Tarski, Alfred, Introduction to Logic, New York: Oxford University Press, 1941, 239 pp.
Woodger, J. H., The Axiomatic Method in Biology, Cambridge, England: The University Press, 1937, 174 pp.
Chapter 2, [pp. 18-52], is an excellent and understandable summary of the concepts of mathematical logic.
Several papers on the application of mathematical logic to the analysis of practical situations are:
Berkeley, Edmund C., Boolean Algebra (The Technique for Manipulating “And,” “Or,” “Not,” and Conditions) and Applications to Insurance, Record of the American Institute of Actuaries, vol. 26, Oct. 1937, pp. 373-414.
Berkeley, Edmund C., Conditions Affecting the Application of Symbolic Logic, Journal of Symbolic Logic, vol. 7, no. 4, Dec. 1942, pp. 160-168.
Shannon, Claude E., A Symbolic Analysis of Relay and Switching Circuits, Transactions of the American Institute of Electrical Engineers, vol. 57, 1938, pp. 713-723.
This paper has had a good deal of influence here and there on the development of electric circuits using relays.
The following report discusses the solution of some problems of mathematical logic by means of a large-scale digital calculator:
Tarski, Alfred, A Decision Method for Elementary Algebra and Geometry, Report R-109, California: Rand Corporation, Aug. 1, 1948, 60 pp.