Studia Logica

, Volume 100, Issue 4, pp 753–785 | Cite as

A Generalized Syllogistic Inference System based on Inclusion and Exclusion Relations

  • Koji Mineshima
  • Mitsuhiro Okada
  • Ryo Takemura


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.


Syllogistic logic Proof theory Natural deduction Normalization 


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© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Keio UniversityTokyoJapan
  2. 2.Keio UniversityTokyoJapan
  3. 3.Nihon UniversityTokyoJapan

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