Compositionality and Systematicity

A feasible model of natural language semantics should also account for the systematicity displayed by language understanding. The idea that compositionality alone is sufficient to guarantee systematic reasoning within a semantic system is rejected. An analysis of systematic inferences involving adjective–noun combinations with intersective adjectives illustrates that more than a compositional semantics is required for their understanding, and that even simple concepts involve hidden structures. It is argued that the same processes used in determining context-dependent meaning are at work in understanding complex concepts where world-knowledge plays a key role. In the latter cases however accumulated experience with the given concept is argued to serve as a contrast set against which complex concepts are interpreted. 1 What is systematicity? The term ‘systematicity’ was first introduced in Fodor and Pylyshyn (1988) as a cognitive capacity on par with productivity which a compositional linguistic system is guaranteed to support. Fodor and Pylyshyn refer to systematicity as ‘a feature of cognition, inferential coherence’. In the following quote they describe what they mean (Fodor and Pylyshyn, 1988, p. 37): The ability to produce/understand some sentences is intrinsically connected to the ability to produce/understand certain others. However, Fodor and Pylyshyn give no formal definition (see van Gelder, 1990, for an attempt to work out the concept formally), instead choosing to illustrate the concept with examples. Here are examples of what types of systematic inferences we can make with language. When an agent understands the sentence ‘John loves the girl’, she understands the sentence ‘The girl loves John’ as well (Fodor and Pylyshyn, 1988, pp. 42, 48–49). (1) When an agent understands the expressions ‘brown triangle’ and ‘black square’, she understands the expressions ‘brown square’ and ‘black triangle’ as well. (Based on examples given in Fodor and Pylyshyn, 1988.) (2) Cognitive Foundations of Interpretation. Royal Netherlands Academy of Arts and Sciences, 2007 163 Initially, these two ‘systematicity clauses’ seem intuitively to be true. Surely understanding ‘brown triangle’ and ‘black square’ means that you will be able to infer what ‘brown square’ means. Systematicity is argued to follow from compositionality because understanding a complex concept like ‘brown triangle’ is achieved through an understanding of ‘brown’ and ‘triangle’, and therefore an agent must be able to use these lexical items in novel combinations. It is true that we understand all the above expressions, but how do we do it and what type of linguistic model will support these inferences? The ability to predict and confirm systematic inferences like these would seem to be a prerequisite for any language model that claims to model natural language understanding. Does understanding the results of the modification of one concept really insure the understanding of the same modification when applied to another concept? We will argue that the answer is not as simple as it first looks, not only for complex cases, but even for so-called simple compounds. Additionally, we will argue that the compositionality of a semantic theory is not sufficient to insure that the semantics predicts systematicity in language understanding. In Section 2 we examine several systematicity inferences that range from those requiring some reasoning to those that lead to compounds that seem only interpretable as idiomatic expressions, or even seem uninterpretable. Section 3 looks at simple adjective–noun compounds involving intersective adjectives. The classic compositional approach is argued to be insufficient for correctly producing even the simplest systematicity clauses. Complex expressions with intersective adjectives are examined in more detail in Section 4. It is first shown that even the simplest concepts have hidden structures that are relevant to their interpretation. Second, it is shown that context affects both how adjective–noun phrases are produced and how they are interpreted. We then argue that the mechanisms at work in cases where context-sets play a role in the meaning of adjective–noun compounds, are the same mechanisms that were at work in determining in what way modification applies to a given object relative to other instances of that object in the world. Finally, Section 5 summarizes what implications this work has for other work in lexical semantics and natural language understanding. 2 Concepts do not relate systematically Lexical items evoke or refer to concepts, but these concepts don’t necessarily relate in predictable ways. Consider the following examples of systematicity clauses where determining the actual meaning of each complex expression is not straightforwardly computable. An agent who understands ‘good writer’ and ‘bad teacher’ also understands ‘bad writer’ and ‘good teacher’. (3) An agent who understands ‘within an hour’ and ‘without a watch’ also understands ‘without an hour’ and ‘within a watch’. (4) An agent who understands ‘Mom drives me to kindergarten’ also understands ‘I drive mom to kindergarten’. (5) 164 Compositionality and systematicity Consider example (3). Do all who understand ‘good writer’ and ‘bad teacher’ also understand ‘bad writer’ and ‘good teacher’? The answer seems to be yes. However, determining the meaning of the new complex is a more involved process. For most of us, a writer is good or bad based on characteristics that are different from those under which a teacher is considered good or bad. Both characteristics can be identified from understanding the first two compound expressions. In order to understand the second two we seem to switch from the one end of the scale to the other. Example (4) seems unlikely. Do all who understand ‘within an hour’ and ‘without a watch’ also understand ‘within a watch’ and ‘without an hour’? (Szabó, 2000.) An interpretation requires some creativity, given that ‘within a watch’ does not seem to have any type of conventional meaning, and even if it did, it would not be part of combination of the meaning of the words ‘within’ and ‘watch’. On hearing it, listeners are more likely to assume that it has some sort of idiosyncratic, noncompositional meaning that they are unaware of. Finally, example (5) illustrates a case where the problem is conceptual. Would a child who understands ‘Mom drives me to kindergarten’ also be understand ‘I drive mom to kindergarten’? Here we are dealing with another type of example where there is a problem of conceptualization and likelihood. A child of kindergarten age may not even initially be able to conceive that he or she could drive the car. All three of these examples illustrate that systematic inferences seem to be heavily dependent on world knowledge, and not just linguistic knowledge. This raises the question what is actually involved in systematicity. If the systematicity that we sometimes find is a feature of language, entailed by virtue of language being a compositional system, then it should be in some ways independent of world knowledge. If however, systematic inferences are in part possible because of the way the world is, and are not really a reflection of linguistic structures, then whether or not your semantic system is compositional would seem to be beside the point. Consider what Clark (1993, p. 148) says: Instead of treating [systematicity] as a property to be directly induced by a canny choice of basic architecture, it may be fruitful to try to treat it as intrinsic to the knowledge we want a