Blending margins: the modal logic K has nullary unification type

摘要

We investigate properties of the formula p ->square p in the basic modal logic K. We show that K satisfies an infinitary weaker variant of the rule of margins phi ->square phi/phi, -phi, and as a consequence, we obtain various negative results about admissibility and unification inK. We describe a complete set of unifiers (i. e. substitutions making the formula provable) of p ->square p, and use it to establish thatK has the worst possible unification type: nullary. In well- behaved transitive m