What's in a Mental Model? On Conceptual Models in Reasoning with Spatial Descriptions

A frequently used concept in Cognitive Science research is the notion of a mesial model Several very different areas of research use the concept as an explanatory construct. In this paper we explore one meaning of the concept developed for explaining cognitive reasoning with spatial concepts. Several experiments have been interpreted as showing that an abstract propositional representation is not sufficient for understanding reasoning in this domain. Another form of representation is the mental model which has been proposed to explain the obtained results. In contrast to this, we discuss some steps towards a computational theory founded on the notions of a conceptua! m o d e l and levels of reasoning which is able to reproduce the experimental results within a single abstract form of representation. Some empirical consequences are outlined and tested. A tentative conclusion is that the experimental results do not reflect fundamental differences in representational form but strategy differences in how to solve the tasks. 1 . I n t r o d u c t i o n An interesting explanatory concept in current Cognitive Science research is the notion of mesial models. The concept has been used in such diverse research areas as rentoning (e.g., |8|), problem tolling (e.g., [2]), and human-computer interaction (e.g., [9]). There must, of course, be several similarities between the different uses. However, no precise definition has been put forward as to what it means for something to be a mental model. That is, there is no definition which is supposed to hold among the different areas of research and it is even hard to find a definition that is not ambiguous within a particular area. So, one can really ask what it is that makes something a mental model or to put it differently, "what's in a mental model"? A common theme within the three research areas is the emphasis on knowledge repretcntation, or perhaps we should say mental repretentation. Of particular interest in this respect is the ongoing debate about the status of images and their relation to mental models. Some researchers claim that images correspond to a basic and concrete form of mental representation that is essential for the brain's way of representing the environment (e.g., [10]). Others hold the view that images can be analyzed into a more fundamental and abstract representation. In this view, images are seen as products of processes operating on an abstract representation (e.g., [14]). Thus, mental models as images could be regarded as either a fundamental format of representation or as a result of a strategy-driven process. The concept of mental models as developed by Johnson-Laird [8] is very interesting in this perspective. In discussing how meaning is mentally represented, Johnson-Laird emphasized the distinction between a statement's eztension (or denotation) in contrast to its istention (or sense) and concluded that current theories of knowledge representation in Cognitive Science (e.g., semantic networks, lexical decomposition etc.) cannot give a satisfactory account of the relation between intension and extension. Instead, what is needed is a concept of a mental moid in order to explain how meaning comes into mind. For example, when a reasoner heart a sentence like, The knife it to the right of the fork, it is encoded in an abstract propositional (or conceptual) representation, e.g., Right(Knife,Fork), but its meaning is not reached unti l the reasoner builds a model of i t , e.g., [Fork Kn i fe ] It is clear that for many domains a mental model corresponds to an image. This is particularly relevant when the domain consists of spatial descriptions as the above example. Thus, a mental model in this conception is basically realized through an introduction of a new representational format. Moreover, it seems as if the notion is based on the assumption that a model, by definition, should be concrete, i.e., the model should have structural similarities to the real world object. In this paper we intend to discuss the concept of a mental model as developed by Johnson-Laird and discussed in |3), [4], and [5]. Naturally, we are also interested in generalizing the theoretical work to mental models in general. The fundamental concept we explore is the notion of a conceptual model showing many resemblances with conceptual ttructuret [15] and structural detcriptiont [7|. The computational theory we try to build is essentially an attempt to realize the " mental model phenomenon" in a conceptual form of representation. The emphasis is on processes operating on an abstract representation and thus creating an " image-like" structure. Let us start by a brief review of some experiments which gives the discussion a concrete content. 2. Experiments w i t h spatial descriptions The task domain we use as a means for the discussion has been studied by, for example, [12] and [8]. Descr ip t ion 1. The spoon it on the left of the knife. The plate it on the right of the knife. The fork it in front of the tpoon. The cup it in front of the knife. Descr ip t ion 2. The tpoon it on the left of the knife. The plate it on the right of the tpoon. The fork it in front of the tpoon. The cup it in front of the knife. F igure 1. Examples of spatial descriptions. Figure 1 shows two spatial descriptions used in the experiments in [12]. The task is to read a description and then (i) to draw a scene, (ii) to recognize a scene, or (iii) to recognize the sentences among a set. In [3] we reviewed five experiments and presented steps towards a computational theory able to reproduce the empirical findings. In the following we concentrate on the notion of spatial determinacy, which is the difference between the descriptions in Figure 1. 2.1 Spat ia l de te rm lnacy and men ta l models The experimental situation for descriptions 1 and 2 is as follows [12). You are instructed to read a set of sentences and afterwards you might be presented with • a diagram and asked to decide whether or not the diagram corresponds to the description jnst read (e.g., Diagram 1) or • four descriptions each containing three sentences and asked to rank order the sets in terms of their resemblance to the original set.