Global Syntax and Semantics for Recursively Enumerable Languages

descriptionPublicationkeyboard_double_arrow_right Article 01 Apr 1981Publisher:SAGE PublicationsJournal:Fundamenta Informaticae, volume 4, pages 245-254 (issn: 0169-2968, eissn: 1875-8681,

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Authors: Cristian Calude; Gheorghe Paun;

doi: 10.3233/fi-1981-4203

Global Syntax and Semantics for Recursively Enumerable Languages

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Abstract

According to (Benson, 1970), a syntax is a category of strings and derivations (modulo similarity) between them. In this paper the semantic domain is an elementary topes. Thus, an interpretation of a syntax is a cofunctor taking strigs to products and derivations to morphisms. It is proved the existence of a free x – category U such that every syntax is a full subcategory of U, which can be determined recursively. Every interpretation of a syntax is the restriction of the interpretation of U.

Keywords

category of strings and derivations, Recursively (computably) enumerable sets and degrees, Monoidal, symmetric monoidal and braided categories, Topoi, elementary topos, type-zero universal grammar, Formal languages and automata, free x-category, semantic domain

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