<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></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.

First Order Languages: Further Syntax and Semantics

Mathematics Department "G. Castelnuovo", Sapienza University of Rome, Piazzale Aldo Moro 5, 00185 Roma, Italy

Formalized Mathematics

{"article-title":"First Order Languages: Further Syntax and Semantics"}

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...

First Order Languages: Further Syntax and Semantics

Publié en ligne: 26 avr. 2012

Pages: 179 - 192

DOI: https://doi.org/10.2478/v10037-011-0027-0

This content is open access.