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First order languages: Further syntax and semantics

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Published
<mark>Journal publication date</mark>30/09/2011
<mark>Journal</mark>Formalized Mathematics
Issue number3
Volume19
Pages (from-to)179-192
Publication StatusPublished
<mark>Original language</mark>English

Abstract

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.