In explicit state model checking of linear temporal logic properties, a Büchi automaton encodes a temporal property. It interleaves with a Kripke model to form a state space, which is searched for counterexamples. Multi-valued model checking considers additional truth values beyond the Boolean $$ true $$ and $$ false $$; these values add extra information to the model, e.g. for the purpose of abstraction or execution steering. This paper presents a method to create Büchi automata for multi-valued model checking using quasi-Boolean logics. It allows for multi-valued propositions as well as multi-valued transitions. A logic for the purpose of execution steering and abstraction is presented as an application.