Abstract The conditional probabilistic representation of propositions based on the uniform, or structural, distribution over the constituents of a propositional language was introduced in Kuipers (2025, J. Logic Comput., 35, exaf016). A main finding was that the corresponding ‘city-block’ similarity between two propositions based on the structural distribution is itself a conditional probability. The present paper shows, in the first place, that this can be generalized to any underlying probability distribution. The meaningfulness of the latter is illustrated by a botanic example. It is also argued that conditional probabilities between two propositions, based on the uniform or any non-uniform distribution, can well be seen as explication of the idea of a degree of entailment of one proposition by the other, or the degree of validity of the argument that the second proposition entails the first one. The general version is again illustrated by the botanic example. The notion of similarity between two propositions is of particular interest in the context of truthlikeness, the idea that one theory can be closer, or more similar, to the truth than another. The paper presents some consequences of the above findings and proposals for truthlikeness and illustrates them with the electric circuit example presented in Kuipers (2025, J. Logic Comput., 35, exaf016).
Theo A F Kuipers (Thu,) studied this question.