An Introduction to the Model Theory of First-Order Predicate Logic and a Related Temporal Logic

摘要

The paper presents the revised analysis of a formal language having greater expressive capabilities than a first-order predicate language. This new, first-order temporal language can express propositions involving tenses, dates, or quantification over temporal entities. The discussion includes a description of the first-order predicate language and the notion of bound and free variables. The notions of a deduction, a theorem of logic, and a consistent set of formulas are introduced, and the deduction theorem and a form of the compactness theorem are stated and proved. Detailed comparison shows that the new, first-order temporal language differs from the traditional one in allowing quantification over intervals and the admission of interval constants.