We performed a simulation experiment to contrast the two ways of combining access and mapping--parallel vs. serial. The experiment also tested whether the AMBR model was capable to access a source analog out of a pool of episodes, and to map it onto a target situation.
The experiment consisted of two conditions. Both conditions involved running the model on a target problem. In the 'parallel condition', AMBR operated in its normal manner with the mechanisms for access and mapping working in parallel. In the 'serial condition', the program was artificially forced to work serially--first to access and only then to map. The target problem and the content of the long-term memory were identical in all runs. The topics of interest fell into two categories--the final mapping constructed by the program and the dynamics of the underlying computation. The latter was monitored by recording a set of variables describing the internal state of the system at regular time intervals throughout each run.
The domain used in the experiment deals with simple tasks in a kitchen. The long-term memory of the model contains semantic and episodic knowledge about this domain. It has been coded by hand according to the representation scheme used in DUAL and AMBR (Kokinov, 1994c; Petrov, 1997). The total size of the knowledge base is about 500 agents (300 'semantic' + 200 'episodic'). It states, for example, that water, milk, and tea are all liquids, that bottles are made of glass, and the relation 'on' is a special case of 'in-touch-with'. The LTM also stores the representations of eight situations related to heating and cooling liquids. Two of these eight situations are most important for the experiment and are described below together with the target problem.
The outcome is that the water is hot. This is caused by the hot immersion heater in it.
Figure 3. Schematized representation of situation A. Objects are shown as boxes and relations with arrows. Dashed arrows stand for relations in the 'outcome'. The actual AMBR representation is more complex--it consists of 19 agents and explicates the causal structure (not shown in the figure). See text for details.
The outcome is that the ice cube is cold. The fact that it is on the glass and the glass is in the fridge entails that the ice cube itself is in the fridge. In turn, this causes the ice cube to be cold, as the fridge is cold.
Figure 4. Schematized representation of situation B. Dashed arrows stand for relations in the 'outcome'. The actual AMBR representation is more complex--it consists of 21 agents and explicates the causal structure (not shown in the figure). See text for details.
What is the outcome of this state of affairs?
Figure 5. Schematized representation of the target situation. The actual AMBR representation is more complex and consists of 15 agents. See text for details.
As evident from Figures 3, 4, and 5, both situations A and B may be considered similar to the target problem. There are some differences, however. Situation B involves the same objects and relations as the target but the structure of the two are different. In contrast, situation A involves different objects but its system of relations is completely isomorphic to that of the target. According to Gentner (1989), the pair A-T may be classified as analogy while B-T as mere appearance. Thus it was expected that situation B would be easier to retrieve from the total pool of episodes stored in LTM. On the other hand, A would be more problematic to retrieve but once accessed it would support better mapping.
The Common Lisp implementation of the AMBR model was run two times on the target problem. The two runs carried out the 'parallel' and the 'serial' conditions of the experiment, respectively. The contents of the long-term memory and the parameters of the model were identical in the two conditions.
Recall that situations have decentralized representations in AMBR. The target problem was represented by a coalition of 15 agents standing for the ice-cube, the glass, two instances of the relation 'in' and so on. 12 of these agents were attached to the special nodes that serve as activation sources in the model. The attachment was the same in the two experimental conditions.
In the parallel condition, the model was allowed to run according to its specification. That is, all AMBR mechanisms ran in parallel, interacting with one another. The program iterated until the system reached a resting state. A number of variables were recorded at regular intervals throughout the run. Out of these many variables, the so-called retrieval index is of special interest. It is computed as the average activation level of the agents involved in each situation.
In short, at the end of the run we had the final mapping constructed by the program as well as a log file of the retrieval indices of all eight situations from the LTM.
In the serial condition, the target problem was attached to the activation source in the same way and the same data were collected. However, the operation of the program was forcefully modified to separate the processes of access and mapping. To that end, the run was divided in two steps.
During step one, all mapping mechanisms in AMBR were manually switched off. Thus, spreading activation was the only mechanism that remained operational. It was allowed to work until the pattern of activation reached asymptote. The situation with the highest retrieval index was then identified. If we hypothesize a 'retrieval module', this is the situation that it would access from LTM.
