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  1. Inclusion and Exclusion in Natural Language.Thomas F. Icard - 2012 - Studia Logica 100 (4):705-725.
    We present a formal system for reasoning about inclusion and exclusion in natural language, following work by MacCartney and Manning. In particular, we show that an extension of the Monotonicity Calculus, augmented by six new type markings, is sufficient to derive novel inferences beyond monotonicity reasoning, and moreover gives rise to an interesting logic of its own. We prove soundness of the resulting calculus and discuss further logical and linguistic issues, including a new connection to the classes of weak, strong, (...)
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  • An extended model of natural logic.Christopher D. Manning & Bill MacCartney - unknown
    We propose a model of natural language inference which identifies valid inferences by their lexical and syntactic features, without full semantic interpretation. We extend past work in natural logic, which has focused on semantic containment and monotonicity, by incorporating both semantic exclusion and implicativity. Our model decomposes an inference problem into a sequence of atomic edits linking premise to hypothesis; predicts a lexical semantic relation for each edit; propagates these relations upward through a semantic composition tree according to properties of (...)
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  • A Generalized Syllogistic Inference System based on Inclusion and Exclusion Relations.Koji Mineshima, Mitsuhiro Okada & Ryo Takemura - 2012 - Studia Logica 100 (4):753-785.
    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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