Intensional FOL for reasoning about probabilities and probabilistic logic programming.

It is important to have a logic, both for computation of probabilities and for reasoning about probabilities, with well-defined syntax and semantics. The current approaches, which are based on Nilssonu0027s probability structures/logics as well as linear inequalities, to reason about probabilities, have some deficiencies. In this research, we have presented a complete revision of those approaches and have shown that the logic for reasoning about probabilities can be naturally embedded into a 2-valued intensional first-order logic (FOL) with intensional abstraction, by avoiding current ad-hoc system composed of two different 2-valued logics: one for the classical propositional logic at a lower-level and a new one, at a higher-level, for probabilistic constraints with probabilistic variables. The theoretical results that are obtained are applied to probabilistic logic programming.