After the source analog was picked up in this way, the experiment proceeded with step two. The mapping mechanism was switched back on again but it was allowed to work only on the source situation retrieved at step one. This situation was mapped to the target. Thus, at the end of the second run we had the final mapping constructed at step two, as well as two logs of the retrieval indices.
In both experimental conditions the model settled in less than 150 time units and produced consistent mappings. By 'consistent' we mean that each element of the target problem was unambiguously mapped to an element from LTM and that all these corresponding elements belonged to one and the same base situation. Stated differently, the mappings were one-to-one and there were no blends between situations.
In the parallel condition, the target problem was mapped to situation A, yielding the correspondences in--in, water--coke, imm.heater--ice.cube, T.of--T.of, high.T--low.T, made.of--made.of, etc. Four elements from the source situation remained unmapped and in particular the agent representing that the water is hot. This proposition is a good candidate for inference by analogy. Mutatis mutandis, it could bring the conclusion that the coke is cold. (In the current version of AMBR the mechanisms for analogical transfer are not implemented yet.)
In the serial condition, situation B won the retrieval stage. This is explained by the high semantic similarity between its elements and those of the target--both deal with ice cubes in glasses, cold temperatures, etc. The asymptotic level of the retrieval index for B was about four times greater than that of any other situation. In particular, situation A ended up with only 5 out of 19 agents passing the working memory threshold.
According to the experimental procedure, situation B was then mapped to the target during the second stage of the run. The correspondences that emerged during the latter stage are shown in Table 1. The semantic similarity constraint has dominated this run. This is not surprising given the high degree of superficial similarity between the two situations. There is, however, a serious flaw in the set of correspondences. The proposition 'T.of (ice.cube, low-T)', which belongs to the initial state of the target, is mapped to the proposition 'T.of (ice.cube, low-T)', which is a consequence in the source. Therefore, the whole analogy between the target problem and the situation B could hardly generate any useful inference.
========================================================= Situation B Target situation --------------------------------------------------------- ice.cube ice.cube fridge coke glass glass in (ice.cube, fridge) in (ice.cube, coke) in (glass, fridge) in (coke, glass) on (ice.cube, glass) on (glass, saucer) T.of (fridge, low-T) <unmapped> T.of (ice.cube, low-T) T.of (ice.cube, low-T) low-T low-T made.of (glass, m.glass) made.of (glass, m.glass) m.glass m.glass initstate1 initstate initstate2 <unmapped> interstate table endstate endstate goalstate <unmapped> follows (initst1, endst) follows (initst, endst) to.reach (initst1, goalst) <unmapped> cause (initst2, in(i.c, fr)) <unmapped> cause (interst, T.of(i.c)) <unmapped> =========================================================
Table 1. Correspondences constructed by the model in the serial condition.
To summarize, when the mechanisms for access and mapping worked together, the model constructed an analogy that can potentially solve the problem. On the other hand, when the two mechanisms were separated, the retrieval stage favored a superficially similar but inappropriate base.
The presentation so far concentrated on the final set of correspondences produced by the model. We now turn to the dynamics of the computation as revealed by the time course of the retrieval indices. Figure 6 plots the retrieval indices for several LTM episodes during the first run of the program (i.e. when access and mapping worked in parallel). Figure 7 concentrates on the early stage of the first run and compares it with the second run (i.e. when only the access mechanism was allowed to work). Note that the two plots are in different scales.
Figure 6. Plot of retrieval indices versus time for the parallel condition. Situation A is in solid line, B in dashed. The 'south-west' corner of the plot is reproduced in Figure 7 with threefold magnification.
These plots tell the following story: At the beginning of the parallel run, several situations were probed tentatively by bringing a few elements from each into the working memory. Of this lot, B looked more promising than any of its rivals as it had so many objects and relations in common with the target. Therefore, about half of the agents belonging to situation B entered the working memory and began trying to establish correspondences between themselves and the target agents. The active members of the rival situations were doing the same thing, although with lower intensity. At about 15 time units since the beginning of the simulation, however, situation A (with the immersion heater) rapidly gained strength and eventually overtook the original leader. At time 40, it had already emerged as winner and gradually strengthened its dominance.
