Classical logic and the problem of uncertainty

TLDR: It is shown herein that probability can be comprehended in terms of a set of formal theories built in similar language, and explained how logical probabilistic methods relate to such techniques, and shows that the perfect formalization of a domain of knowledge requires them.

Abstract: The uncertainty of knowledge, in contrast to that of data, can be assessed by its probability in the logical sense. The logical concept of probability has been developed since the 1930s but, to date, no complete and accepted framework has been found. This paper approaches this problem from the point of view of logical entailment and natural sequential calculus of Classical logic. It is shown herein that probability can be comprehended in terms of a set of formal theories built in similar language. This measure is compliant with general understanding of probability, can be both conditional and unconditional, accounts for learning new evidence and complements Bayes’s rule. The approach suggested is practically infeasible at present and requires further theoretical research in the domain of geoscience. Nevertheless, even within the framework of existing methods of expert judgement processing, there is a way of implementing logic that will improve the quality of judgements. Also, to reach the state of formalization necessary to use logical probability, techniques of knowledge engineering are required; this paper explains how logical probabilistic methods relate to such techniques, and shows that the perfect formalization of a domain of knowledge requires these methods. Hence, the lines for future research should be: (1) the development of a strategy of co-application of existing expert judgement-processing techniques, knowledge engineering and classical logic; and (2) further research into logic enabling the development of formal languages and theories in