Probabilistic logic with independence
International Journal of Approximate Reasoning
Probabilistic Logic over Paths
Electronic Notes in Theoretical Computer Science (ENTCS)
A branching time logic with two types of probability operators
SUM'11 Proceedings of the 5th international conference on Scalable uncertainty management
A probabilistic temporal logic that can model reasoning about evidence
FoIKS'10 Proceedings of the 6th international conference on Foundations of Information and Knowledge Systems
On real-valued evaluation of propositional formulas
FoIKS'12 Proceedings of the 7th international conference on Foundations of Information and Knowledge Systems
A propositional probabilistic logic with discrete linear time for reasoning about evidence
Annals of Mathematics and Artificial Intelligence
A survey on temporal logics for specifying and verifying real-time systems
Frontiers of Computer Science: Selected Publications from Chinese Universities
A first-order dynamic probability logic
ECSQARU'13 Proceedings of the 12th European conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
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We introduce a propositional and a first-order logic for reasoning about discrete linear time and finitely additive probability. The languages of these logics allow formulae that say 'sometime in the future, α holds with probability at least s'. We restrict our study to so-called measurable models. We provide sound and complete infinitary axiomatizations for the logics. Furthermore, in the propositional case decidability is proved by establishing a periodicity argument for ω-sequences extending the decidability proof of standard propositional temporal logic LTL. Complexity issues are examined and a worst-case complexity upper bound is given. Extensions of the presented results and open problems are described in the final part of the paper.