Reasoning About Truth in First-Order Logic

Claes Strannegård*, Fredrik Engström, Abdul Rahim Nizamani, Lance Rips

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)115-137
Number of pages23
JournalJournal of Logic, Language and Information
Volume22
Issue number1
DOIs
StatePublished - 2013

Keywords

  • Bounded cognitive resources
  • First-order logic
  • Proof system
  • Truth

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • Philosophy
  • Linguistics and Language

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