A Computational Model of Control Mechanisms in Spatial Term Use

A Computational Model of Control Mechanisms in Spatial Term Use Holger Schultheis (schulth@sfbtr8.uni-bremen.de) SFB/TR 8 Spatial Cognition, Universit¨at Bremen, Enrique-Schmidt-Str. 5, 28359 Bremen, Germany Abstract The apprehension of spatial terms like “above” or “left” is cru- cial for communicating about spatial configurations. One im- portant part of apprehension has been shown to be the selection of a reference frame (RF). Yet, how this selection is controlled has remained unclear so far. This paper presents a computa- tional analysis and model of the control mechanisms involved in RF selection. Developing the model not only gives a de- tailed account of the mechanisms involved in RF selection, but also provides new insights regarding the overall sequence of steps involved in spatial term apprehension. Keywords: spatial terms; control; reference frames; computa- tional model; connectionism Spatial Term Use Everyday communication often involves exchanging infor- mation about spatial configurations. For instance, to iden- tify the location of some object, say, a fly one might state “The fly is above the table”. Spatial terms like “above” figure prominently in such descriptions and successful communica- tion crucially depends on the communication partners’ abili- ties to apprehend such spatial terms. To better understand the processes and representations in- volved in the apprehension of spatial terms a number of em- pirical studies (e.g., Burigo & Coventry, 2005; Carlson & Logan, 2001; Regier & Carlson, 2001) have investigated the specifics of human spatial term processing. The empir- ical results obtained have lead to the development of several conceptual (e.g., Logan & Sadler, 1996) and computational (Coventry et al., 2005; Regier & Carlson, 2001) models of spatial term processing. In particular the model of Logan and Sadler (1996) which has been extended and refined in subse- quent works (Carlson & Logan, 2001; Carlson-Radvansky & Logan, 1997) has been proven to be a valuable framework for analyzing and accounting for empirical data. The model assumes that the representations involved in apprehension comprise reference frames (RF) and spatial templates. RF are assumed to be sets of three orthogo- nal axes having a distinct origin, orientation, direction, and scale. Spatial templates are thought of as array-like represen- tation structures associated with spatial terms which assign goodness-of-fit values to points in space. Based on these rep- resentations the processes engaged in, for example, under- standing the utterance “The fly is above the table”, include the following steps: (a) spatially indexing all objects in the scene, (b) identifying the table, (c) imposing multiple RF on the table, (d) aligning the spatial template associated with the term above to the RF, (e) selecting one of the RF (due to steps (d) and (e) the spatial template now assigns certain values to regions of space indicating how well the respective points correspond to the spatial term “above” with respect to the ta- ble), and (f) identifying the objects which are assigned a high value by the spatial template. This model constitutes a successful framework for ana- lyzing and accounting for empirical data. However, it is mainly conceptual and, thus, rather coarse-grained regarding the mechanisms underlying human spatial term use. Since the model as a whole is so successful, it seems desirable to un- ravel the details of mechanisms underlying the different steps. One way to achieve this is to develop computational models from careful analyzes of the available data. The aim of this contribution is to refine the overall frame- work by devising a computational model of the mechanisms underlying step (e) of the above sequence, that is, the selec- tion of RF. Like existing empirical research, in developing the model, we will concentrate on the spatial term “above” as used for describing configurations in the plane (see, e.g., Figure 1). Importantly, model development not only refines the framework regarding this particular step but also provides new insights regarding the nature of the overall sequence of steps and specifics of step (c) of the above sequence. In the following we will first present the computational model / analysis comprising a more detailed description of the RF selection phenomenon, the specifics of the implemented model and its main predictions. Second, the developed model will be evaluated by comparing its behavior with human be- havior. Finally, we identify issues for future work and present some speculations as to the applicability / suitability of the devised control mechanisms for other spatial cognition tasks. Computational Analysis and Model Reference Frames and the Need for Selection Based on Levinson (1996), (psycho)linguistic theories often distinguish between three types of RF: absolute, relative, and intrinsic. All of them partition the space into regions which are thought of as above, below, left, right, etc. The essential difference between these three types is the (source of) infor- mation that is used to determine where in the perceived space these regions lie. In the case of the absolute RF, environmen- tal information like the experienced gravitational force or the sides of an enclosing room is used, that is, “above” is the op- posite direction to the gravitational force. The relative RF, on the contrary, partitions space on the basis of the viewer: The line from head to feet defines the above-below axis. Intrin- sic RF are defined only for objects with distinguishable sides, since these define the axis of the RF. A table for example has a top (where things are usually put on) and a bottom (where it usually touches the ground). Similar to the relative RF the above-below axis of the intrinsic RF can then be established as the line from top to bottom.