Absolute probability functions for intuitionistic propositional logic

Journal of Philosophical Logic 28 (3):223-234 (1999)
Provided here is a characterisation of absolute probability functions for intuitionistic (propositional) logic L, i.e. a set of constraints on the unary functions P from the statements of L to the reals, which insures that (i) if a statement A of L is provable in L, then P(A) = 1 for every P, L's axiomatisation being thus sound in the probabilistic sense, and (ii) if P(A) = 1 for every P, then A is provable in L, L's axiomatisation being thus complete in the probabilistic sense. As there are theorems of classical (propositional) logic that are not intuitionistic ones, there are unary probability functions for intuitionistic logic that are not classical ones. Provided here because of this is a means of singling out the classical probability functions from among the intuitionistic ones
Keywords intuitionistic logic  probability functions  probability semantics
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Reprint years 2004
DOI 10.1023/A:1004385411641
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The Mathematics of Metamathematics.Helena Rasiowa - 1963 - Warszawa, Państwowe Wydawn. Naukowe.
Probabilistic Semantics Objectified: I. Postulates and Logics.Bas C. Van Fraassen - 1981 - Journal of Philosophical Logic 10 (3):371-394.
Conditionals, Probability, and Non-Triviality.Charles G. Morgan & Edwin D. Mares - 1995 - Journal of Philosophical Logic 24 (5):455-467.
Probabilistic Semantics for Intuitionistic Logic.C. G. Morgan & H. Leblanc - 1983 - Notre Dame Journal of Formal Logic 24 (2):161-180.

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