A Proposed Formalism for ECG Schemas, Constructions, Mental Spaces, and Maps

The traditional view has been that Cognitive Linguistics (CL) is incompatible with formalization. Cognitive linguistics is serious about embodiment and grounding, including imagery and image-schemas, force-dynamics, real-time processing, discourse considerations, mental spaces, context, and so on. It remains true that some properties of embodied language, such as context sensitivity, can not be fully captured in a static formalism, but a great deal of CL can be stated formally in a way that is compatible with a full treatment. It appears that we can specify rather complete embodied construction grammars (ECG) using only four types of formal structures: schemas, constructions, maps, and spaces. The purpose of this note is to specify these structures and present simple examples of their use.