Conditional p-adic probability logic

LOGICAL APPROACH TO p - ADIC PROBABILITIES

In this paper we considered a moving from classical logic and Kolmogorov’s probability theory to non-classical p-adic valued logic and p-adic valued probability theory. Namely, we defined p-adic valued logic and further we constructed probability space for some ideals on truth values of p-adic valued logic. We proposed also p-adic valued inductive logic. Such a logic was considered for the firs...

A PROPOSITIONAL p-ADIC PROBABILITY LOGIC

We present the p-adic probability logic LpPP based on the paper [5] by A. Khrennikov et al. The logical language contains formulas such as P=s(α) with the intended meaning “the probability of α is equal to s", where α is a propositional formula. We introduce a class of Kripke-like models that combine properties of the usual Kripke models and finitely additive p-adic probabilities. We propose an...

A Logic with Kolmogorov Style Conditional Probabilities

In this paper we investigate a probability logic with conditional probability operators. The logic (denoted LPP ) allows making statements such as CP≥s(α | β), with the intended meaning ”the conditional probability of α given β is at least s”. Conditional probabilities are defined in the usual Kolmogorv style: P (α | β) = P (α∧β) P (β) , P (β) > 0. A possible-world approach is used to give sema...

A Logic with Higher Order Conditional Probabilities

We investigate probability logic with the conditional probability operators. This logic, denoted LCP , allows making statements such as: P sα, CP s(α | β), CP 0(α | β) with the intended meaning “the probability of α is at least s”, “the conditional probability of α given β is at least s”, “the conditional probability of α given β at most 0”. A possible-world approach is proposed to give semanti...

A p-adic probability logic