  We introduce and investigate a range of general notions of a game. Our
principal notion is based on a set of agents modifying a relational structure
in a discrete evolution sequence. We also introduce and study a variety of ways
to model partial and erroneous information in the setting. We discuss the
connection of the related general setting to logic and computation formalisms,
with emphasis on the recently introduced Turing-complete logic based on
game-theoretic semantics.
