![[Above canonical spatial template]](fig2a.gif)
In order to help people find objects in the world, we often describe the location of one object with respect to a second object, such as "Your keys are behind the bowl." Work in psychology, linguistics, and artificial intelligence has focused on how such spatial relations are computed and described (e.g., Carlson-Radvansky & Irwin, 1994; Hayward & Tarr, 1994; Herskovits, 1986; Levelt, 1984; Logan & Sadler, in press; Miller & Johnson-Laird, 1976; Talmy, 1983).
According to many of these theories, of central importance in the use of spatial relations is the assignment of roles to the objects whose locations are being specified. The located object is the object whose location is being described, and as such is the goal of the utterance. The reference object is the object whose location in space serves as a starting point from which to begin search for the located object. In the example above, the located object is the keys and the reference object is the dryer.
Also of central importance is the selection of a reference frame, the representation within which spatial relations are defined. A reference frame consists of three orthogonal coordinate axes that serve to parse up space. One axis specifies the vertical above/below direction, and the other two specify the horizontal front/back and left/right directions.
The following basic steps are necessary in order to find a located object, given a reference frame and a spatial relation.
1. The reference object is identified.
2. A reference frame is superimposed on the reference object.
3. Search proceeds in the direction assigned to the spatial relation by the relevant axis of the reference frame
4. Verification that the located object is present occurs.
At least two important components are missing from this outline. First, there is no specification of how a reference frame is selected. A reference frame's axes are not fixed in space, but may be rotated in accordance with various sources of information. On account of this flexibility, three different classes of reference frames have been identified. According to an environment-centered reference frame, the axes are oriented with respect to salient aspects of the environment, such as gravity. According to the object-centererd reference frame, the axes are oriented with respect to the intrinsic sides of the reference object. According to the viewer-centered reference frame the axes are oriented with respect to the head/feet, front/back and left/right sides of the viewer. These reference frames are normally aligned, since objects and viewers are naturally upright. However, when viewers are reclined or objects are overturned, the reference frames are dissociated, and thus assign conflicting directions to spatial terms.
Given that there are different types of reference frames, how is one selected to assign a direction to a spatial term? Carlson-Radvansky & Irwin (1994) found that multiple reference frames were initially active and competed when their axes were dissociated and assigned different directions to the same spatial term. However, Carlson-Radvansky (1996) showed that when reference frames all agree and assign the same direction to a spatial relation such as above, there is no competition, and multiple reference frames do not seem to be active. These results suggest that the context in which a reference frame is selected (among other reference frames that are aligned or dissociated) is an important factor.
The second component that is unspecified is how search for the located object actually proceeds. That is, since space is all encompassing, only a restricted region can conceivably be searched. But what defines the to-be-searched area? Recent work by Logan and Sadler (in press), Franklin, Henkel, & Zengas, 1995; Hayward & Tarr, 1994 has begun to examine how spatial relations can be used to parse up space. For example, Logan and Sadler presented participants with a central reference object (an "O") that was located in the middle of an invisible 7 X 7 grid (in cell 4,4). Across trials, they placed the located object (an "X") in each of the remaining cells in the grid, and asked participants to rate the acceptability of many different spatial terms as describing the relation between the located object and reference object. I am going to focus on their data for "above".
The data can be plotted in three dimensions, as a function of the row, column, and magnitude of the rating. This 3-d plot will be referred to as a spatial template. Three regions can be identified. Good regions received the highest acceptability ratings and corresponded to the best uses of a spatial term. This region fell along the vertical axis of the reference frames centered on the reference object. Acceptable regions received intermediate acceptability ratings, and covered a larger area than the good regions. There was a graded distinction between the good region and the acceptable regions and the acceptable regions were roughly symmetrical. Finally, the bad regions corresponded to very low acceptability ratings, and were sharply distinct from the acceptable and good regions.
In the present research, done in collaboration with Gordon Logan, I examined the relationship between reference frame selection and spatial template construction. More specifically, we wanted to know whether these processes were independent. To test this, we asked whether spatial template construction was influenced by
1. The type of reference frame that is selected
2. The context in which a reference frame is selected
The first question is whether a spatial template is independent of the type of reference frame that is used to align it. According to this idea, each spatial relation has its own spatial template that is applied in a similar fashion to all reference frames, regardless of type. When the template for `above' is needed, it is applied to the selected reference frame, regardless of whether that reference frame is environment-centered, viewer-centered or object-centered. So, the spatial template will always look the same, in terms of its shape and the relative sizes of its three regions.
The second question examines whether the context in which a reference frame is selected (such as amid reference frames that are aligned or dissociated) affects the construction of the spatial template. If these processes are independent, with spatial template construction taking place after a reference frame has been selected, then the same spatial template should always be constructed, regardless of whether the other reference frames are aligned with or dissociated from the selected reference frame.
