Computing most general unifiers in Euclidean modal logics

We prove that all extensions of K5 have unitary unification, even with parameters. Our proof is constructive in the sense that we can effectively compute, in 4-exponential space, a most general unifier for any unifiable formula. In particular, this proves that unification and admissibility are decidable. We also investigate special unification types: we show that K5 and KD5 are transparent, and we characterize the projective extensions of K5.