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

R. Mattison

ResearchPublished 1969

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 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.

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Mattison, R., An Introduction to the Model Theory of First-Order Predicate Logic and a Related Temporal Logic. Santa Monica, CA: RAND Corporation, 1969. https://www.rand.org/pubs/research_memoranda/RM5580-1.html.
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