Purpose - To elaborate a theory for modeling concepts that incorporates how a context influences the typicality of a single exemplar and the applicability of a single property of a concept. To investigate the structure of the sets of contexts and properties.

Design/methodology/approach - The effect of context on the typicality of an exemplar and the applicability of a property is accounted for by introducing the notion of "state of a concept", and making use of the state-context-property formalism (SCOP), a generalization of the quantum formalism, whose basic notions are states, contexts and properties.

Findings - The paper proves that the set of context and the set of properties of a concept is a complete orthocomplemented lattice, i.e. a set with a partial order relation, such that for each subset there exists a greatest lower bound and a least upper bound, and such that for each element there exists an orthocomplement. This structure describes the "and", "or", and "not", respectively for contexts and properties. It shows that the context lattice as well as the property lattice are non-classical, i.e. quantum-like, lattices.

Originality/value - Although the effect of context on concepts is widely acknowledged, formal mathematical structures of theories that incorporate this effect have not been successful. The study of this formal structure is a preparation for the elaboration of a theory of concepts that allows the description of the combination of concepts.