Constructing Spatial Concepts from Universal Primitives

Constructing Spatial Concepts from Universal Primitives Yang Xu ∗ and Charles Kemp † Machine Learning Department ∗ School of Computer Science ∗ Department of Psychology † Carnegie Mellon University {yx1@cs.cmu.edu, ckemp@cmu.edu} simple baseline approach assumes that every concept in ev- ery language corresponds to one of the semantic primitives, and we compare this approach to alternatives which assume that concepts correspond to combinations of primitives. In Figure 1b, for example, “on” is defined as the conjunction of support and contact. A second dimension specifies whether primitives are differentially weighted. In Figure 1b, all com- binations are assumed to be conjunctions, and we compare this approach with an alternative that relies on weighted com- binations. The final dimension specifies whether or not nega- tions of primitives are allowed—for example, whether “no contact” is included in addition to “contact. ” Our three di- mensions produce a collection of eight possible models, and we explore the five most interesting cases (Table 1). Com- paring the performance of these models suggests that combi- nations of primitives are important, but we find only limited evidence for weighted combinations. None of the models we consider is rich enough to capture the true complexity of spa- tial cognition, but these simple models are a useful starting point for the computational approach that we advocate. Our work is inspired in part by several recent studies of cross-cultural spatial cognition (Feist, 2000; Bowerman & Choi, 2001; Levinson & Meira, 2003; Feist, 2008; Khetarpal, Majid, & Regier, 2009). A consistent theme in the previ- ous literature is that spatial concepts correspond to regions in some kind of similarity space. To mention just two examples, Bowerman and Choi (2001) suggest that scenes described us- ing “on” and “in” by English speakers can be arranged along a similarity gradient, and that different languages carve up this similarity space in different ways. Levinson and Meira (2003) propose that spatial terms correspond to attractors in a similarity space, and use multidimensional scaling to support their proposal. Approaches like these have helped to illumi- nate the basis of spatial cognition, but they rely on a notion of similarity that is rarely made precise, and are unable to ex- plain exactly how humans recognize similarities between spa- tial configurations. Our work is compatible with many of the insights that have emerged from these previous approaches, and could be viewed as an attempt to ground the notion of similarity in terms of concrete spatial primitives. We prefer, however, to treat similarity as an epiphenomenon, and expect that similarity will play no explanatory role once the building blocks of spatial concepts are understood. We begin by introducing the semantic primitives that we will consider and the cross-linguistic data that we will at- tempt to explain. We then evaluate five simple models which Abstract Spatial terms such as on and in are found in every language, and psychologists have suggested that the meanings of these terms may be constructed from a universal set of spatial primi- tives. We develop a computational version of this idea and ex- plore whether the primitives typically proposed are sufficient to account for the meanings of spatial terms across languages. We compare a model where spatial terms correspond directly to primitives with models that represent spatial terms as dis- crete or weighted combinations of primitives. Our results sug- gest that combinations play an critical role, and we find limited evidence for weighted combinations. Keywords: spatial cognition; cross-cultural; semantics; com- putational model. Every documented language includes some machinery for describing spatial relationships. For example, an English speaker might say that the cup in Figure 1b is on the table and that the spoon is under the cloth. Spatial terms like these are acquired relatively early by children (Antell & Caron, 1985) and are used so frequently that they may come to seem unremarkable. Researchers have found, however, that it is surprisingly difficult to specify the meanings of spatial terms (Brown, 1994), and that different cultures make use of very different spatial concepts (Levinson & Meira, 2003; Levinson & David, 2006). This paper presents computa- tional models that explore how spatial concepts might be con- structed from more basic components, and that help to estab- lish whether spatial concepts across cultures are constructed from a universal set of spatial primitives. Many previous researchers have discussed the idea that spatial concepts might be constructed as combinations of primitive notions such as “support”, “contact” and “contain- ment”. (Piaget & Inhelder, 1956; Jackendoff, 1983; Feist, 2000) For example, Figure 1b suggests that on in English may be roughly defined as the conjunction of “support” and “contact”. Although this basic proposal is very familiar, there have been few sustained attempts to evaluate how well it can account for cross-linguistic data. Here we focus on primitives gathered from the existing literature and ask whether the dis- tinctions that they capture are sufficient to account for spatial concepts across 25 different languages. Future work in this area can compare different sets of candidate primitives and compare how well they account for the data. Any attempt to study semantic primitives must include some proposal about how these primitives combine to cre- ate spatial concepts. Here we compare proposals that vary along three dimensions. One of these dimensions specifies whether combinations of primitives are or are not allowed. A