Note, however, as I discussed earlier, there is a difference in the reference frame selection process when the reference frames are aligned versus when they are dissociated. When the reference frames are aligned, only a single reference frame is active; however, when reference frames are dissociated, multiple reference frames are initially active and compete.
How would this difference interact with spatial template construction? Assume that each active reference frame has its own spatial template associated with it. Thus, when multiple reference frames are active, multiple spatial templates are constructed. This would mean that the parsing of space into good, acceptable and bad regions will necessarily reflect some mixture of the two spatial templates, with ratings predicted by some combination of corresponding cells in the constructed templates. Figure 1a shows a schematic template based on the viewer/environment reference frame. G, A, and B stand for Good, Acceptable and Bad regions, respectively. The face in cell 4, 4 represents the reference object rotated 90 degrees counter-clockwise so that the top-side points to the viewer/environmental left. Figure 1b shows a schematic template based on the object-centered reference frame. Figure 1c shows a template resulting from a mixture of the templates in 1a and 1b, with each weighted equally at .5.
Figure 1a. Schematic template based on viewer/environment reference frame.
A A A G A A A A A A G A A A A A A G A A A B B B (:->) B B B B B B B B B B B B B B B B B B B B B B B B
Figure 1b. Schematic template based on object-centered reference frame.
A A A B B B B A A A B B B B A A A B B B B G G G (:->) B B B A A A B B B B A A A B B B B A A A B B B B
Figure 1c. Equally weighted mixture of templates from 1a and 1b
.5AVE .5AVE .5AVE .5GVE .5AVE .5AVE .5AVE + + + + + + + .5AO .5AO .5AO .5BO .5BO .5BO .5BO ---------------------------------------------------------------------------------------------------------------------- .5AVE .5AVE .5AVE .5GVE .5AVE .5AVE .5AVE + + + + + + + .5AO .5AO .5AO .5BO .5BO .5BO .5BO ---------------------------------------------------------------------------------------------------------------------- .5AVE .5AVE .5AVE .5GVE .5AVE .5AVE .5AVE + + + + + + + .5AO .5AO .5AO .5BO .5BO .5BO .5BO ---------------------------------------------------------------------------------------------------------------------- .5BVE .5BVE .5BVE .5BVE .5BVE .5BVE + + + (:->) + + + .5GO .5GO .5GO .5BO .5BO .5BO ---------------------------------------------------------------------------------------------------------------------- .5BVE .5BVE .5BVE .5BVE .5BVE .5BVE .5BVE + + + + + + + .5AO .5AO .5AO .5BO .5BO .5BO .5BO ---------------------------------------------------------------------------------------------------------------------- .5BVE .5BVE .5BVE .5BVE .5BVE .5BVE .5BVE + + + + + + + .5AO .5AO .5AO .5BO .5BO .5BO .5BO ---------------------------------------------------------------------------------------------------------------------- .5BVE .5BVE .5BVE .5BVE .5BVE .5BVE .5BVE + + + + + + + .5AO .5AO .5AO .5BO .5BO .5BO .5BO ----------------------------------------------------------------------------------------------------------------------
In Figure 1c are the three types of acceptable regions: One is defined as acceptable according to both templates (the VEO acceptable region). One is defined as acceptable within the viewer/environment template and as bad within the object template (the VE acceptable region). Finally, one is defined as acceptable within the object template and as bad within the viewer/environment template (the O acceptable region). If a spatial template is constructed for each active reference frame, then the acceptable region that is defined by multiple reference frames (e.g., the VEO region) should be somewhat privileged (in terms of higher acceptability ratings or easier and more accurate access) relative to the acceptable regions defined by a single templates (the VE region or the O region).
To test these ideas, we modified the procedure used by Logan and Sadler to include trials in which the reference frames were dissociated. Therefore, on some trials the central reference object was upright (canonical trials) and on other trials the central reference object was rotated (noncanonical trials). The reference object was a tree and the located object was a box. sake of time, I am just going to focus on the data for the spatial relation above. For each trial, a sentence of the form "The box is above the tree." was presented for 2 seconds followed by the presentation of the picture. Participants rated the acceptability of the sentence as a description of the picture on a scale from 0 = not at all acceptable to 9 = perfectly acceptable.
The data are plotted in the in the form of a spatial template, with rows, columns as two dimensions, and mean acceptability rating across participants for each position as the third dimension. The central reference object was in the empty cell (row 4, column 4). Figure 2a presents the template for canonical trials, and Figure 2b presents the template for noncanonical trials in which the reference object has been rotated 90 degrees counter-clockwise, so that the top side of the tree is to the environmental left.
For the canonical trials when the reference object was upright, the spatial template nicely replicates pattern found by Logan and Sadler (in press): there is a good region along the vertical axes of the reference frames, two acceptable regions sloping downward and symmetrical about the good region, and bad regions corresponding to nonacceptable uses of "above."
