Logical Formalizations of Syntactical Properties (Extended Abstract)

In this paper first order logic is used for expressing syntax of formal languages. A model Syn is introduced and it is shown that whitin it syntactic relations and classes of languages are representable by means of first order formulae. The class of Sigma*(1) formulae is defined as an extension of arithmetical Sigma(1) formulae; then, a theory is considered where many syntactical notions can be developed in terms of axiomatic representability. This logical approach seems adequate to analyze and to integrate in a unique framework several grammatical models that emerge in the search for new computational paradigms.