A Generalized Syllogistic Inference System based on Inclusion and Exclusion Relations

Koji Mineshima, Mitsuhiro Okada, Ryo Takemura

Research output: Contribution to journalArticle

5 Citations (Scopus)


We introduce a simple inference system based on two primitive relations between terms, namely, inclusion and exclusion relations. We present a normalization theorem, and then provide a characterization of the structure of normal proofs. Based on this, inferences in a syllogistic fragment of natural language are reconstructed within our system. We also show that our system can be embedded into a fragment of propositional minimal logic.

Original languageEnglish
Pages (from-to)753-785
Number of pages33
JournalStudia Logica
Issue number4
Publication statusPublished - 2012 Aug 1



  • Natural deduction
  • Normalization
  • Proof theory
  • Syllogistic logic

ASJC Scopus subject areas

  • Logic
  • History and Philosophy of Science

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