Rigid analytic reconstruction of Hyodo--Kato theory

We give a new and very intuitive construction of Hyodo–Kato cohomology and the Hyodo–Kato map, based on logarithmic rigid cohomology. We show that it is independent of the choice of a uniformiser and study its dependence on the choice of a branch of the $p$-adic logarithm. Moreover, we show the compatibility with the classical construction of Hyodo–Kato cohomology and the Hyodo–Kato map.)