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A Generalized Syllogistic Inference System based on Inclusion and Exclusion Relations

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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.

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Correspondence to Koji Mineshima.

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Mineshima, K., Okada, M. & Takemura, R. A Generalized Syllogistic Inference System based on Inclusion and Exclusion Relations. Stud Logica 100, 753–785 (2012). https://doi.org/10.1007/s11225-012-9428-5

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