Multi-dimensional Type Theory: Rules, Categories, and Combinators for Syntax and Semantics

We investigate the possibility of modelling the syntax and semantics of natural language by constraints, or rules, imposed by the multi-dimensional type theory Nabla. The only multiplicity we explicitly consider is two, namely one dimension for the syntax and one dimension for the semantics, but the general perspective is important. For example, issues of pragmatics could be handled as additional dimensions. One of the main problems addressed is the rather complicated repertoire of operations that exists besides the notion of categories in traditional Montague grammar. For the syntax we use a categorial grammar along the lines of Lambek. For the semantics we use so-called lexical and logical combinators inspired by work in natural logic. Nabla provides a concise interpretation and a sequent calculus as the basis for implementations.Comment: 20 page

CHR Grammars

A grammar formalism based upon CHR is proposed analogously to the way Definite Clause Grammars are defined and implemented on top of Prolog. These grammars execute as robust bottom-up parsers with an inherent treatment of ambiguity and a high flexibility to model various linguistic phenomena. The formalism extends previous logic programming based grammars with a form of context-sensitive rules and the possibility to include extra-grammatical hypotheses in both head and body of grammar rules. Among the applications are straightforward implementations of Assumption Grammars and abduction under integrity constraints for language analysis. CHR grammars appear as a powerful tool for specification and implementation of language processors and may be proposed as a new standard for bottom-up grammars in logic programming. To appear in Theory and Practice of Logic Programming (TPLP), 2005Comment: 36 pp. To appear in TPLP, 200

Logical grammars based on constraint handling rules

Abstract. A grammar formalism called GHRG based on CHR is proposed analogously to the way Definite Clause Grammars are defined and implemented on top of Prolog. A CHRG executes as a robust bottom-up parser with an inherent treatment of ambiguity. The rules of a CHRG may refer to grammar symbols on either side of a sequence to be matched and this provides a powerful way to let parsing and attribute evaluation depend on linguistic context; examples show disambiguation of simple and ambiguous context-free rules and a handling of coordination in natural language. CHRGs may have rules to produce and consume arbitrary hypothesis and as an important application is shown an implementation of Assumption Grammars.