Cut Might Cautiously
J. van der Does · Logic Journal of IGPL · 1995
This note is on cautious cut elimination for one of Veitman's might logics. Syntactically, the logic is presented as an extension of a sequent system for classical proposition logic (hence: CPL). I show that this extension preserves the completeness and decidability of CPL. The proof has cautious cut elimination as a corollary. I also give a rather general syntactic proof of cautious cut elimination. It states that any ‘base’ logic which has a reflexive, monotone consequence relation that allows cautious cut to be eliminated preserves cautious cut elimination when extended to a might logic.