This article constructs a theoretical framework enabling the logic of plausibility to be axiomatised and for decisions about plausibility to be automated. One result is that undecidability presented in the initial theory is resolved. To arrive at a logical-mathematical basis of the theory of plausibility an axiomatization of plausibility logic based on notions of evidence is proposed. It is through these axioms that this logic is characterized and its properties deduced.

The aim of this article is to study some new properties of the plausibility logic. Besides, is analyzed the behavior of the logical operators, in the logic of plausibility and in the formal logic. All the results are showed using the theory of the weight graphs.