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An Analytic Tableau System for Natural Logic

In Maria Aloni, H. Bastiaanse, T. De Jager & Katrin Schulz (eds.), Logic, Language and Meaning. Springer. pp. 104-113 (2010)

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  1. Cut-Based Abduction.Marcello D'agostino, Marcelo Finger & Dov Gabbay - 2008 - Logic Journal of the IGPL 16 (6):537-560.
    In this paper we explore a generalization of traditional abduction which can simultaneously perform two different tasks: given an unprovable sequent Γ ⊢ G, find a sentence H such that Γ, H ⊢ G is provable ; given a provable sequent Γ ⊢ G, find a sentence H such that Γ ⊢ H and the proof of Γ, H ⊢ G is simpler than the proof of Γ ⊢ G . We argue that the two tasks should not be distinguished, (...)
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  • The Proper Treatment of Quantification in Ordinary English.Richard Montague - 1973 - In Patrick Suppes, Julius Moravcsik & Jaakko Hintikka (eds.), Approaches to Natural Language. Dordrecht. pp. 221--242.
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  • The Logic of Natural Language.G. B. Keene - 1984 - Philosophical Quarterly 34 (135):174-175.
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  • A 'Natural Logic' Inference System Using the Lambek Calculus.Anna Zamansky, Nissim Francez & Yoad Winter - 2006 - Journal of Logic, Language and Information 15 (3):273-295.
    This paper develops an inference system for natural language within the ‘Natural Logic’ paradigm as advocated by van Benthem, Sánchez and others. The system that we propose is based on the Lambek calculus and works directly on the Curry-Howard counterparts for syntactic representations of natural language, with no intermediate translation to logical formulae. The Lambek -based system we propose extends the system by Fyodorov et~al., which is based on the Ajdukiewicz/Bar-Hillel calculus Bar Hillel,. This enables the system to deal with (...)
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  • Natural Logic for Natural Language.Jan van Eijck - manuscript
    We implement the extension of the logical consequence relation to a partial order ≤ on arbitary types built from e (entities) and t (Booleans) that was given in [1], and the definition of monotonicity preserving and monotonicity reversing functions in terms of ≤. Next, we present a new algorithm for polarity marking, and implement this for a particular fragment of syntax. Finally, we list the reseach agenda that these definitions and this algorithm suggest. The implementations use Haskell [8], and are (...)
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  • Questions About Quantifiers.Johan van Benthem - 1984 - Journal of Symbolic Logic 49 (2):443-466.
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  • Meaning and Partiality.Reinhard Muskens - 1995 - Stanford, CA: CSLI Publications.
    This book radically simplifies Montague Semantics and generalizes the theory by basing it on a partial higher order logic. The resulting theory is a synthesis of Montague Semantics and Situation Semantics. In the late sixties Richard Montague developed the revolutionary idea that we can understand the concept of meaning in ordinary languages much in the same way as we understand the semantics of logical languages. Unfortunately, however, he formalized his idea in an unnecessarily complex way - two outstanding researchers in (...)
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  • Meaning and Partiality.Reinhard Muskens - 1989 - Dissertation, University of Amsterdam
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  • The Logic of Natural Language.Fred Sommers - 1983 - Revue Philosophique de la France Et de l'Etranger 173 (3):367-368.
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  • Order-Based Inference in Natural Logic.Yaroslav Fyodorov, Yoad Winter & Nissim Francez - 2003 - Logic Journal of the IGPL 11 (4):385-416.
    This paper develops a version of Natural Logic – an inference system that works directly on natural language syntactic representations, with no intermediate translation to logical formulae. Following work by Sánchez, we develop a small fragment that computes semantic order relations between derivation trees in Categorial Grammar. The proposed system has the following new characteristics: It uses orderings between derivation trees as purely syntactic units, derivable by a formal calculus. The system is extended for conjunctive phenomena like coordination and relative (...)
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  • Essays in Logical Semantics.J. F. A. K. van Benthem - 1986
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  • Representation and Inference for Natural Language: A First Course in Computational Semantics.Patrick Blackburn - 2005 - Center for the Study of Language and Information.
    How can computers distinguish the coherent from the unintelligible, recognize new information in a sentence, or draw inferences from a natural language passage? Computational semantics is an exciting new field that seeks answers to these questions, and this volume is the first textbook wholly devoted to this growing subdiscipline. The book explains the underlying theoretical issues and fundamental techniques for computing semantic representations for fragments of natural language. This volume will be an essential text for computer scientists, linguists, and anyone (...)
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  • Seeking Explanations: Abduction in Logic, Philosophy of Science and Artificial Intelligence.Atocha Aliseda-Llera - 1997 - Dissertation, Stanford University
    In this dissertation I study abduction, that is, reasoning from an observation to its possible explanations, from a logical point of view. This approach naturally leads to connections with theories of explanation in the philosophy of science, and to computationally oriented theories of belief change in Artificial Intelligence. ;Many different approaches to abduction can be found in the literature, as well as a bewildering variety of instances of explanatory reasoning. To delineate our subject more precisely, and create some order, a (...)
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