A Model-Theoretic Framework for Grammaticality Judgements

Abstract

Abstract. 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.

A logical approach to grammar description

“…Our representation of syntactic structures has a lot in common with f-structures in Lexical Functional Grammars (LFG; Bresnan 2001, Dalrymple 2001, except that we use logic, rather than unification, to describe them. This makes our approach very close in spirit to dependency grammars such as Bröker (1998), Debusmann et al (2004), and Foth et al (2005), property grammars (Blache 2001) and their model theoretic formalization (Duchier et al 2009(Duchier et al , 2012(Duchier et al , 2014. Most of the fundamental ideas we use in our formalization are similar to those works, in particular Bröker (1998) also proposes to separate syntactic description from linearization.…”

Property Grammar Parsing Seen as a Constraint Optimization Problem

“…These constraints rely on linguistic observations, such as linear precedence between constituents, coocurrency between constituents, exclusion between constituents, etc. As suggested by Duchier et al [3], a property grammar can be usefully understood as exploding classical phrase structure rules into collections of fine-grained properties. Each property has the form A : ψ meaning that, in a syntactic tree, for a node of category A, the constraint ψ applies to its children.…”

“…In this section, we give a summary of the model-theoretic semantics of PG developed by Duchier et al [3].…”

“…Prost [5] developed an approach based on PG and capable not only of providing analyses for any utterances, but also of making accurate judgements of grammaticality about them. Duchier et al [3] provided model-theoretical semantics for PG and a formal logical account of Prost's work. In this paper, we show how such a formalization can be converted into a Constraint Optimization Problem, thus yielding a constraint-based parser that finds optimal parses using classical constraint programming techniques, such as branch-and-bound.…”

“…We first introduce property grammars (section 2). In section 3, we then summarize the model-theoretic semantics of PG, as defined by Duchier et al [3]. This semantics is used to define PG parsing as a Constraint Optimization Problem.…”