Simulating Context Effects in Problem Solving with AMBR

This paper presents a computer simulation of context effects on problem solving with AMBR — a model of human analogy-making. It demonstrates how perceiving some incidental objects from the environment may change the way the problem is being solved. It also shows that the timing of this perception is important: while the context element may have crucial influence during the initial stages of problem solving it has virtually no effect during the later stages. The simulation also explores the difference between an explicit hint condition where the focus of attention is drawn towards a context situation which is analogous to the target problem and an implicit context condition where an arbitrary object from the environment makes us remind an old episode. 1. Context Effects: Psychological Data and Cognitive Models Imagine you are sitting at your desk struggling with a difficult problem with a roving look. At some point your eyes incidentally fall on a steaming cup of tea or on a drawing in an open book and you are suddenly reminded of an old analogous problem and its solution that might be adopted to the current case as well. You may not realize that there was a relationship between the cup of tea and the old episode, you may even not notice that you have perceived the steaming liquid, finally, it is possible that you even do not remember that there was a cup of tea on the desk, but still the very fact of perceiving it may have had an influence on your problem solving process. We call this “context effect” on problem solving and we are interested whether such effects really exist and if yes, what might be the mechanisms responsible for that. Context effects on language understanding [39], perception [36], decision-making [38], memory [9, 10, 27], concepts and categorization [4], affect and social cognition [3, 16, 33] have been extensively studied in psychology. Context effects on problem solving and reasoning are still not well explored. Gestalt psychologies have first demonstrated such effects [11, 29, 30]. Gick and Holyoak [12] have demonstrated how an explicit hint may influence the problem solving process. Lockhart [28] and Schunn and Dunbar [37] discuss the influence context may have on accessibility of concepts and therefore on thinking. Recently, Kokinov and his collaborators have studied in a Kokinov & Grinberg 2 systematic way the influence one incidental element from the environment may have on the problem solving process [25, 26]. In their first experiment Kokinov and Yoveva [26] have demonstrated that when solving a problem about boiling water in the forest in a wooden bowl, subjects, who have seen an illustration of a river by a forest with many rocks and stones around, tend to produce significantly more solutions using stones than control subjects, who have not seen the illustration. In a second experiment subjects received sheets of paper with two problems on each sheet, but they had to solve only the first one. The illustration accompanying the second problem and thus seeming to be irrelevant to the first problem played the role of an incidental environmental element. The results have clearly shown that this seemingly irrelevant picture may be crucial in the problem solving process and subjects may produce completely different solutions being exposed to different pictures, even though they claim they have not seen and used them. Being suspicious about participants’ unawareness of the second picture on the page another experiment was carried out by Kokinov, Hadjiilieva, and Yoveva [25]. In this experiment the context condition described above was compared to an explicit hint condition in which the same picture was put on the sheet of paper, but an explicit instruction was given to subjects to try to use it when solving the target problem. The results were significantly different from the context condition which suggests that in the context condition subject have perceived and used the picture unconsciously. Moreover, in some cases, the same picture had opposite effect when used explicitly as a hint. This supports the hypothesis that different mechanisms are responsible for the picture influence and use in the context and in the hint condition. Computational models of problem solving suggested by AI researchers tend to focus on the later case: when the external stimulus is intentionally and consciously perceived and used in the problem solving process [1, 5, 7, 8, 13, 14, 31, 32, 40]. Thus context is typically explicitly represented, moreover a complex structure is used for its representation (e.g. a schema or a frame [40], a feature vector [1], a logical constant [31, 32] or even a whole logical theory [5, 13, 14]) and a complex organization of contexts is introduced (hierarchy of contexts, network of bridges between different possible contexts, etc.). This was described as the “box metaphor”: context is considered as a set of propositions grouped together and embedded in a box [14, 24]. This approach was criticized for not taking into account the possibility for automatic unconscious context influence and for the continuous dynamic changes in the context as reviewed in [24]. In an attempt to build a cognitive model of human problem solving and how it is influenced by the dynamically evolving context Kokinov [21, 24] has put forward a dynamic theory of context. According to it context is considered as the dynamic state of mind of the cognitive system and thus is not necessarily explicitly represented. This state may be reflected by the system itself and thus partially represented, but as seen above, other parts of the context may still have an influence on our behavior without our awareness of that fact. The theory was implemented in a general cognitive architecture, DUAL, and a model of problem solving, AMBR, has been built on it. The current paper describes some simulation experiments with AMBR demonstrating context effects. Kokinov & Grinberg 3 2. A Context-Sensitive Model of Problem Solving 2.1. Dynamic Theory of Context The essence of the dynamic theory [21, 24] is that context is considered as the dynamic state of human mind which state is crucial for all cognitive processes. If we paraphrase this in computational terms, the algorithms that compute a particular cognitive process and the data they are using are changing dynamically with the changes in the state of mind. Since the state evolves continuously the algorithms and data are never the same. That is why we can never replicate a given act of human thinking, perception, or learning fully — since the context will have been changed and the processes will change as well. Of course, in many cases the changes might be small and even unnoticeable, but it can also happen that even small changes turn out to be crucial for the computation and the generated behavior becomes radically different. This is analogous to the theory of catastrophes developed in mathematics. According to the dynamic theory the state of mind is determined by the content of human working memory (WM) and the relative weight each memory element has in it. The WM elements are both operations and structures — thus changing the content of WM may result in changing the operations available for application or in changing the data we are currently using in the computation. The dynamic theory of context is not bound to a symbolic computational interpretation, it can possibly be implemented in connectionist or dynamic systems terms where no differentiation between data and operations will be necessary. 