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Reasoning about truth in first-order logic

Journal article
Authors Claes Strannegård
Fredrik Engström
Abdul Rahim Nizamani
Lance Rips
Published in Journal of Logic, Language and Information
Volume 22
Issue 1
Pages 115–137
ISSN 0925-8531
Publication year 2013
Published at Department of Applied Information Technology (GU)
Department of Philosophy, Linguistics and Theory of Science
Pages 115–137
Language en
Keywords First-order logic · Proof system · Bounded cognitive resources · Truth
Subject categories Logic


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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