The productivity and compositionality of language and thought have often been taken as evidence that higher cognitionis a form of information processing on systems of symbols with combinatorial syntax and semantics. We present anon-symbolic neural dynamic architecture that can ground combinatorial concepts in perception, i.e., establish a linkbetween a combinatorial concept and an object in the perceptual array. The components of a combinatorial concept treeare sequentially grounded from the leaves to the root, while the output of each grounding step is passed on to the nextgrounding step by means of a mental map. This way, compositionality is an emergent property of the neural dynamics anddoes not require any form of symbolic information processing. We discuss how this process account contrasts with otherneural accounts of compositionality and conclude with implications for the modeling of higher cognition.