Cut Might Cautiously
Jaap van der Does
This note is on cautious cut elimination for one of Veltman's might
logics. Syntactically, the logic is presented as an extension of a sequent
system for classical propositional 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.