A Probabilistic Logic for Reasoning about Uncertain Temporal Information

Dragan Doder, Zoran Ognjanovic Mathematical Institute Serbian Academy of Sciences and Arts
Proceedings of the 31st Conference on Uncertainty in Artificial Intelligence, PMLR R13:780-789, 2015.

Abstract

The main goal of this work is to present the proof-theoretical and model-theoretical approach to a probabilistic logic which allows reasoning about temporal information. We extend both the language of linear time logic and the language of probabilistic logic, allowing statements like “A will always hold"and “the probability that A will hold in next moment is at least the probability that B will always hold," where A and B are arbitrary statements. We axiomatize this logic, provide corresponding semantics and prove that the axiomatization is sound and strongly complete. We show that the problem of deciding decidability is PSPACE-complete, no worse than that of linear time logic.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR13-doder15a, title = {A Probabilistic Logic for Reasoning about Uncertain Temporal Information}, author = {Doder, Dragan and Arts, Zoran Ognjanovic Mathematical Institute Serbian Academy of Sciences and}, booktitle = {Proceedings of the 31st Conference on Uncertainty in Artificial Intelligence}, pages = {780--789}, year = {2015}, editor = {Meila, Marina and Heskes, Tom}, volume = {R13}, series = {Proceedings of Machine Learning Research}, month = {12--16 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r13/main/assets/doder15a/doder15a.pdf}, url = {https://proceedings.mlr.press/r13/doder15a.html}, abstract = {The main goal of this work is to present the proof-theoretical and model-theoretical approach to a probabilistic logic which allows reasoning about temporal information. We extend both the language of linear time logic and the language of probabilistic logic, allowing statements like “A will always hold"and “the probability that A will hold in next moment is at least the probability that B will always hold," where A and B are arbitrary statements. We axiomatize this logic, provide corresponding semantics and prove that the axiomatization is sound and strongly complete. We show that the problem of deciding decidability is PSPACE-complete, no worse than that of linear time logic.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T A Probabilistic Logic for Reasoning about Uncertain Temporal Information %A Dragan Doder %A Zoran Ognjanovic Mathematical Institute Serbian Academy of Sciences and Arts %B Proceedings of the 31st Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2015 %E Marina Meila %E Tom Heskes %F pmlr-vR13-doder15a %I PMLR %P 780--789 %U https://proceedings.mlr.press/r13/doder15a.html %V R13 %X The main goal of this work is to present the proof-theoretical and model-theoretical approach to a probabilistic logic which allows reasoning about temporal information. We extend both the language of linear time logic and the language of probabilistic logic, allowing statements like “A will always hold"and “the probability that A will hold in next moment is at least the probability that B will always hold," where A and B are arbitrary statements. We axiomatize this logic, provide corresponding semantics and prove that the axiomatization is sound and strongly complete. We show that the problem of deciding decidability is PSPACE-complete, no worse than that of linear time logic. %Z Reissued by PMLR on 04 October 2026.
APA
Doder, D. & Arts, Z.O.M.I.S.A.o.S.a.. (2015). A Probabilistic Logic for Reasoning about Uncertain Temporal Information. Proceedings of the 31st Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R13:780-789 Available from https://proceedings.mlr.press/r13/doder15a.html. Reissued by PMLR on 04 October 2026.

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