 YUJOR
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
