The last years have witnessed a flurry of new results in the area of partial evaluation. These tutorial notes survey the field and present a critical assessment of the state of the art.

Tutorial notes on partial evaluation

This article introduces a logical system, called BV, which extends multiplicative linear logic by a noncommutative self-dual logical operator. This extension is particularly challenging for the sequent calculus, and so far, it is not achieved therein. It becomes very natural in a new formalism, called the calculus of structures, which is the main contribution of this work. Structures are formulas subject to certain equational laws typical of sequents. The calculus of structures is obtained by generalizing the sequent calculus in such a way that a new top-down symmetry of derivations is observed, and it employs inference rules that rewrite inside structures at any depth. These properties, in addition to allowing the design of BV, yield a modular proof of cut elimination.

/pdf/a-system-of-interaction-and-structure-10g3mj64t9.pdf

A system of interaction and structure

In this paper, we introduce the Lefff , a freely available, accurate and large-coverage morphological and syntactic lexicon for French, used in many NLP tools such as large-coverage parsers. We ﬁrst describe Alexina, the lexical framework in which the Lefff is developed as well as the linguistic notions and formalisms it is based on. Next, we describe the various sources of lexical data we used for building the Lefff , in particular semi-automatic lexical development techniques and conversion and merging of existing resources. Finally, we illustrate the coverage and precision of the resource by comparing it with other resources and by assessing its impact in various NLP tools.

/pdf/the-lefff-a-freely-available-and-large-coverage-4qvmccvxbl.pdf

The Lefff, a freely available and large-coverage morphological and syntactic lexicon for French

/pdf/linear-logic-and-noncommutativity-in-the-calculus-of-3nxxwtizsd.pdf

Linear Logic and Noncommutativity in the Calculus of Structures

Handsome proof-nets: perfect matchings and cographs

Series-parallel orders are defined as the least class of partial orders containing the one-element order and closed by ordinal sum and disjoint union. From this inductive definition, it is almost immediate that any series-parallel order may be represented by an algebraic expression, which is unique up to the associativity of ordinal sum and to the associativivity and commutativity of disjoint union. In this paper, we introduce a rewrite system acting on these algebraic expressions that axiomatises completely the sub-ordering relation for the class of series-parallel orders.

A Complete Axiomatisation for the Inclusion of Series-Parallel Partial Orders

In this paper, we define Dependency Structure Grammars (DSG), which are rewriting rule grammars generating sentences together with their dependency structures, are more expressive than CF-grammars and non-equivalent to mildly context-sensitive grammars

We show that DSG are weakly equivalent to Categorial Dependency Grammars (CDG) recently introduced in [6,3] In particular, these dependency grammars naturally express long distance dependencies and enjoy good mathematical properties

Dependency structure grammars

The paper presents a way to transform pregroup grammars into contextfree grammars using functional composition The same technique can also be used for the proof-nets of multiplicative cyclic linear logic and for Lambek calculus allowing empty premises

Parsing Pregroup Grammars and Lambek Calculus Using Partial Composition

This paper is concerned with learning in the model of Gold the Categorial Dependency Grammars (CDG), which express discontin- uous (non-projective) dependencies. We show that rigid and k-valued CDG (without optional and iterative types) are learnable from strings. In fact, we prove that the languages of dependency nets coding rigid CDGs have nite elasticity, and we show a learning algorithm. As a standard corollary, this result leads to the learnability of rigid or k- valued CDGs (without optional and iterative types) from strings.

https://hal.archives-ouvertes.fr/hal-00487058/document

On learning discontinuous dependencies from positive data

Pregroup grammars are a context-free grammar formalism which may be used to describe the syntax of natural languages. However, this formalism is not able to naturally define types corresponding to optional and iterated arguments such as optional complements of verbs or verbs' adverbial modifiers. This paper introduces two constructions that make up for this deficiency.

Denis Béchet

Papers

A Complete Axiomatisation for the Inclusion of Series-Parallel Partial Orders

Dependency structure grammars

Parsing Pregroup Grammars and Lambek Calculus Using Partial Composition

On learning discontinuous dependencies from positive data

Optional and Iterated Types for Pregroup Grammars