A propositional calculus for inconsistent deductive systems

Editorial note. Read at the meeting of section A, Societatis Scientiarum Torunensis, 19th March 1948. Published in Polish under the title “Rachunek zdan dla systemow dedukcyjnych sprzecznych”, in: Studia Societatis Scientiarum Torunensis, Sectio A, Vol. I, No. 5, Torun 1948, pp. 57–77. In original version the Polish notation was used. It is the second English version of this paper. The first one — translated by Olgierd Wojtasiewicz — was published under the title “Propositional calculus for contradictory deductive systems”, in Studia Logica, Vol. XXIV (1969), pp. 143–157. The present version is a small variation of the previous one. The chief difference is the change of the original Polish notation (done by A. Pietruszczak) into modern and standard one. For further Editorial Notes see Notes (denoted in the text by natural numbers) at the end of the paper.