GENTZEN'S CUT-FREE CALCULUS VERSUS THE LOGIC OF PARADOX
Alexej P. Pynko · 2010
The main result of the paper is that the sequent calculus g obtained from Gentzen’s LK by eliminating Cut and adding the rules inverse to logical ones is equivalent to the logic of paradox. As a consequence, we prove that LK and the sequent calculus d which results from adding instances of Cut without side formulas to g LK are the only proper consistent extensions of g LK.