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.
@article{bwmeta1.element.doi-10_2478_v10037-011-0027-0,
author = {Marco Caminati},
title = {First Order Languages: Further Syntax and Semantics},
journal = {Formalized Mathematics},
volume = {19},
year = {2011},
pages = {179-192},
zbl = {1276.03032},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10037-011-0027-0}
}
Marco Caminati. First Order Languages: Further Syntax and Semantics. Formalized Mathematics, Tome 19 (2011) pp. 179-192. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10037-011-0027-0/
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