In this paper, we evaluate Button’s claim that knot is a nasty connective. Knot’s nastiness is due to the fact that, when one extends the set \ with knot, the connective provides counterexamples to a number of classically valid operational rules in a sequent calculus proof system. We show that just as going non-transitive diminishes tonk’s nastiness, knot’s nastiness can also be reduced by dropping Reflexivity, a different structural rule. Since doing so restores all other rules in the system as (...) validity-preserving, we are inclined to conclude that there, knot is not that nasty. However, since motivating non-reflexivity is harder than motivating non-transitivity, we also acknowledge that disagreement with our conclusion is possible. (shrink)

After some motivating remarks in Section 1, in Section 2 we show how to replace an axiomatic basis for any one of a broad range of sentential logics having finitely many axiom schemes and Modus Ponens as the sole proper rule, by a basis with the same axiom schemes and finitely many one-premiss rules. Section 3 mentions some questions arising from this replacement procedure , explores another such procedure, and discusses some aspects of the consequence relations associated with the different (...) axiomatizations in play. Several open problems are mentioned. An appendix briefly treats the issue of a similar ‘at most one-premiss rules’ reformulation of proof systems with sequent-to-sequent rules. (shrink)