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First order languages: further syntax and semantics. (English) Zbl 1276.03032
Summary: Third of a series of articles laying down the bases for classical first-order model theory. Interpretation of a language in a universe set. Evaluation of a term in a universe. Truth evaluation of an atomic formula. Reassigning the value of a symbol in a given interpretation. Syntax and semantics of a non-atomic formula are then defined concurrently. As a consequence, the evaluation of any w.f.f. string and the relation of logical implication are introduced. Depth of a formula. Definition of satisfaction and entailment (aka entailment or logical implication) relations.

03C07 Basic properties of first-order languages and structures
03B35 Mechanization of proofs and logical operations
68T15 Theorem proving (deduction, resolution, etc.) (MSC2010)
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