First order languages: Further syntax and semantics

Caminati, Marco (2011) First order languages: Further syntax and semantics. Formalized Mathematics, 19 (3). pp. 179-192.

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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 (this point is explained in [16], 4.2.1).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, see [18] III.3.2 and III.4.1 respectively.

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Formalized Mathematics
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01 Feb 2023 10:05
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28 Nov 2023 10:37