2014/07/22 by Citkin, Alex
#FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.1407.5812
A set F of formulas is complete relative to a given class of logics, if every logic from this class can be axiomatized by formulas from F. A set of formulas F is Ł-complete relative to a given class of logics, if every logic of this class can be Ł-axiomatized by formulas from F, that is, every of these logics can be defined by an Ł-deductive system with axioms and anti-axioms from F and inference rules modus ponens, modus tollens, substitution and reverse substitution. We prove that every complete relative to \Ext\Int (or \Ext\KF) set of formulas is Ł-complete. In particular, every logic from \Ext\Int (or \Ext\KF) can be Ł-axiomatized by Zakharyaschev's canonical formulas.