Denys Duchier

A model-theoretic framework for grammaticality judgements

Although the observation of grammaticality judgements is well acknowledged, their formal representation faces problems of different kinds: linguistic, psycholinguistic, logical, computational. In this paper we focus on addressing some of the logical and computational aspects, relegating the linguistic and psycholinguistic ones in the parameter space. We introduce a model-theoretic interpretation of Property Grammars, which lets us formulate numerical accounts of grammaticality judgements. Such a representation allows for both clear-cut binary judgements, and graded judgements. We discriminate between problems of Intersective Gradience (i.e., concerned with choosing the syntactic category of a model among a set of candidates) and problems of Subsective Gradience (i.e., concerned with estimating the degree of grammatical acceptability of a model). Intersective Gradience is addressed as an optimisation problem, while Subsective Gradience is addressed as an approximation problem.

Fractal Parallelism: Solving SAT in Bounded Space and Time

Abstract geometrical computation can solve NP-complete problems efficiently: any boolean constraint satisfaction problem, instance of SAT, can be solved in bounded space and time with simple geometrical constructions involving only drawing parallel lines on a Euclidean space-time plane. Complexity as the maximal length of a sequence of consecutive segments is quadratic. The geometrical algorithm achieves massive parallelism: an exponential number of cases are explored simultaneously. The construction relies on a fractal pattern and requires the same amount of space and time independently of the SAT formula.

Computing in the fractal cloud: modular generic solvers for SAT and Q-SAT variants

Abstract geometrical computation can solve hard combinatorial problems efficiently: we showed previously how Q-SAT --the satisfiability problem of quantified boolean formulae-- can be solved in bounded space and time using instance-specific signal machines and fractal parallelization. In this article, we propose an approach for constructing a particular generic machine for the same task. This machine deploys the Map/Reduce paradigm over a discrete fractal structure. Moreover our approach is modular : the machine is constructed by combining modules. In this manner, we can easily create generic machines for solving satifiability variants, such as SAT, #SAT, MAX-SAT.

Property grammar parsing seen as a constraint optimization problem

Blache [1] introduced Property Grammar as a formalism where linguistic information is represented in terms of non hierarchical constraints. This feature gives it an adequate expressive power to handle complex linguistic phenomena, such as long distance dependencies, and also agrammatical sentences [2]. n nRecently, Duchier et al. [3] proposed a model-theoretic semantics for property grammar. The present paper follows up on that work and explains how to turn such a formalization into a constraint optimization problem, solvable using constraint programming techniques. This naturally leads to an implementation of a fully constraint-based parser for property grammars.

Massively Parallel Automata in Euclidean Space-Time

In the cellular automata (CA) literature, discrete lines in discrete space-time diagrams are often idealized as Euclidean lines in order to design CA or analyze their dynamic behavior. In this paper, we present a parallel model of computation corresponding to this idealization: dimensionless particles move uniformely at fixed velocities along the real line and are transformed when they collide. Like CA, this model is parallel, uniform in space-time and uses local updating. The main difference is the use of the continuity of space and time, which we proceed to illustrate with a construction to solve Q-SAT, the satisfiability problem for quantified boolean formulae, in bounded space and time, and quadratic collision depth.

Model-theory and implementation of property grammars with features

Property Grammar (PG) is a formalism introduced by Blache (Blache, 2000), which aims at describing syntax in terms of local constraints that can be independently violated. A promising feature of this formalism lies in its ability to account for ungrammatical utterances, thus departing from classical formalisms of generative-enumerative syntax. In this article, we present a model-theoretic description of PG that improves on previous work by providing support for properties augmented with feature constraints. (e.g., the requirement and agreement properties). While providing a formal definition of the semantics of feature-based PG, we illustrate various uses of features within this formalism and give a general framework to interpret them. In a second part, we show how this formalization of PG can be turned into a Constraint Optimization Problem to implement a PG parser that supports the computation of both syntactic trees (for grammatical sentences) and quasi-syntactic trees (i.e., linguistically motivated syntactic structure for ungrammatical utterances). Finally we briefly report on the implementation of such a parser using the Gecode library for Constraint Programming.

High-level methodologies for grammar engineering, introduction to the special issue

Grammar Engineering is the task of designing and implementing linguistically motivated electronic descriptions of natural language (so-called grammars). These grammars are expressed within well-defined theoretical frameworks, and offer a fine-grained description of natural language. While grammars were first used to describe syntax, that is to say, the relations between constituents in a sentence, they often go beyond syntax and include semantic information. Grammar engineering provides precise descriptions which can be used for natural language understanding and generation, making these valuable resources for various natural language applications, including textual entailment, dialogue systems, or machine translation. The first attempts at designing large-scale resource grammars were costly because of the complexity of the task (Erbach et al. 1990) and of the number of persons that were needed (see e.g. Doran et al. 1997). Advances in the field have led to the development of environments for semi-automatic grammar engineering, borrowing ideas from compilation (grammar engineering is compared with software development) and machine learning. This special issue reports on new trends in the field, where grammar engineering benefits from elaborate high-level methodologies and techniques, dealing with various issues (both theoretical and practical).

XMGź2: Describing Description Languages

This paper introduces XMGi¾ź2, a modular and extensible tool for various linguistic description tasks. Based on the notion of meta-compilation that is, compilation of compilers, XMGi¾ź2 reuses the main concepts underlying XMG, namely logic programming and constraint satisfaction, to generate on-demand XMG-like compilers by assembling elementary units called bricks. This brick-based definition of compilers permits users to design description languages in a highly flexible way. In particular, it makes it possible to support several levels of linguistic description e.g. syntax, morphology within a single description language. XMGi¾ź2 aims to offer means for users to easily define description languages that fit as much as possible the linguistic intuition.

Constraint Solving and Language Processing

In this talk, we argue for a shift of perspective into defining grammars as mechanisms for incremental growth of interpretation reflecting the time-line of processing (Dynamic Syntax: Kempson et al. 2001, Cann et al. 2005, Chatzikyriakidis & Kempson 2011). The core syntactic notion of this framework is that of monotonic context-relative tree growth (following Blackburn & Meyer-Viol 1994), with both content and structural parameters of underspecification and update. Our case study is the puzzle of clitic pronoun clusters of Modern Greek dialects, which illustrate both the low level morphological idiosyncracy of such clusterings, and yet the broad cross-linguistic constraints to which they are subject: these dialects display variants of the so-called Person Case Constraint, a constraint whose generality continues to provide a major challenge for current theoretical frameworks (Adger & Harbour 2007, Heap 2005, among others). We show first how the limits on variation displayed in such clusters are explicable in terms of a constraint debarring more than one underspecified tree relation of a type at a time, a constraint only expressible in a dynamical grammar framework; and we give an analysis of Greek dialectal variation in these terms. Then we explore the consequences of this theoretical perspective, viz. the domaingenerality of the system of growth underpinning natural-language syntax; and we will suggest that metrical ambiguities and metrical dissonance displayed in music (Vazan & Schober 2004, London 2012) are subject to the same restriction on real-time structural processing.