Authors: Ognjanović, Zoran 
Ilić Stepić, Angelina 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Logics with Probability Operators
First page: 1
Last page: 35
Related Publication(s): Probabilistic Extensions of Various Logical Systems
Issue Date: 2020
Rank: M13
ISBN: 978-3-030-52953-6
DOI: 10.1007/978-3-030-52954-3_1
Abstract: 
This chapter presents the logic LFOP1 which may be suitable to formalize reasoning about degrees of beliefs. The aim is that this chapter serves as an illustration for syntax, semantics and the main proof techniques used elsewhere in the book. The logic enriches first order calculus with probabilistic operators of the form P≥s with the intended meaning “probability is at least s”. We define a possible-world semantics with a finitely additive probability measure on sets of worlds. We provide an infinitary axiomatization which contains an infinitary rule with countable many premisses and one conclusion, related to the Archimedean property of real numbers. Other probability logics considered by the authors of this book are then presented, and an overview of related works of other authors is given.
Publisher: Springer Link

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