¹ References are made to the following works: C. C. Fries, The structure of English (New York, 1952); Z. S. Harris, From morpheme to utterance, Lg. 22.161-83 (1946); id., Methods in structural linguistics (Chicago, 1951); id., Discourse analysis, Lg. 28.1-30 (1952); id., Discourse analysis: A sample text, Lg. 28.474-94 (1952); S. C. Kleene, Introduction to metamathematics (Amsterdam, 1952); C. E. Shannon, The mathematical theory of communication, Bell System technical journal (1948); id., Prediction and entropy of printed English, ibid. (1951); E. L. Thorndike and I. Lorge, A teacher's word book of 30,000 words (New York, 1944).

Since part of this paper is an application of ideas from the field of mathematical logic, the following is a short list of additional references in which these ideas are more fully treated: G. Birkhoff and S. Maclane, A survey of modern algebra (New York, 1953); R. B. Braithwaite, Scientific explanation (Cambridge, 1953); R. Carnap, Logical syntax of language (London, 1937); E. V. Huntington, Postulates for the algebra of logic, Transactions of the American Mathematical Society 35.274-304 (1933); C. I. Lewis and C. H. Langford, Symbolic logic (New York, 1932); H. Reichenbach, Essentials of symbolic logic (New York, 1952); C. E. Shannon, A symbolic analysis of relay and switching circuits, Transactions of the American Institute of Electrical Engineers 57.713-23 (1938).

² Although this paper concentrates on axiomatizing syntax as formation rules, the procedures described also have applications to the problem of getting ‘fairly good approximations’ to the transformation rules of a natural language discussed by Y. Bar-Hillel, Logical syntax and semantics, Lg. 30.230-7 (1954). These applications and other aspects of the problem of transformation rules will be treated in another paper.