Verification, Falsification, and Cancellation in KT

The main result of this paper is that KT (=T) is closed under a cancellation principle (if LA is provably equivalent to LB and MA is provably equivalent to MB then A is provably equivalent to B). This result extends to KTG1, but it does not extend to modal systems associated with the provability interpretation of L, such as KW (=G) and KT4Grz (=S4Grz). Following Williamson, these results are applied to philosophical concerns about the proper form for theories of meaning, via the interpretation of L as some kind of verifiability