an:01958274
Zbl 1022.03011
Markovi??, Zoran; Ognjanovi??, Zoran; Ra??kovi??, Miodrag
A probabilistic extension of intuitionistic logic
EN
Math. Log. Q. 49, No. 4, 415-424 (2003).
00095153
2003
j
03B48 03B25 68T37
probabilistic logic; intuitionistic logic; completeness; decidability
Summary: We introduce a probabilistic extension of propositional intuitionistic logic. The logic allows for making statements such as \(P_{\geq s} \alpha\), with the intended meaning ``the probability of truthfulness of \(\alpha\) is at least \(s\)''. We describe the corresponding class of models, which are Kripke models with a naturally arising notion of probability, and give a sound and complete infinitary axiomatic system. We prove that the logic is decidable.