Absolute Probability Functions for Intuitionistic Propositional Logic
Date
1999
Authors
Roeper, Peter
LeBlanc, B P
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Kluwer Academic Publishers
Abstract
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.
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Keywords
Keywords: Intuitionistic logic; Probability functions; Probability semantics
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Source
Journal of Philosophical Logic
Type
Journal article
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Restricted until
2037-12-31
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