|Alexander A. Petrov *||Boicho N. Kokinov *#|
Department of Cognitive Science
New Bulgarian University
Institute of Mathematics and Informatics
Bulgarian Academy of Science
|A camera-ready version of this document is available in pdf format (56K).|
This paper contrasts two views about the relationship between the processes of access and mapping in analogy-making. According to the modular view, analog access and mapping are two separate 'phases' that run sequentially and relatively independently. The interactionist view assumes that they are interdependent subprocesses that run in parallel. The paper argues in favor of the second view and presents a simulation experiment demonstrating its advantages. The experiment is performed with the computational model AMBR and illustrates one particular way in which the subprocess of mapping can influence the subprocess of access.
A crucial point in analogy-making is the retrieval of a base (or source) analog. Accessing an appropriate base from the vast pool of episodes stored in the long-term memory is not only a logical necessity (one cannot make analogies without a source) but apparently is the most difficult and capricious element of analogy-making. Starting with the classical experiments of Gick and Holyoak (1980) it has been repeatedly demonstrated that people have difficulties in spontaneously accessing a base analog, especially when its domain is very different from that of the target problem. In the aforementioned study only about 20% of the subjects were able to solve the so-called radiation problem even though an analogous problem (with solution) was presented shortly before the test phase. When provided with an explicit hint to use this source analog, however, 75% of the subjects achieved the solution. This great difference between the two experimental conditions was attributed to the difficulty of analog access.
On the other hand, we know a lot of stories about great scientists making discoveries by spontaneously using remote analogies. We have also personal experience in everyday usage of remote analogies. A recent study by Wharton, Holyoak, and Lange (1996) has demonstrated that about 35% of their subjects were successfully reminded about a remote analog story studied 7 days earlier when cued by the target story. (They have used a directed reminding task, not a problem solving task, however.)
Researchers of analogical access have become interested in the features of a remote analog that facilitate retrieval. Most data in the field (Holyoak and Koh, 1987, Ross 1989) suggest that analogical access is almost exclusively guided by superficial semantic similarities between base and target--similar objects and relations, similar themes, similar story lines, etc. In contrast, analogical mapping is dominated by the structural similarity between target and base, i.e. having common systems of relations (Gentner, 1983, 1989). This explains why remote analogs are much more difficult to access than to map--they lack the superficial similarities needed for access but do have the (quasi)isomorphic relational structure necessary for mapping.
This clear separation stimulated the researchers in the field to build separate models of mapping and retrieval and even to claim that they are different cognitive modules. Thus Gentner (1989) claims that 'the analogy processor (the mapping machine) is a well-defined separate cognitive module whose results interact with other processes, analogous to the way some natural language models have postulated semi-autonomous interacting subsystems for syntax, semantics, and pragmatics.' Although she explicitly mentions in a footnote that this should not be considered in the Fodorian sense as innate and impenetrable, the actual models built are quite impenetrable. This line of research has generated a number of quite successful models that explained the data and made some new predictions. Typically, a model of mapping is coupled with a (separate) model of retrieval. The best-known examples are SME + MAC/FAC (Falkenhainer, Forbus, & Gentner, 1986; Forbus, Gentner, & Law, 1995) and ACME + ARCS (Holyoak & Thagard, 1989; Thagard, Holyoak, Nelson, & Gochfeld, 1990).
However, the experimental work soon revealed that the pattern is not that clear and straightforward. It has been demonstrated that superficial similarities do play an important role in mapping as well. In particular cross-mapping is difficult (Ross, 1989). This led Holyoak and Thagard to include syntactic, semantic, and pragmatic constraints in their model of mapping ACME (Holyoak & Thagard, 1989) and to develop their multi-constraint theory (Holyoak & Thagard, 1995).
There are also some indications that structural similarity might play a role in access as well. Thus Ross (1989) demonstrated that in some cases (when the general story line is similar) structural similarity plays a positive role in retrieval, while in other cases (when the general story line is dissimilar) it does not play any role or can even worsen the results. The results of Wharton, Holyoak, & Lange (1996) also support indirectly the hypothesis that structural correspondences might affect the access. This was reflected in the models being proposed. Both MAC/FAC and ARCS included a submodule of partial mapping in the module of retrieval, thus considering structural similarities at an early stage.
To sum up, the initial separation between retrieval and mapping was founded on their different psychological characteristics--semantic factors govern the retrieval, structural factors govern the mapping. Subsequent more precise experiments, however, cast doubt on this clear separation. These complications were accommodated by making patches to the original models. Finally, it was acknowledged that all kinds of constraints affected all phases of analogy-making, although to different extent (Holyoak & Thagard, 1995).
