Authors: Ilić-Stepić, Angelina 
Ognjanović, Zoran 
Ikodinović, Nebojša
Perović, Aleksandar
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: A p-adic probability logic
Journal: Mathematical Logic Quarterly
Volume: 58
Issue: 4-5
First page: 263
Last page: 280
Issue Date: 1-Aug-2012
Rank: M22
ISSN: 0942-5616
DOI: 10.1002/malq.201110006
In this article we present a p-adic valued probabilistic logic which is a complete and decidable extension of classical propositional logic. The key feature of lies in ability to formally express boundaries of probability values of classical formulas in the field of p-adic numbers via classical connectives and modal-like operators of the form K r, ρ. Namely, is designed in such a way that the elementary probability sentences K r, ρα actually do have their intended meaning-the probability of propositional formula α is in the -ball with the center r and the radius ρ. Due to modal nature of the operators K r, ρ, it was natural to use the probability Kripke like models as structures, provided that probability functions range over instead of or.
Keywords: p-adic numbers | Probability logic
Publisher: Wiley
Project: 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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