Enhancing the inference mechanism of Nilsson's probabilistic logic

Nilsson's Probabilistic Logic is a set-theoretic mechanism for reasoning with uncertainty. We propose a new way of looking at the probability constraints enforced by the framework, which allows the expert to include conditional probabilities in the semantic tree, thus making Probabilistic Logic more expressive. The meaning of entailment in an uncertain environment is explored. An algorithm is presented which will find the maximum entropy point probability for a rule of entailment without resorting to solution by iterative approximation. Also presented are a number of methods for employing the conditional probabilities.