Absolute probability functions for intuitionistic propositional logic

Peter Roeper*, Hugues Leblanc

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    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.

    Original languageEnglish
    Pages (from-to)223-234
    Number of pages12
    JournalJournal of Philosophical Logic
    Volume28
    Issue number3
    DOIs
    Publication statusPublished - 1999

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