Authors: Doder, Dragan
Ognjanović, Zoran 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: A probabilistic logic for reasoning about uncertain temporal information
Journal: Uncertainty in Artificial Intelligence - Proceedings of the 31st Conference, UAI 2015
First page: 248
Last page: 257
Conference: 31st Conference on Uncertainty in Artificial Intelligence, UAI 2015; Amsterdam; Netherlands; 12 July 2015 through 16 July 2015
Issue Date: 1-Jan-2015
Rank: M33
URL: http://auai.org/uai2015/proceedings/papers/258.pdf
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.
Keywords: Probabilistic logics | Temporal information | Temporal logic
Publisher: AUAI Press
Project: National Research Fund (FNR) of Luxembourg, project PRIMAT
Representations of logical structures and formal languages and their application in computing 
Development of new information and communication technologies, based on advanced mathematical methods, with applications in medicine, telecommunications, power systems, protection of national heritage and education 

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