A Logic with Kolmogorov Style Conditional Probabilities ⋆

Abstract. In this paper we investigate a probability logic with conditional probability operators. The logic (denoted LP P) 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 P (α∧β) P (β) defined in the usual Kolmogorv style: P (α | β) = , P (β)> 0. A possible-world approach is used to give semantics to probability formulas. An infinitary axiomatic system for our logic is given and the corresponding strong completeness theorem is proved. It is proved that the logic is decidable.

Measures of inconsistency and defaults

AbstractWe introduce a method for measuring inconsistency based on the number of formulas needed for deriving a contradiction. The relationships to previously considered methods based on probability measures are discussed. Those methods are extended to conditional probability and default reasoning

Weighted logics for artificial intelligence : an introductory discussion

International audienceBefore presenting the contents of the special issue, we propose a structured introductory overview of a landscape of the weighted logics (in a general sense) that can be found in the Artificial Intelligence literature, highlighting their fundamental differences and their application areas