2.2. DUAL: A Dynamic Context-Sensitive Cognitive Architecture DUAL [19, 20, 22, 35] is a general cognitive architecture which has been developed with the dynamic theory of context in mind and it provides a basis for modeling context-sensitive cognitive processes. This is a massively parallel and highly decentralized system consisting of micro-agents each of whom represents a small piece of procedural and declarative knowledge. Thus all operations in DUAL are performed by some agents. The agents are connected via links (which can be dynamically changed) and exchange messages via these links. The overall behavior of the system, or what is being computed at the particular moment, is an emergent phenomenon which reflects the collective behavior of the acting micro-agents. There is no central mechanism which controls which agents to act and in what sequence. On the contrary, each agent acts independently and in parallel to the acting of other agents and it uses only local information coming from its neighboring agents. Each agent has an activation level which is determined by the incoming activation from neighboring agents and its residual activation from earlier stages. This activation level determines the degree of availability of that agent in that particular moment. If the degree of activation of a given agent is below a certain threshold than the agent is “sleeping”, i.e. it cannot take part in any computation. The higher the activation level, the more active the agent is and the faster its operations are performed. The connectionist activation is considered as a power supply for the symbolic operations performed by the agent [35]. Kokinov & Grinberg 4 Working memory in DUAL is considered to be the set of active agents in a particular moment of time. Thus the content of WM determines which agents will take part in the computation, how fast will each of them act, how they will compete, etc. and therefore it determines the outcome of the global emergent process that they generate. That is, in different contexts different sets of agents will act and with different levels of activation and therefore they will produce different outcomes. This is how context-sensitive behavior is implemented in DUAL. The content of WM is determined by several factors: direct activation of agents from the environment via perception (modeled by connecting some of the agents to the INPUT node), direct activation of agents by internal motivational factors (modeled by connecting some of the agents to the GOAL node), residual activation of agents from previous memory states (modeled by a decay function of activation), and by receiving activation from neighboring agents via the links (modeled by a process of spreading activation). Similar approaches to context modeling have been followed by John Anderson [2] where the semantic network has its internal dynamics, and by Douglas Hofstadter [15] where the Slipnet is also dynamically changing its structure as well as the codelets run with various probability depending on the context as represented in the workspace. 2.3. AMBR: A Context-Sensitive Model of Analogy-Making AMBR [17, 18, 23, 34] is a model of human problem solving built upon the DUAL architecture. The program has semantic knowledge about various concepts and general facts as well as a number of past problem-solving episodes from everyday kitchen life. A target problem is presented to the program and it has to find its solution basically by analogy with one of the old episodes. There are many important differences between AMBR and other models of analogy-making. For example, mapping and retrieval are emergent processes based on the local computations and interactions of many micro-agents and thus they are running in parallel which makes it possible for mutual interaction between mapping and retrieval, including mapping guidance of retrieval. Since episodes are represented in a decentralized way (by a coalition of agents) they can be partially retrieved, they can be extended by intrusions from general knowledge or from other episodes, finally blending between episodes is possible. AMBR is sensitive to priming and context influences. The rest of this paper will present simulation data which demonstrate AMBR’s context-sensitivity. Kokinov & Grinberg 5 3. Simulation Experiments The knowledge base (KB) of the system contains 570 agents representing about 270 concepts and 12 old episodes. Concepts include tea, milk, water, drinkableliquid, liquid, temperature-of, high-temp, low-temp, made-of, color-of, cause, etc. The old episodes include the following ones (Table 1). Table 1: Old episodes in the long-term memory of the system. Short name of the episode Short informal description of the episode WTP heating Water in a Teapot on a hot Plate BF heating water in a wooden Bowl on the Fire and burning the bowl GP heating water in a Glass on a hot Plate and breaking the glass IHC heating water by Immersion Heater in a Cup MTF cooling Milk in a Teapot in the Fridge ICF cooling Ice Cube on a glass in the Fridge BPF cooling Butter on a Plate in the Fridge FDO baking Food on a Dish in the Oven STC sweetening by putting sugar in the tea being in a cup SFF salting by putting salt into the food in the fridge ERW coloring an Egg put in Red Water GWB keeping a Glass in a Wooden Box Here is a simple target problem HM: “How can you Heat some Milk which is put in a teapot?” This problem has to be solved by making analogy with one of the known episodes in the KB. A simplified propositional representation of this example is presented in Table 2. Each proposition is represented by a separate DUAL agent. Table 2: Representation of the target problem HM — “heating milk”. Content of input list, goal list, and primary WM are described. Agent External Activation Propositional representaion