Decidability of a conditional-probability logic with non-standard valued probabilities

Abstract

A probabilistic logic was defined in (Rašković, Ognjanović & Marković 2004; 2004) with probabilistic operators, both conditional and ”absolute”, which are applied to propositional formulas. The range of probabilistic operators is syntactically restricted to a recursive subset of a non standard interval *[0,1] which means that it contains infinitesimals. In this paper we prove the decidability of that logic. This means that the logicmay be a suitable candidate for AI applications such as, e.g. modelling the default reasoning.