Higher-order Linear Logic Programming of Categorial Deduction

We show how categorial deduction can be implemented in higher-order (linear) logic programming, thereby realising parsing as deduction for the associative and non-associative Lambek calculi. This provides a method of solution to the parsing problem of Lambek categorial grammar applicable to a variety of its extensions.Comment: 8 pages LaTeX, uses eaclap.sty, to appear EACL9

Efficient Normal-Form Parsing for Combinatory Categorial Grammar

Under categorial grammars that have powerful rules like composition, a simple n-word sentence can have exponentially many parses. Generating all parses is inefficient and obscures whatever true semantic ambiguities are in the input. This paper addresses the problem for a fairly general form of Combinatory Categorial Grammar, by means of an efficient, correct, and easy to implement normal-form parsing technique. The parser is proved to find exactly one parse in each semantic equivalence class of allowable parses; that is, spurious ambiguity (as carefully defined) is shown to be both safely and completely eliminated.Comment: 8 pages, LaTeX packaged with three .sty files, also uses cgloss4e.st

LexGram - a practical categorial grammar formalism -

We present the LexGram system, an amalgam of (Lambek) categorial grammar and Head Driven Phrase Structure Grammar (HPSG), and show that the grammar formalism it implements is a well-structured and useful tool for actual grammar development.Comment: 16 page

A Structural Interpretation of Combinatory Categorial Grammar

This paper gives an interpretation of Combinatory Categorial Grammar derivations in terms of the construction of traditional phrase structure trees. This structural level of representation not only shows how CCG is related to other grammatical investigations, but this paper also uses it to extend CCG in ways which are useful for analyzing and parsing natural language, including a better analysis of coordination

Parsing/theorem-proving for logical grammar CatLog3

CatLog3 is a 7000 line Prolog parser/theorem-prover for logical categorial grammar. In such logical categorial grammar syntax is universal and grammar is reduced to logic: an expression is grammatical if and only if an associated logical statement is a theorem of a fixed calculus. Since the syntactic component is invariant, being the logic of the calculus, logical categorial grammar is purely lexicalist and a particular language model is defined by just a lexical dictionary. The foundational logic of continuity was established by Lambek (Am Math Mon 65:154–170, 1958) (the Lambek calculus) while a corresponding extension including also logic of discontinuity was established by Morrill and Valentín (Linguist Anal 36(1–4):167–192, 2010) (the displacement calculus). CatLog3 implements a logic including as primitive connectives the continuous (concatenation) and discontinuous (intercalation) connectives of the displacement calculus, additives, 1st order quantifiers, normal modalities, bracket modalities, and universal and existential subexponentials. In this paper we review the rules of inference for these primitive connectives and their linguistic applications, and we survey the principles of Andreoli’s focusing, and of a generalisation of van Benthem’s count-invariance, on the basis of which CatLog3 is implemented.Peer ReviewedPostprint (author's final draft

Geometry of language

Girard (1987) introduced proof nets as a syntax of linear proofs which eliminates inessential rule ordering manifested by sequent calculus. Proof nets adapted to the Lambek calculus (Roorda 1991) fulfill a role in categorial grammar analogous to that of phrase structure trees in CFG so that categorial proof nets have a central part to play in computational syntax and semantics; in particular they allow a reinterpretation of the "problem" of spurious ambiguity as an opportunity for parallelism. This article aims to make three contributions: i) provide a tutorial overview of categorial proof nets, ii) apply and provide motivation for proof nets by showing how a partial execution eschews the need for semantic evaluation in language processing, and iii) analyse the intrinsic geometry of partially commutative proof nets for the kinds of discontinuity attested in language, offering proof nets for the in situ binder type-constructor Q(., ., .) of Moortgat (1991/6).Postprint (published version

Type-driven natural language analysis

The purpose of this thesis is in showing how recent developments in logic programming can be exploited to encode in a computational environment the features of certain linguistic theories. We are in this way able to make available for the purpose of natural language processing sophisticated capabilities of linguistic analysis directly justified by well developed grammatical frameworks. More specifically, we exploit hypothetical reasoning, recently proposed as one of the possible directions to widen logic programming, to account for the syntax of filler-gap dependencies along the lines of linguistic theories such as Generalized Phrase Structure Grammar and Categorial Grammar. Moreover, we make use, for the purpose of semantic analysis of the same kind of phenomena, of another recently proposed extension, interestingly related to the previous one, namely the idea of replacing first-order terms with the more expressive λ-terms of λ-Calculus

Towards a constraint parser for categorial type logics

This thesis shows how constraint programming can be applied to the processing of Categorial Type Logics(CTL). It presents a novel formalisation of the parsing task for categorial grammars as a tree configuration problem, and demonstrates how a recent proposal for emph{structural constraints} on CTL parse trees can be integrated into this framework. The resulting processing model has been implemented using the Mozart programming environment. It appears to be a promising starting point for further research on the application of constraint parsing to CTL and the investigation of the practical processing complexity of CTL grammar fragments.}