Tactic-Based Modeling of Cognitive Inference on Logically StructuredNotation
Computational (algorithmic) models of high-level cognitive inference tasks such as logical inference, mathematical inference, and decision making can have both theoretical and practical impact. They can improve our theoretical understanding of how people think and also provide practical direction for applications such as automated reasoning systems, systems attuned to user-interaction in decision-critical environments, and computer-aided education. To support those benefits, cognitive models need to be detailed, compositional, based in well-understood mathematics, and, to whatever extent possible, descriptively accurate. We introduce a new, interdisciplinary approach that could be used to develop cognitive models of high-level inference with these properties. Two significant aspects of this approach are tactics and eyetracking methods. Tactics are used to express high-level inferences in fully formalized mathematics for automated theorem proving systems; eyetracking methods provide insight into real-time and microcognitive information processing by permitting analysis of the visual attention of people performing cognitive tasks. Combining tactics and eyetracking methods with traditional techniques from applied logic, artificial intelligence, and cognitive science can result in more deeply detailed and accurate cognitive models. We demonstrate the feasibility of this new approach to modeling by describing its application to a calculational logic system that supports schematic reasoning via metalinguistic operations (such as textual substitution) without resorting to higher-order logic. We discuss several computational, psychological, and pedagogical insights that resulted from this approach, and we present a detailed, tactic-based model of calculational logic inference. Specific results include: an explanation of calculational logic as a formalized metalogic; a tactic-based implementation of calculational logic inference; some pedagogical observations on the teaching of calculational logic; and experimental results that demonstrate that eyetracking methods can provide insight into theorem proving that could not be achieved by studies of written work alone.
computer science; technical report
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