A p‐adic probability logic

Mathematical Logic Quarterly 58 (4-5):263-280 (2012)

Abstract

In this article we present a p-adic valued probabilistic logic equation image which is a complete and decidable extension of classical propositional logic. The key feature of equation image lies in ability to formally express boundaries of probability values of classical formulas in the field equation image of p-adic numbers via classical connectives and modal-like operators of the form Kr, ρ. Namely, equation image is designed in such a way that the elementary probability sentences Kr, ρα actually do have their intended meaning—the probability of propositional formula α is in the equation image-ball with the center r and the radius ρ. Due to modal nature of the operators Kr, ρ, it was natural to use the probability Kripke like models as equation image-structures, provided that probability functions range over equation image instead of equation image or equation image

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References found in this work

A Treatise on Probability.John Maynard Keynes - 1921 - London, England: Dover Publications.
Uncertain Inference.Henry E. Kyburg Jr, Jr. Kyburg & Choh Man Teng - 2001 - Cambridge University Press.
Probabilistic Logic.Nils J. Nilsson - 1986 - Artificial Intelligence 28 (1):71-87.
The Uncertain Reasoner’s Companion.J. B. Paris - 1997 - Erkenntnis 46 (3):397-400.

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