Our group will present two papers on logic and cognition at 40th Annual Meeting of the Cognitive Science Society. In the first paper, we present a natural logic for reasoning with quantifiers that can predict human performance in appropriate reasoning tasks. In the second paper, we provide a model based on dynamic epistemic logic (eliminating hypotheses) that can predict the empirical difficulty ratings in Deductive Mastermind game – a deductive reasoning game implemented in the online educational game system Math Garden.
Abstract:
We present a natural logic for reasoning with quantifiers that can predict human performance in appropriate reasoning tasks. The model is an extension of that in (Geurts, 2003) but allows for better fit with data on syllogistic reasoning and is extended to account for reasoning with iterated quantifiers. We assign weights to inference rules and operationalize the complexity of a reasoning pattern as weighted length of proof in our logic – this results in a measure of complexity that outperforms other models in their predictive capacity and allows for the derivation of empirically testable hypotheses.
Abstract:
Deductive Mastermind is a deductive reasoning game that is implemented in the online educational game system Math Garden. A good understanding of the difficulty of Deductive Mastermind game instances is essential for optimizing the learning experience of players. The available empirical difficulty ratings, based on speed and accuracy, provide robust estimations but do not explain why certain game instances are easy or hard. In previous work a logic-based model was proposed that successfully predicted these difficulty ratings. We add to this work by providing a model based on a different logical principle— that of eliminating hypotheses (dynamic epistemic logic) instead of reasoning by cases (analytical tableaux system)—that can predict the empirical difficulty ratings equally well. We show that the informational content of the different feedbacks given in game instances is a core predictor for cognitive difficulty ratings and that this is irrespective of the specific logic used to formalize the game.