Infinitary Model Finding in Support of Scientific Discovery

Introduction Model finding technology is highly useful in nearly every stage of logico-mathematical discovery. In the initial formalization of domain knowledge, model finders may be employed to ensure that formulae intended to capture some real domain knowledge are not contradictory; in conjecture generation and verification, the presence or absence of certain models can indicate whether or not the conjecture is actually a logical consequence of its premises. The task of a model finder is straightforward: given a set of formulae in a logical system, the finder seeks a single interpretation which satisfies every formula. In other words, for every function symbol, relation symbol, and constant symbol present in the logical system, the desired result is a mapping of those otherwise semantically meaningless symbols to real functions, real relations, and real constants ranging over one or more non-empty sets (or domains). For example, consider the following two axioms in a standard first-order logic: