TY - JOUR
T1 - Absolute probability functions for intuitionistic propositional logic
AU - Roeper, Peter
AU - Leblanc, Hugues
PY - 1999
Y1 - 1999
N2 - 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.
AB - 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.
KW - Intuitionistic logic
KW - Probability functions
KW - Probability semantics
UR - http://www.scopus.com/inward/record.url?scp=53149137861&partnerID=8YFLogxK
U2 - 10.1023/A:1004385411641
DO - 10.1023/A:1004385411641
M3 - Article
SN - 0022-3611
VL - 28
SP - 223
EP - 234
JO - Journal of Philosophical Logic
JF - Journal of Philosophical Logic
IS - 3
ER -