The experimental data themselves became more and more complex and controversial. These controversies can be explained in terms of more and more sophisticated classifications of the types of similarities involved in access and mapping (Ross, 1989; Ross & Kilbane, 1997). We argue, however, that these problems are resolved more parsimoniously by adopting a principally different view of analogy-making.
This resembles an episode of the history of astronomy. The geocentric system of Ptolemy started as a straightforward theory that described the observable movement of both stars and planets remarkably well. As accuracy of measurement increased, however, discrepancies between theory and data crept in every now and then. It became routine for astronomers to deal with such 'anomalies' by adding more and more epicycles. But as time went on, it became evident that astronomy's complexity was increasing far more rapidly than its accuracy and that a discrepancy corrected in one place was likely to show up in another (Kuhn, 1970).
Back to the domain of analogy-making, most classical models assume sequential processing: first the retrieval process finds the base for analogy and then the mapping process builds the correspondences between the target and the retrieved base (Figure 1). Thus MAC/FAC+SME and ARCS+ACME are linear models separating retrieval and mapping in time and space. This view underlies most of the experimental work in the field as well. Researchers often contrast hint versus non-hint conditions in problem solving supposing that in the first case only mapping takes place, while in the second retrieval and mapping are running one after the other. However, as Ross (1989) has noted, even when explicitly hinted to use a certain analog subjects still must access the details of its representation. Another common experimental technique uses a memory task (typically recall) for studying access with the assumption that the same processes take place during analogical problem solving.
Figure 1. Dominating sequential models of analogy-making.
The limitations of both the models and experimental methods can be overcome by giving up the linearity assumption. This might look strange at first glancehow can you map the source analog onto the base if you have not even accessed it?! If, however, one reconsiders one more assumption--that there are centralized representations of situations/problems in human memory--then it becomes clear that whenever we have partial retrieval of the base (having recalled a few details) we can start looking for corresponding elements in the target. This allows us to conceptualize access and mapping as parallel processes that can interact (Figure 2). In this paradigm, access and mapping refer not to phases or other behavioral steps, but rather to separate mechanisms that both play a role in selecting and activating a base and in finding the correspondences between base and target.
Figure 2. Parallel and interactive models of analogy-making.
The current paper explores the implications of the parallel and interactive view on access and mapping by running simulation experiments with an integrated model of human (analogical) reasoning called AMBR (Kokinov, 1994c; Petrov, 1997). These experiments provide a detailed example of how these two processes can interact and thus open space for new theoretical speculations as well as for new experimental paradigms. AMBR's predictions about the development of the process over time call for appropriate experimental methods capturing the dynamics of human analogy-making--RT studies, think-aloud protocols, etc. Some of the controversies around the role of superficial and structural similarities in access and mapping 'phases' can now be expressed in terms of the interactions between the two mechanisms.
A very important contribution of the simulation is that it demonstrates how the supposedly later 'phase' of mapping can influence the supposedly earlier 'phase' of access. A detailed example shows how the access process develops over time and how it is influenced by the concurrent mapping process. This is contrasted with the case of isolated access. Different results are obtained in the two cases. These results correspond to the data of Ross and Sofka (unpublished) which main conclusions are summarized in (Ross, 1989) as follows:
... other work (Ross & Sofka, 1986) suggests the possibility that the retrieval may be greatly affected by the use. In particular, we found that subjects, whose task was to recall the details of an earlier example that the current test problem reminded them of, used the test problem not only as an initial reminder but throughout the recall. For instance, the test problem was used to probe for similar objects, and relations and to prompt recall of particular numbers from the earlier example. The retrieval of the earlier example appeared to be interleaved with its use because subjects were setting up correspondences between the earlier example and the test problem during the retrieval.The simulation data presented in the current paper (obtained absolutely independently and based only on the theoretical assumptions of DUAL and AMBR) exhibit exactly the same pattern of interaction.
We must admit that even in a highly parallel and interactive model such as AMBR the effects of interactions are not predominating. In the majority of cases the independent work of the access mechanism might well yield the same results as the interaction between mapping and access described above. That is why the classical linear models of analogy have been successful and have contributed a lot to our understanding of human analogy-making. However, exactly the few exceptional cases that do provide different results in a parallel model are the more interesting and those who make the interpretation of the experimental data look controversial if analyzed in the spirit of the sequential models.
