1.  70
    Proof Nets for the Multimodal Lambek Calculus.Richard Moot & Quintijn Puite - 2002 - Studia Logica 71 (3):415-442.
    We present a novel way of using proof nets for the multimodal Lambek calculus, which provides a general treatment of both the unary and binary connectives. We also introduce a correctness criterion which is valid for a large class of structural rules and prove basic soundness, completeness and cut elimination results. Finally, we will present a correctness criterion for the original Lambek calculus Las an instance of our general correctness criterion.
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  2.  40
    Linguistic Applications of First Order Intuitionistic Linear Logic.Richard Moot & Mario Piazza - 2001 - Journal of Logic, Language and Information 10 (2):211-232.
    In this paper we will discuss the first order multiplicative intuitionistic fragment of linear logic, MILL1, and its applications to linguistics. We give an embedding translation from formulas in the Lambek Calculus to formulas in MILL1 and show this translation is sound and complete. We then exploit the extra power of the first order fragment to give an account of a number of linguistic phenomena which have no satisfactory treatment in the Lambek Calculus.
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  3.  12
    Generalized Quantifiers in Declarative and Interrogative Sentences.Raffaella Bernardi & Richard Moot - 2003 - Logic Journal of the IGPL 11 (4):419-434.
    In this paper we present a logical system able to compute the semantics of both declarative and interrogative sentences. Our proposed analysis takes place at both the sentential and at the discourse level. We use syntactic inference on the sentential level for declarative sentences, while the discourse level comes into play for our treatment of questions. Our formalization uses a type logic sensitive to both the syntactic and semantic properties of natural language. We will show how an account of the (...)
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  4.  10
    Natural Language Semantics and Computability.Richard Moot & Christian Retoré - 2019 - Journal of Logic, Language and Information 28 (2):287-307.
    This paper is a reflexion on the computability of natural language semantics. It does not contain a new model or new results in the formal semantics of natural language: it is rather a computational analysis, in the context for type-logical grammars, of the logical models and algorithms currently used in natural language semantics, defined as a function from a grammatical sentence to a set of logical formulas—because a statement can be ambiguous, it can correspond to multiple formulas, one for each (...)
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