Exploring a type-theoretic approach to accessibility constraint modelling

Accessibility constraints When dealing with anaphora resolution, anaphoric expressions are often considered to have access to a restricted set of discourse referents. The choice of the relevant discourse referent inside this set may depends on various kinds of information (morphosyntactic features, semantic features, salience. . . ). But theories that give a dynamic interpretation of language also provide some ways to restrict the set of discourse referents by stating accessibility constraints. The description of these constraints depends on the chosen formal theory of discourse interpretation. For instance, DRT [5] describes the accessibility constraints using DRS subordination. Taking into account the hierarchical structure of discourse, SDRT [2] uses DRS subordination together with an outscoping relation between discourse units. In both cases, the constraints are based on the structure of the discourse: for DRT, the structure arises from the negation while for SDRT it also arises from the nature of the relation between discourse units. In the latter case, it gives a formal definition of the Right Frontier Constraint (RFC) [1]. [3] proposes a modelling of DRT that fits Montague’s semantic framework. In this approach, the logical quantifiers have their standard scoping definitions and free and bound variables also have their standard definitions. One of the advantages is to use standard notions (such as De Bruijn’s indices for λ-calculus) for implementing variable renaming in semantic systems based on λ-calculus, instead of implementing specific and complex work-around. [3] also advocates its independence from any specific theory. While [3] exemplifies the DRT view on accessibility constraints, the work we propose here consists in exploring this approach in modelling two other kinds of accessibility constraints: the accessibility to proper nouns in DRT and the RFC.