Beyond Symbolic: Prolegomena to a Kama-Sutra of Compositionality1

Consider some of the obvious differences between a printed and a spoken version of the very same English sentence. Both contain the same words, but in the printed sentence they are static ink configurations, while in the utterance they are temporally extended sound patterns. In the printed case, words are combined by juxtaposition in space; in the utterance, by juxtaposition in time. The printed words are combined in a very discrete way there is, quite literally, space between each and all occurrences of a given word are effectively identical, whatever words happen to surround them. In the utterance, by contrast, juxtaposition is not discrete and context free; words flow into each other, and their physical shape is typically affected by their neighbors. Printed and uttered tokens of the very same sentence, then, are physically constructed or built up in quite different ways. These days, the most common technical term for building up a complex representation out of parts is composition, and so we can say that the two sentences exhibit very different kinds of compositionality, despite being syntactically and semantically identical4. This point has two very important consequences. First, compositionality itself comes in at least two, and possibly many, different kinds. Second, the very notion of compositionality can be a subject of study, quite independent of syntax and semantics. Whereas syntax and semantics focus on a language in the abstract, the study of compositionality focuses on the concrete implementations. How many kinds of compositionality are there? What are the fundamental issues? And, if our ultimate interests happen to be in cognitive science: what kinds of compositionality are typically found in mainstream artificial intelligence, in connectionism, and in natural cognitive systems such as