A legacy recalled and a tradition continued

Since the first presentation of classical sentential logic as an axiomatic system by Frege in 1879, the study of a variety of sentential calculi has flourished. One major area of investigation, initiated by Lukasiewicz and his colleagues in the first half of the twentieth century and carried into the second half by Meredith, Thomas, Prior, et al., focuses on alternative axiom sets for such logics, and on formal proofs within them. This paper recalls a sampling of the results obtained heretofore, noting along the way how the papers in this special issue of the Journal of Automated Reasoning fit into that larger tradition of which they now form a part. It also suggests a number of further questions, open problems, and projects to which the methods developed in these papers seem ideally suited and might well be fruitfully applied.