Reasoning About Truth in First-Order Logic

Journal of Logic, Language and Information 22 (1):115-137 (2013)
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Abstract

First, we describe a psychological experiment in which the participants were asked to determine whether sentences of first-order logic were true or false in finite graphs. Second, we define two proof systems for reasoning about truth and falsity in first-order logic. These proof systems feature explicit models of cognitive resources such as declarative memory, procedural memory, working memory, and sensory memory. Third, we describe a computer program that is used to find the smallest proofs in the aforementioned proof systems when capacity limits are put on the cognitive resources. Finally, we investigate the correlation between a number of mathematical complexity measures defined on graphs and sentences and some psychological complexity measures that were recorded in the experiment

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Fredrik Engström
University of Gothenburg

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References found in this work

Natural deduction: a proof-theoretical study.Dag Prawitz - 1965 - Mineola, N.Y.: Dover Publications.
Structural Proof Theory.Sara Negri, Jan von Plato & Aarne Ranta - 2001 - New York: Cambridge University Press. Edited by Jan Von Plato.
Symbolic logic.Frederic Brenton Fitch - 1952 - New York,: Ronald Press Co..

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