  Within the field of phylogenetics there is growing interest in measures for
summarising the dissimilarity, or 'incongruence', of two or more phylogenetic
trees. Many of these measures are NP-hard to compute and this has stimulated a
considerable volume of research into fixed parameter tractable algorithms. In
this article we use Monadic Second Order logic (MSOL) to give alternative,
compact proofs of fixed parameter tractability for several well-known
incongruency measures. In doing so we wish to demonstrate the considerable
potential of MSOL - machinery still largely unknown outside the algorithmic
graph theory community - within phylogenetics. A crucial component of this work
is the observation that many of these measures, when bounded, imply the
existence of an 'agreement forest' of bounded size, which in turn implies that
an auxiliary graph structure, the display graph, has bounded treewidth. It is
this bound on treewidth that makes the machinery of MSOL available for proving
fixed parameter tractability. We give a variety of different MSOL formulations.
Some are based on explicitly encoding agreement forests, while some only use
them implicitly to generate the treewidth bound. Our formulations introduce a
number of "phylogenetics MSOL primitives" which will hopefully be of use to
other researchers.
