There is a probabilistic semantics for every extension of classical sentence logic

@article{Morgan1982ThereIA,
title={There is a probabilistic semantics for every extension of classical sentence logic},
author={Charles G. Morgan},
journal={J. Philosophical Logic},
year={1982},
volume={11},
pages={431-442}
}

It is possible to characterize conditional probability theory by constraints which do not employ concepts from classical proof theory or semantics. Probability functions so characterized can be used in place of traditional valuation functions to give a sound and complete semantic theory for classical logical; see [I], [3], [6], [9]. Probabilistic semantic theories have also been devised for intuitionistic logic (see [4] and [9]) and for the standard modal systems T, B, S4, and S5 (see [S]). In… CONTINUE READING