Authors: Savić, Nenad
Doder, Dragan
Ognjanović, Zoran 
Title: Logics with lower and upper probability operators
Journal: International Journal of Approximate Reasoning
Volume: 88
First page: 148
Last page: 168
Issue Date: 1-Sep-2017
Rank: M21
ISSN: 0888-613X
DOI: 10.1016/j.ijar.2017.05.013
Abstract: 
We present a first-order and a propositional logic with unary operators that speak about upper and lower probabilities. We describe the corresponding class of models, and we discuss decidability issues for the propositional logic. We provide infinitary axiomatizations for both logics and we prove that the axiomatizations are sound and strongly complete. For some restrictions of the logics we provide finitary axiomatic systems.1
Keywords: Axiomatization | Completeness theorem | Probabilistic logic | Upper and lower probabilities
Publisher: Elsevier
Project: National Research Fund (FNR) of Luxembourg, project PRIMAT
Swiss National Science Foundation, grant 200021_165549
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 
Advanced Techniques of Cryptology, Image Processing and Computational Topology for Information Security 

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