An Expectation - Transformer Model Forprobabilistic Temporal

We reinterpret the modal-calculus 16] to act over expectations rather than predicates, where expectations generalise predicates by taking states into the interval 0; 1] rather than the two-point set f0; 1g; our interest is in the idioms of the-calculus that correspond to operators of temporal logic, in particular in establishing reasoning principles for them. Our model includes both probabilistic and demonic choice, and the interpretation exploits the characterisation 20] of probabilistic healthiness for expectation transformers to determine the algebraic properties of probabilistic next, and thence those of the other probabilistic temporal operators. The results connrm that many nonprobabilistic temporal axioms have close probabilistic analogues, and that they can indeed be used for quantitative reasoning about probabilistic behaviour. Often the proofs are just generalisations of the original nonprobabilistic versions. In the-calculus more generally the new interpretation may be useful for describing`gambling games' containing demonic, angelic and probabilistic choice.