Richard Moot

The Logic of Categorial Grammars

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Proof nets for the multimodal Lambek calculus

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.

Extended Lambek Calculi and First-Order Linear Logic

The Syntactic Calculus [27] — often simply called the Lambek calculus, L, — is a beautiful system in many ways: Lambek grammars give a satisfactory syntactic analysis for the (context-free) core of natural language and, in addition, it provides a simple and elegant syntax-semantics interface

A type-logical treebank for French

The goal of the current paper is to describe the TLGbank, a treebank of type-logical proof semi-automatically extracted from the French Treebank. Though the framework chosen for the treebank are multimodal type-logical grammars, we have ensured that the analysis is compatible with other mondern type-logical grammars, such the displacement calculus and first-order linear logic. We describe the extraction procedure, analyse first results and compare the treebank to the CCGbank.

Using tree transducers for grammatical inference

We present a novel way of extracting a categorial grammar from annotated data. Using the sentences from the Paris VII annotated treebank [2] as our starting point, we use a tree transducer to convert the annotated trees from the corpus into categorial grammar derivations. n nWe describe both the formal aspects and the implementation of the tree transducer, which is a conservative extension of standard tree transducers allowing a compact specification of the transductions rules relevant for our purposes, and we discuss the specific set of transduction rules we use to convert the corpus into AB grammar derivation trees. n nEvaluating the resulting tree transducer on the entire corpus, we find that it produces a treebank finds lexical entries for 90, 0% of the corpus, though it produces complete derivations for only 75% of all sentence in the corpus.

CGN to Grail: Extracting a Type-logical Lexicon From the CGN Annotation.

The tag set for the CGN syntactic annotation is designed in such a way as to enable a transparent mapping to the derivational structures of current ‘lexicalized’ grammar formalisms. Through such translations, the CGN tree bank can be used to train and evaluate computational grammars within these frameworks.In this paper we will discuss some preliminary work on the mapping between the CGN annotation graphs and the proof net format of the Grail parser/theorem prover (Moot 2001, Moot 1999). Grail is a general grammar development environment for type-logical categorial grammars (TLG, (Moortgat 1997, Morrill 1994, Carpenter 1998)). To a large extent, there is a straightforward transfer between the type-logical format and the analyses provided by other lexicalized grammar formalisms such as LTAG (lexicalized Tree Adjoining Grammars, (Sarkar 2001)) and MG (computational versions of Minimalist Grammars, (Stabler 1997)). An attractive feature of TLG, which is not shared by these other frameworks, is its full support for hypothetical reasoning.In this paper, we exploit the hypothetical reasoning facilities to extract a type-logical grammar from the CGN annotation graphs. This task can be naturally divided in two subtasks. The first of these consists in solving type equations: in the TLG setting this means breaking up the CGN annotation graph into the subgraphs that correspond to lexical type assignments. In the presence of discontinuous dependencies, the lexical type assignments will not always be compatible with surface word order. The second subtask then consists in calibrating the lexicon in such a way that it has controlled access to the structural reasoning component of the grammar.

The Multimodal Lambek Calculus

The multimodal Lambek calculus extends the (non-associative) Lambek calculus in two ways. First, it provides a way of mixing different resource management possibilities — for example associative and non-associative or commutative and non-commutative — without collapse, that is to say that associativity can be valid for certain formulae but not for others. Second, it introduces unary connectives, which introduce new derivability patterns and which provide us with another way to lexically anchor the structural rules of associativity and commutativity.

The Non-associative Lambek Calculus

In this chapter we will look at NL, the non-associative Lambek calculus, which was introduced by Lambek a few years after the Syntactic Calculus, L. The Gentzen-style presentation of the Lambek calculus uses a list of formulae as antecedents, whereas NL uses binary branching trees instead.

Categorial grammars and minimalist grammars

This paper explores some of the connections between minimalist grammars and categorial grammars in the tradition of the Lambek calculus and its various extensions. It provides a new graphical perspective on the lexical items of both minimalist and categorial grammars and uses this perspective to suggest a reconciliation between two different ways of embedding minimalist grammars into categorial grammars, while keeping the good properties of both.

Logical Aspects of Computational Linguistics

LACL.- k-Valued Non-associative Lambek Grammars (Without Product) Form a Strict Hierarchy of Languages.- Dependency Structure Grammars.- Towards a Computational Treatment of Binding Theory.- Translating Formal Software Specifications to Natural Language.- On the Selective Lambek Calculus.- Grammatical Development with Xmg.- Lambek-Calculus with General Elimination Rules and Continuation Semantics.- A Note on the Complexity of Constraint Interaction: Locality Conditions and Minimalist Grammars.- Large Scale Semantic Construction for Tree Adjoining Grammars.- A Compositional Approach Towards Semantic Representation and Construction of ARABIC.- Strict Deterministic Aspects of Minimalist Grammars.- A Polynomial Time Extension of Parallel Multiple Context-Free Grammar.- Learnable Classes of General Combinatory Grammars.- On Expressing Vague Quantification and Scalar Implicatures in the Logic of Partial Information.- Describing Lambda Terms in Context Unification.- Category Theoretical Semantics for Pregroup Grammars.- Feature Constraint Logic and Error Detection in ICALL Systems.- Linguistic Facts as Predicates over Ranges of the Sentence.- How to Build Argumental Graphs Using TAG Shared Forest: A View from Control Verbs Problematic.- When Categorial Grammars Meet Regular Grammatical Inference.- The Expressive Power of Restricted Fragments of English.- The Complexity and Generative Capacity of Lexicalized Abstract Categorial Grammars.- More Algebras for Determiners.