A Generalized Syllogistic Inference System based on Inclusion and Exclusion Relations

Studia Logica 100 (4):753-785 (2012)
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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