Compactness in finite probabilistic inference (Q918960)

The author refers to his book \underbar{Chance and structure} (1988; Zbl 0707.03015), reviewed above, in which a system of probability quantifiers is developed. A probability logic is a classical first-order logic with identity in which, beside universal and existential quantifiers, there are also probability quantifiers. For the author, the motivation for probability logic is to give logical consistency conditions for sets of probability judgements, and to do this in such a way that the probability of a probability is smoothly and recursively accommodated. The author has shown in his book that inconsistency in probability logic is not compact. There are infinite sets of formulae which have no models though all of their finite subsets have models. In the paper the author shows that for each finite integer k, inconsistency in models of size k is compact.