Image schemas are mental patterns learned from perceptual experiences capturing conceptual constructions in expressions. In linguistic analysis, their visualizations are often context-dependent without a generalizable structure. Addressing this, we introduce The Diagrammatic Image Schema Language: a formal representation language that systematizes a set of visual combination rules for different conceptual primitives from the cognitive science literature. These primitives are distinguished from a formal point of view to allow for more general application. DISL also contains a logical exchange format in which the diagrams may be made machine-readable. Using DISL, the semantic structure of complex scenarios can be represented and computed.