SOAR: an architecture for general intelligence
Artificial Intelligence
Basic proof theory
A Tutorial on Stålmarck‘s Proof Procedure for PropositionalLogic
Formal Methods in System Design - Special issue on formal methods for computer-added design
Handbook of automated reasoning
Handbook of automated reasoning
Human Problem Solving
A system of interaction and structure
ACM Transactions on Computational Logic (TOCL)
Transparent neural networks: integrating concept formation and reasoning
AGI'12 Proceedings of the 5th international conference on Artificial General Intelligence
Reasoning About Truth in First-Order Logic
Journal of Logic, Language and Information
A cognitive architecture based on dual process theory
AGI'13 Proceedings of the 6th international conference on Artificial General Intelligence
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We conducted a computer-based psychological experiment in which a random mix of 40 tautologies and 40 non-tautologies were presented to the participants, who were asked to determine which ones of the formulas were tautologies. The participants were eight university students in computer science who had received tuition in propositional logic. The formulas appeared one by one, a time-limit of 45 s applied to each formula and no aids were allowed. For each formula we recorded the proportion of the participants who classified the formula correctly before timeout (accuracy) and the mean response time among those participants (latency). We propose a new proof formalism for modeling propositional reasoning with bounded cognitive resources. It models declarative memory, visual memory, working memory, and procedural memory according to the memory model of Atkinson and Shiffrin and reasoning processes according to the model of Newell and Simon. We also define two particular proof systems, T and NT, for showing propositional formulas to be tautologies and non-tautologies, respectively. The accuracy was found to be higher for non-tautologies than for tautologies (p T was .89 and for non-tautologies the correlation between latency and minimum proof length in NT was .87.