There are a few other models that advocate a parallel, overlapping, and interactive view on analogy--Copycat (Mitchell, 1993, Hofstadter, 1995), Tabletop (French, 1995, Hofstadter, 1995), and LISA (Hummel & Holyoak, 1997). However, Copycat and Tabletop do not model retrieval at all--they model the parallel work and interaction between perception/representation building and mapping. LISA also integrates access and mapping and performs them in parallel. Thus the mapping mechanism (connectionist learning in this case) influences the access. As a result, LISA could in principle demonstrate effects similar to those reported here.
The basis for the simulation experiment discussed in this paper is a model called AMBR (Associative Memory-Based Reasoning). It is built on the cognitive architecture DUAL. Space limitations allow only an extremely sketchy description of DUAL and AMBR here. The interested reader is referred to earlier publications (Kokinov, 1988, 1994a, 1994b, 1994c; Petrov, 1997).
DUAL is a multi-agent cognitive architecture that supports dynamic emergent computation (Kokinov,Nikolov, and Petrov, 1996). All knowledge representation and information processing in the architecture is carried out by small entities called DUAL agents. Each DUAL-based system consists of a large number of them. There is no central executive in the architecture that controls its global operation. Instead, each individual agent is relatively simple and has access only to local information, interacting with a few neighboring agents. The overall behavior of the system emerges out of the collective activity of the whole population. This 'society of mind' (Minsky, 1986) provides a substrate for concurrent processing, interaction, and emergent computation.
Each DUAL agent is a hybrid entity that has symbolic and connectionist aspects (Kokinov 1994a,b,c). On the symbolic side, each agent 'stands for' something and is able to perform certain simple manipulations on symbols. On the connectionist side, it sends/receives activation to and from its immediate neighbors. Thus, we may adopt an alternative terminology and speak of nodes and links instead of agents and interactions. The population of agents may be conceptualized as a network of nodes.
The long-term memory of a DUAL-based system consists of the network of all agents in that system. The size of this network can be very large. Only a small fraction of it, however, may be active at any particular moment. The active subset of the long-term memory together with some temporary agents constitutes the working memory (WM) of the architecture. The mechanism of spreading activation plays a key role for controlling the size and the contents of the WM. There is a threshold that sets the minimal level of activation that must be obtained by an agent to enter the WM. There is also a spontaneous decay factor that pushes the activation levels back to zero. As the pattern of activation changes over time, some agents from the working memory fall back to dormancy, others are activated, etc. Only active agents may perform symbolic computation. Moreover, the speed of this computation depends on the level of activation of the respective agent. This makes the computation in DUAL dynamic and context-sensitive (Kokinov et al.,1996; Kokinov, 1994a,b,c). One particular consequence of this dynamic emergent nature of the architecture is that, although all micro-level processing is strictly deterministic, the macroscopic behavior of a DUAL system can be described only probabilistically.
The AMBR model takes advantage of these architectural features to account for some phenomena of human reasoning and in particular reasoning by analogy (Kokinov, 1988, 1994c). Again, due to space limitations we will consider only a small fraction of the model's mechanisms.
Analog access in AMBR is done by means of spreading activation by the connectionist aspects of the DUAL agents. In particular, only few of the many episodes stored in the long-term memory are active during a run and only they are accessible for processing. The episodes or 'situations' have decentralized representations--it is not a single agent but a whole coalition that represents the elements of a situation and the relationships among them. Therefore, it is possible that an episode is only partially accessed because only some of the agents have entered the WM.
The process of analogical mapping is done in AMBR by a combination of three mechanisms-- marker passing, constraint satisfaction, and structure correspondence (Kokinov, 1994c; Petrov, 1997). The main idea is to build a constraint satisfaction network (CSN) to determine the mapping between two situations. This network consists of hypothesis agents representing tentative correspondences between two elements. Consistent hypotheses support, and incompatible ones inhibit each other.
This is similar to other models of analogy-making and notably ACME (Holyoak and Thagard, 1989). AMBR differs from the latter model, however, in several ways: (i) the CSN is constructed dynamically, (ii) only hypotheses that have some justification are created, (iii) the CSN is incorporated into the bigger working memory network, and (iv) there is no separate relaxation phase so there is a partial mapping at each moment.
The implication of these four points is that, unlike ACME and most other analogy models, the processes of access and mapping run in parallel and influence each other in AMBR. In other words, the model departs from the classical 'pipeline' paradigm and aims at a more interactive account of analogy making.
The influence between the two subprocesses in AMBR goes in both directions. The present paper concentrates on the 'backward' direction--from mapping to access. The next section describes a simulation experiment that sheds light on this kind of influence.
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