A Generalized Syllogistic Inference System based on Inclusion and Exclusion Relations

Koji Mineshima; Mitsuhiro Okada; Ryo Takemura

doi:10.1007/s11225-012-9428-5

A Generalized Syllogistic Inference System based on Inclusion and Exclusion Relations

Koji Mineshima, Mitsuhiro Okada, Ryo Takemura

Department of Philosophy

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

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 language	English
Pages (from-to)	753-785
Number of pages	33
Journal	Studia Logica
Volume	100
Issue number	4
DOIs	https://doi.org/10.1007/s11225-012-9428-5
Publication status	Published - 2012 Aug

Keywords

Natural deduction
Normalization
Proof theory
Syllogistic logic

ASJC Scopus subject areas

Logic
History and Philosophy of Science

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10.1007/s11225-012-9428-5

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abstract = "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.",

keywords = "Natural deduction, Normalization, Proof theory, Syllogistic logic",

author = "Koji Mineshima and Mitsuhiro Okada and Ryo Takemura",

note = "Funding Information: Acknowledgements. We are grateful to Larry Moss and the anonymous reviewers for their useful comments and suggestions. This work was supported by MEXT KAKENHI 23120002 and partly by MEXT KAKENHI 23520036.",

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doi = "10.1007/s11225-012-9428-5",

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AU - Mineshima, Koji

AU - Okada, Mitsuhiro

AU - Takemura, Ryo

N1 - Funding Information: Acknowledgements. We are grateful to Larry Moss and the anonymous reviewers for their useful comments and suggestions. This work was supported by MEXT KAKENHI 23120002 and partly by MEXT KAKENHI 23520036.

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N2 - 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.

AB - 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.

KW - Natural deduction

KW - Normalization

KW - Proof theory

KW - Syllogistic logic

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ER -

A Generalized Syllogistic Inference System based on Inclusion and Exclusion Relations

Abstract

Keywords

ASJC Scopus subject areas

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