  This paper continues the investigation of the logic of competing theories, be
they scientific, social, political etc. We introduce a many-valued, multi-type
modal language which we endow with relational semantics based on enriched
reflexive graphs, inspired by Plo\v{s}\v{c}ica's representation of general
lattices. We axiomatize the resulting many-valued, non-distributive modal logic
of these structures and prove a completeness theorem. We illustrate the
application of this logic through a case study in which we model competition
among interacting political promises and social demands within an arena of
political parties social groups.
