We establish the pragmatic manifold MPrag as the 9-point diagonal in the intention cube (Sem × Syn × Prag), contrasting two approaches to pragmatic communication: (1) geodesic navigation along MPrag representing optimal intention transitions, and (2) fiber bundle projection from the 720-point non-pragmatic space Mc onto MPrag via contextual repair.

We prove that geodesic distance induces a discrete metric on MPrag, while the fiber bundle structure admits a natural connection encoding Gricean maxims.

Our main result shows these approaches are complementary: geodesics describe ideal communication, while fibers capture actual linguistic performance.

Abstract

We establish the pragmatic manifold MPrag as the 9-point diagonal in the intention cube (Sem × Syn × Prag), contrasting two approaches to pragmatic communication: (1) geodesic navigation along MPrag representing optimal intention transitions, and (2) fiber bundle projection from the 720-point non-pragmatic space Mc onto MPrag via contextual repair. 

We prove that geodesic distance induces a discrete metric on MPrag, while the fiber bundle structure admits a natural connection encoding Gricean maxims. 

Our main result shows these approaches are complementary: geodesics describe ideal communication, while fibers capture actual linguistic performance.