Full Sentential Logic
The idea of a separate development of purely implicational logic seems to have originated with Alfred Tarski well before 1930; in that year a compilation of results by J. Łukasiewicz, Tarski, and a few other logicians was published. The subject was discussed later on by M. Wajsberg (1936), L. Henkin (1949), and K. Schröter (1958). The introduction of sequents, with its deduction-theoretic motivation, is due independently to G. Gentzen (1934) and to S. Jaskowski (1934); its semantic motivation seems to be original. An advancement, as compared to Gentzen’s and Jaskowski’s technique, seems to be the conception of their rules of inference as rules of reduction.
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