Reasoning About Truth in First-Order Logic

Authors:
Claes Strannegård;Fredrik Engström;Abdul Rahim Nizamani;Lance Rips
Affiliations:
Department of Philosophy, Linguistics and Theory of Science, University of Gothenburg, Gothenburg, Sweden and Department of Applied Information Technology, Chalmers University of Technology, Gothe ...;Department of Philosophy, Linguistics and Theory of Science, University of Gothenburg, Gothenburg, Sweden;Department of Applied Information Technology, University of Gothenburg, Gothenburg, Sweden;Department of Psychology, Northwestern University, Evanston, USA
Venue:
Journal of Logic, Language and Information
Year:
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.