The expressibility of fragments of Hybrid Graph Logic on finite digraphs

Hybrid Graph Logic is a logic designed for reasoning about graphs and is built from a basic modal logic, augmented with the use of nominals and a facility to verify the existence of paths in graphs. We study the finite model theory of Hybrid Graph Logic. In particular, we develop pebble games for Hybrid Graph Logic and use these games to exhibit strict infinite hierarchies involving fragments of Hybrid Graph Logic when the logic is used to define problems involving finite digraphs. These fragments are parameterized by the quantifier-rank of formulae along with the numbers of propositional symbols and nominals that are available. We ascertain exactly the relative definability of these parameterized fragments of the logic.