Authors: Ikodinović, Nebojša
Rašković, Miodrag 
Marković, Zoran 
Ognjanović, Zoran 
Title: A first-order probabilistic logic with approximate conditional probabilities
Journal: Logic Journal of the IGPL
Volume: 22
Issue: 4
First page: 539
Last page: 564
Issue Date: 1-Jan-2014
Rank: M21
ISSN: 1367-0751
DOI: 10.1093/jigpal/jzt048
We define a first-order probabilistic logic with Keisler-style probabilistic quantifiers allowing non-standard values of probabilistic functions. An axiomatic system with two infinitary rules of inference is given and proved to be sound and strongly complete. The decidability of two quite expressive fragments of this logic is proved. The fragments may be used to model not only the usual defaults but also a generalized version of defaults with several variables.
Keywords: Approximate probability | Decidability | Non-standard analysis | Probabilistic first-order logic | Strong completeness
Publisher: Oxford University Press
Project: 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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