Probability Space for First-Order Predicate Logic

In the spirit of Tarski’s 1930 work, “The concept of Truth in Formalized languages,” we define probability in terms of satisfaction. The novelty here consists in giving quantified sentences an extension, rather than a truth-value, in the domain of a specific first-order model. Quantified sentences are interpreted as defining events in a probability space, constructed from domain and sentences of the language. In standard models, sentences (closed quantified formulas) are true or false according to their satisfaction either by all sequences, or by none. In the extended models here, bound variables in quantified expressions can be satisfied with selected subsets of the domain, rather than the whole domain.