Now consider the noncanonical trials, which can be examined in order to assess the independence of reference frame selection and spatial template construction by looking for evidence that the spatial template was not influenced by either the type of reference frame selected or the context within which a reference frame was selected.
Consider the context issue first. If context did not matter, then the noncanonical spatial template should look similar to the canonical template. However, it is readily apparent that the shape is very different: There is no "good" region. The acceptable regions are bigger and are asymmetrical, whereas the bad regions are much smaller. So, clearly the context in which the spatial template is constructed greatly influences its shape: when reference frames were dissociated, a very different spatial template emerged for above than when reference frames were aligned.
The three acceptable regions (VEO, VE, and O) were examined more closely. Recall that these regions were classified based on whether the region is acceptable according to both the viewer/environment-centered and object-centered reference frames, or only the viewer/environment-centered reference frame or only the object-centered reference frame. Comparing mean ratings across the 9 cells in each quadrant, the VEO region was rated significantly higher (M = 6.4) than the VE (M= 3.1) or O region (M = 3.8). This pattern can be predicted by the mixture of the spatial templates associated with multiple active reference frames that we discussed earlier. That is, the VEO region could be considered more acceptable than the VE or the O region was that it was rated as acceptable within both the VE and the O spatial templates, whereas the VE region was rated as acceptable within the VE template but bad within the O template, and vice versa for the O region.
![[Above noncanonical spatial template]](fig2b.gif)
Underlying this logic is the other question that we were examining, namely that the type of reference frame would not influence the shape of the spatial template. In other words, for noncanonical trials, the templates for the object-centered and environment-centered reference frames should be the same, albeit rotated 90 degrees. If this is true, then the canonical templates can be used to represent use of the viewer/environment-centered reference frame, and then this same template can be rotated 90 degrees to represent use of the object-centered reference frame. If the noncanonical trials represent some mixture of the viewer/environment-centered template and the object-centered template, and if the only difference between these templates is the rotation of 90 degrees, then the spatial template for the noncanonical trials should be well predicted from a mixture of these two templates. If, however, the shapes of the templates vary greatly depending on the type of reference frame selected, then the noncanonical trials should not be well predicted by a combination of the canonical environment template and the rotated object template.
To test this we performed a regression analysis, trying to predict the observed noncanonical ratings from a mixture of the canonical viewer/environment plot and the rotated object plot. The best fitting line assigned beta weights of .38 for the viewer/environment template, and .58 for the object template, with a goodness of fit of .96. This result suggests that the noncanonical spatial templates are a mixture of a spatial template based on the object-centered reference frame and a spatial template based on the viewer/environment-centered reference frame. In addition, these spatial templates are similar in shape, the size of the relative areas, etc.
What do these analyses suggest about the initial two questions? The first question was whether the type of reference frame selected would affect the construction of a spatial template. The success of the regression analyses where the same spatial templates albeit rotated 90 degrees were able to predict very well the resulting noncanonical spatial templates suggests that this is true. The spatial template defined by the object-centered reference frame was similar in shape and the sizes of the regions to the template defined by the environment-centered reference frame.
The second question was whether the context of reference frame selection would influence the construction of spatial templates. The spatial templates emerging for canonical trials when all reference frames agreed were very different than the spatial templates emerging for noncanonical trials when the reference frames disagreed, thus indicating an influence of the context of reference frame selection on spatial template construction. Additional analyses were also done on groups of participants, based on their patterns of responding. These indicated that this influence of reference frame selection on spatial template construction was graded, and depended on how strongly participants activated multiple reference frames.
Carlson-Radvansky, L. A. (1996). The absence of cooperation among spatial reference frames Manuscript submitted for publication.
Carlson-Radvansky, L. A. & Irwin, D. E. (1994). Reference frame activation during spatial term assignment. Journal of Memory and Language, 33, 646-671.
Franklin, N., Henkel, L. A., & Zengas, T. (1995). Parsing surrounding space into regions. Memory & Cognition, 23, 397-407.
Hayward, W. G. & Tarr, M. J. (1995). Spatial language and spatial representation. Cognition, 31, 45-60.
Herskovits, A. (1986). Language and spatial cognition Cambridge: Cambridge University Press.
Levelt, W. J. M. (1984). Some perceptual limitations on talking about space. In A. J. van Doorn, W. A. van der Grind, & J. J. Koenderink (Eds.), Limits in perception (pp. 323-358). Utrecht: VNU Science Press.
Logan, G. D., & Sadler, D. D. (in press). A computational analysis of the apprehension of spatial relations. In P. Bloom, M. A. Peterson, L. Nadel, & M. Garrett (Eds). Language and space Cambridge, MA: MIT Press.
Miller, G. A. & Johnson-Laird, P. N. (1976). Language and perception (pp. 374-410). Cambridge, MA: Harvard University Press.
Talmy, L. (1983). How language structures space. In H. L. Pick & L. P. Acredolo (Eds.) Spatial orientation: Theory, research and application (pp. 225-282). New York: Plenum Press.