  Game comonads give a categorical semantics for comparison games in Finite
Model Theory, thus providing an abstract characterisation of logical
equivalence for a wide range of logics, each one captured through a specific
choice of comonad. However, data-aware logics such as CoreDataXPath present
sophisticated notions of bisimulation which defy a straightforward comonadic
encoding. In this work we begin the comonadic treatment of data-aware logics by
introducing a generalisation of Modal Logic that allows relation symbols of
arbitrary arity as atoms of the syntax, which we call Path Predicate Modal
Logic or PPML. We motivate this logic as arising from a shift in perspective on
a already studied restricted version of CoreDataXPath, called DataGL, and prove
that PPML recovers DataGL for a specific choice of signature. We argue that
this shift in perspective allows the capturing and designing of new data-aware
logics. On the other hand, PPML enjoys an intrinsic motivation in that it
extends Modal Logic to predicate over more general models. Having defined the
simulation and bisimulation games for PPML and having proven a
Hennessy-Milner-type theorem, we define the PPML comonad and prove that it
captures these games, following analogous results in the literature. Our
treatment is novel in that we explicitly prove that our comonad satisfies the
axioms of arboreal categories and arboreal covers. Using the comonadic
machinery, we immediately obtain a tree-model property for PPML. Finally, we
define a translation functor from relational structures into Kripke structures
and use its properties to prove a series of polynomial-time reductions from
PPML problems to their Basic Modal Logic counterparts. Our results explain
precisely in what sense PPML lets us view general relational structures through
the modal lens.
