Definition of first order language with arbitrary alphabet. Syntax of terms, atomic formulas and their subterms

Caminati, Marco (2011) Definition of first order language with arbitrary alphabet. Syntax of terms, atomic formulas and their subterms. Formalized Mathematics, 19 (3). pp. 169-178.

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Abstract

Second of a series of articles laying down the bases for classicalfirst order model theory. A language is defined basically as a tuple made of aninteger-valued function (adicity), a symbol of equality and a symbol for the NORlogical connective. The only requests for this tuple to be a language is that thevalue of the adicity in = is -2 and that its preimage (i.e. the variables set) in 0is infinite. Existential quantification will be rendered (see [11]) by mere prefixinga formula with a letter. Then the hierarchy among symbols according to theiradicity is introduced, taking advantage of attributes and clusters.The strings of symbols of a language are depth-recursively classified as termsusing the standard approach (see for example [16], definition 1.1.2); technically,this is done here by deploying the ‘-multiCat’ functor and the ‘unambiguous’ at-tribute previously introduced in [10], and the set of atomic formulas is introduced.The set of all terms is shown to be unambiguous with respect to concatenation;we say that it is a prefix set. This fact is exploited to uniquely define the subtermsboth of a term and of an atomic formula without resorting to a parse tree.

Item Type:
Journal Article
Journal or Publication Title:
Formalized Mathematics
ID Code:
185178
Deposited By:
Deposited On:
01 Feb 2023 10:00
Refereed?:
Yes
Published?:
Published
Last Modified:
15 Jul 2024 23:29