The final victory of situation A, despite its lower semantic similarity compared to situation B, is due to the interaction between the mechanisms of access and mapping in AMBR. More precisely, in this particular case it is the mapping that radically changes the course of access. To illustrate the importance of this influence, Figure 7 contrasts the retrieval indices with and without mapping.
Figure 7. Retrieval indices for situations A and B with and without mapping influence on access. The thick lines correspond to the parallel condition and replicate (with threefold magnification) the lines from the 'south-west' corner of Figure 6. The thin lines show 'pure' retrieval indices. See text for details.
The thin lines in Figure 7 show the retrieval indices for the two situations when mapping mechanisms are suppressed. Thus, they indicate the 'pure' retrieval index of each situation--the value that is due to the access mechanism alone. The index for situation B is much higher than that of A and, therefore, B was used as source when the mapping was allowed to run only after the access had finished.
The step-like increases of the plots indicate moments in which an agent (or usually a tight sub-coalition of two or three agents) passes the working memory threshold. This happens, for example, with situation B between time 20 and 30 of the serial condition (the thin dashed line in Figure 7). Thus, accessing a source episode in AMBR is not an all-or-nothing affair. Instead, situations enter the working memory agent by agent and this process extends far after the beginning of the mapping. In this way, not only can the access influence the mapping but also the other way around.
In the interactive condition the mapping mechanism boosted the retrieval index via what we call a 'bootstrap cascade'. This cascade operates in AMBR in the following way. First, the access mechanism brings two or three agents of a given situation into the working memory. If the mapping mechanism then detects that these few agents can be plausibly mapped to some target elements, it constructs new correspondence nodes and links in the AMBR network. This creates new paths for the highly active target elements to activate their mates. The latter in turn can then activate their 'coalition partners', thus bringing a few more agents into the working memory and so on.
The bootstrap cascade is possible in AMBR due to two important characteristics of this model. First, situations have decentralized representations which may be accessed piece by piece. Second, AMBR is based on a parallel cognitive architecture which provides for concurrent operation of numerous interacting processes. Taken together, these two factors enable seamless integration of the subprocesses of access and mapping in analogy-making.
The simulation experiment reported in this paper provides a clear example of mapping influence on analog access and of the advantages of the parallel interactionist view on analogy-making. Furthermore, the computational model AMBR provides a theoretical framework for explaining the controversies in the psychological data on access and reminding. It is possible to explore in which cases the interaction between access and mapping produces results different from a sequential and independent processing. It provides also a framework for generating more precise hypotheses and new experimental designs for their testing. Thus, for example, the detailed logs of the running model might be used for comparison with protocols of think-aloud experiments.
Analogy-making has certainly no clear cut boundaries. Most literature has concentrated on explicit analogies, i.e. consciously retrieving an analog and noticing the analogy. However, there are other cases which might be called implicit or partial analogies, e.g. subconsciously accessing part of a previously solved problem and mapping it to part of the target description without consciously noticing the analogy. However, there are other cases which might be called implicit or partial analogies, e.g. subconsciously accessing part of a previously solved problem and mapping it to part of the target description without consciously noticing the analogy.
The decentralized representations of situations in AMBR make it possible to model the process of partial access, access with distortions, blending (Turner & Fauconnier, 1995), and interference. A previously solved problem can influence the course of problem solving in an even more subtle way by priming some concepts or situations which then trigger a particular solution (Kokinov, 1990; Schunn & Dunbar, 1996). The AMBR model can be used to analyze such cases. It has already been successfully applied for predicting priming and context effects (Kokinov, 1994c).
Priming effects are an example of the influence of access on mapping which is the opposite direction of the one discussed in the current paper. Order effects are another kind of effect that goes in 'forward' direction. Such effects may be due to non-simultaneous perception of the elements of the target problem (Keane, Ledgeway, & Duff, 1994) and/or non-simultaneous retrieval of relevant pieces of information from LTM. Thus the mutual influence between analog access and mapping offers many opportunities for investigation.
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