Unifying Deduction, Induction, and Analogy by the AMBR Model

Unifying Deduction, Induction, and Analogy by the AMBR Model Georgi Petkov (gpetkov@cogs.nbu.bg) Ivan Vankov (i.i.vankov@gmail.com) Boicho Kokinov (bkokinov@nbu.bg) Central and East European Center for Cognitive Science, Department of Cognitive Science and Psychology, New Bulgarian University, 21 Montevideo Street Sofia 1618, Bulgaria 2001, Grinberg & Kokinov, 2003; Petkov & Kokinov, 2009), analogy and perception (Petkov & Shahbazyan, 2007, Petkov & Kokinov, 2009; Kokinov, Vankov & Bliznashki, 2009), analogy and judgement (Petkov & Kokinov, 2006). In this paper we return to the initial idea to model the three traditionally considered separate types of reasoning (since the time of Aristotle) by the same mechanisms. Meanwhile other models of analogy started to explore the relations between analogy and induction (schema generalization). The SME has been used in the generalization of structurally similar situations (Kuehne, Forbus, Gentner, & Quinn, 2000; Lovett, Lockwood, Dehghani, & Forbus, 2007). The LISA model and its close relative DORA have been specifically addressing the generalization problem and its integration with the analogical mapping (Hummel & Holyoak, 2003; Doumas, Hummel, & Sandhofer, 2008). There are not that many attempts to integrate analogy and deduction with the exception of PI (Holland, Holyoak, Nisbett, & Thagard, 1986) and of integrating the SME and qualitative reasoning (Forbus, 2001). The current paper describes an attempt to demonstrate that deduction, induction, and analogy can be produced by a common pool of simple mechanisms (those postulated in the DUAL architecture) and that only the context and the specific interplay between these mechanisms will determine which of these processes will emerge out of the computational process. Thus this is an attempt to model examples of these three processes in a single simulation experiment – without tuning the parameters or changing the mechanisms for each of the cases. Abstract This paper presents a series of simulations performed with the AMBR model that demonstrate how deduction, induction, and analogy can emerge from the interaction of several simple mechanisms. First, a case of deductive reasoning is demonstrated when a problem is solved based on general knowledge. The system represents the target in different ways depending on the goal, and different solutions are generated. Second, the constructed solutions of the problems are remembered and later on used as a base for remote analogy. Finally, on the basis of the analogy made, a generalized solution of the class of problems is induced. One important characteristic of the model is that representation of the task, problem-solving, and learning are not viewed as separate modules. Instead, they are different aspects of one and the same joined work of the basic mechanisms of the architecture. Keywords: cognitive generalization. modeling, analogy, deduction, Introduction It has been suggested that analogy is the core of human cognition (Hofstadter, 2001; Holyoak, Gentner, & Kokinov, 2001). The reason is that “relational reasoning” can be found in a variety of cognitive processes. Traditionally, however, models of analogy-making have been isolated from and contrasted to models of deductive reasoning (Gentner, 1983, 1989; Holyoak & Thagard, 1989, Hummel & Holyoak, 1997, Hofstadter, 1995). Somehow gradually analogy-making became a separate and important domain of study (Gentner, Holyoak, Kokinov, 2001). When the AMBR model was first launched (Kokinov, 1988) it was suggested as a unified model of deduction, induction, and analogy. It has been claimed that deduction, induction, and analogy “are not separate cognitive mechanisms, but rather a slightly different manifestations of the same basic mechanisms” (Kokinov, 1988). A few experiments have been run to demonstrate that deduction, induction, and analogy have common properties – being primed by recent experience (Kokinov, 1990), and transferred knowledge being evaluated on the basis of the structural correspondence between the target and the memorized base (Kokinov, 1992). Even though AMBR was suggested as a unified model of these three “kinds” of reasoning, the line of its further development has gone in different directions like exploring the relations between analogy and memory (Kokinov, 1994a, Kokinov & Petrov, Brief description of the DUAL architecture The DUAL architecture was launched (Kokinov, 1994b, 1994c) as a general cognitive architecture that will provide mechanisms for modeling various cognitive processes. The knowledge in DUAL is represented by a huge number of interconnected micro-agents. Each agent‟s symbolic aspect represents a small piece of knowledge while its level of activation represents the relevance of this piece of knowledge to the current context. The activation spreads through the network as in connectionists networks. There are two sources of activation – INPUT and GOAL nodes. Each agent may also have a residual activation that