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We investigate properties of the formula  p  → □ p  in the basic modal logic  K . We show that  K  satisfies an infinitary weaker variant of the rule of margins  ϕ  → □ ϕ / ϕ , ¬ ϕ , and as a consequence, we obtain various negative results about admissibility and unification in  K . We describe a complete set of unifiers (i.e. substitutions making the formula provable) of  p  → □ p , and use it to establish that  K  has the worst possible unification type: nullary. In well-behaved transitive modal logics, admissibility and unification can be analysed in terms of projective formulas, introduced by Ghilardi; in particular, projective formulas coincide for these logics with formulas that are admissibly saturated (i.e. derive all their multiple-conclusion admissible consequences) or exact (i.e. axiomatize a theory of a substitution). In contrast, we show that in  K , the formula  p  → □ p  is admissibly saturated, but neither projective nor exact. All our results for  K  also apply to the basic description logic    ALC   .

Blending margins: the modal logic K has nullary unification type