Title :
Programs, grammars and arguments: a personal view of some connections between computation, language and logic
Author_Institution :
McGill Univ., Montreal, Que., Canada
Abstract :
The question of what is an effective process or algorithm arose form the statement of Hilbert´s tenth problem. It was soon seen to be related to the question of which numerical functions Nn→N are computable. Among the early answers to this question the author singles out three. A numerical function is computable if and only if it is recursive, it is computable on a Turing machine, or it is definable in the untyped λ-calculus. Some aspects of the relevance of these three notions of computability to linguistics and logic, in particular, categorial logic, are discussed
Keywords :
Turing machines; category theory; computability; formal logic; grammars; lambda calculus; Hilbert´s tenth problem; Turing machine; categorial logic; computable; numerical function; numerical functions; recursive; untyped lambda-calculus; Algebra; Arithmetic; Concrete; Equations; Humans; Logic; Mathematics; Turing machines; Zinc;
Conference_Titel :
Logic in Computer Science, 1993. LICS '93., Proceedings of Eighth Annual IEEE Symposium on
Conference_Location :
Montreal, Que.
Print_ISBN :
0-8186-3140-6
DOI :
10.1109/LICS.1993.287583