A lattice theory approach to the structure of mental models

Lattice theory is proposed to provide a formalism for the knowledge base used as a mental model by the operator of a complex system. The ordering relation 'greater than or equal to' is interpreted as 'is caused by', and the lattice becomes a representation of the operator's causal hypotheses about the system. A given system can be thought of causally in different ways (purposes, mechanics, physical form, etc.). Each gives rise to a separate lattice. These are related to each other and to an objective description of the structure and function of the physical system by homomorphic mappings. Errors arise when nodes on the mental lattices are not connected in the same way as the physical system lattice; when the latter changes so that the mental lattice no longer provides an accurate map, even as a homomorphism; or when inverse one-to-many mapping gives rise to ambiguities. Some suggestions are made about the design of displays and decision aids to reduce error.