Journal of Logic, Language and Information

, Volume 19, Issue 3, pp 283–314 | Cite as

Reasoning Processes in Propositional Logic

  • Claes Strannegård
  • Simon Ulfsbäcker
  • David Hedqvist
  • Tommy Gärling
Article
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Abstract

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 < .0001). For tautologies the correlation between latency and minimum proof length in T was .89 and for non-tautologies the correlation between latency and minimum proof length in NT was .87.

Keywords

Bounded resources Proof system Propositional logic Psychological experiment Reasoning 
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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • Claes Strannegård
    • 1
  • Simon Ulfsbäcker
    • 2
  • David Hedqvist
    • 2
  • Tommy Gärling
    • 3
  1. 1.Department of Applied Information TechnologyChalmers University of TechnologyGothenburgSweden
  2. 2.Department of Computer ScienceChalmers University of TechnologyGothenburgSweden
  3. 3.Department of PsychologyUniversity of GothenburgGothenburgSweden

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