Comparing and evaluating extended Lambek calculi

Lambeks Syntactic Calculus, commonly referred to as the Lambek calculus, was innovative in many ways, notably as a precursor of linear logic. But it also showed that we could treat our grammatical framework as a logic (as opposed to a logical theory). However, though it was successful in giving at least a basic treatment of many linguistic phenomena, it was also clear that a slightly more expressive logical calculus was needed for many other cases. Therefore, many extensions and variants of the Lambek calculus have been proposed, since the eighties and up until the present day. As a result, there is now a large class of calculi, each with its own empirical successes and theoretical results, but also each with its own logical primitives. This raises the question: how do we compare and evaluate these different logical formalisms? To answer this question, I present two unifying frameworks for these extended Lambek calculi. Both are proof net calculi with graph contraction criteria. The first calculus is a very general system: you specify the structure of your sequents and it gives you the connectives and contractions which correspond to it. The calculus can be extended with structural rules, which translate directly into graph rewrite rules. The second calculus is first-order (multiplicative intuitionistic) linear logic, which turns out to have several other, independently proposed extensions of the Lambek calculus as fragments. I will illustrate the use of each calculus in building bridges between analyses proposed in different frameworks, in highlighting differences and in helping to identify problems.Comment: Empirical advances in categorial grammars, Aug 2015, Barcelona, Spain. 201

Computational coverage of type logical grammar: The Montague test

It is nearly half a century since Montague made his contributions to the field of logical semantics. In this time, computational linguistics has taken an almost entirely statistical turn and mainstream linguistics has adopted an almost entirely non-formal methodology. But in a minority approach reaching back before the linguistic revolution, and to the origins of computing, type logical grammar (TLG) has continued championing the flags of symbolic computation and logical rigor in discrete grammar. In this paper, we aim to concretise a measure of progress for computational grammar in the form of the Montague Test. This is the challenge of providing a computational cover grammar of the Montague fragment. We formulate this Montague Test and show how the challenge is met by the type logical parser/theorem-prover CatLog2.Peer ReviewedPostprint (published version

Semantically inactive multiplicatives and words as types

The literature on categorial type logic includes proposals for semantically inactive additives, quantifiers, and modalities (Morrill 1994[17]; Hepple 1990[2]; Moortgat 1997[9]), but to our knowledge there has been no proposal for semantically inactive multiplicatives. In this paper we formulate such a proposal (thus filling a gap in the typology of categorial connectives) in the context of the displacement calculus Morrill et al. (2011[16]), and we give a formulation of words as types whereby for every expression w there is a corresponding type W(w). We show how this machinary can treat the syntax and semantics of collocations involving apparently contentless words such as expletives, particle verbs, and (discontinuous) idioms. In addition, we give an account in these terms of the only known examples treated by Hybrid Type Logical Grammar (HTLG henceforth; Kubota and Levine 2012[4]) beyond the scope of unaugmented displacement calculus: gapping of particle verbs and discontinuous idioms.Peer ReviewedPostprint (author’s final draft

RDF Knowledge Graph Visualization From a Knowledge Extraction System

In this paper, we present a system to visualize RDF knowledge graphs. These graphs are obtained from a knowledge extraction system designed by GEOLSemantics. This extraction is performed using natural language processing and trigger detection. The user can visualize subgraphs by selecting some ontology features like concepts or individuals. The system is also multilingual, with the use of the annotated ontology in English, French, Arabic and Chinese

Grammar logicised: relativisation

Many variants of categorial grammar assume an underlying logic which is associative and linear. In relation to left extraction, the former property is challenged by island domains, which involve nonassociativity, and the latter property is challenged by parasitic gaps, which involve nonlinearity. We present a version of type logical grammar including ‘structural inhibition’ for nonassociativity and ‘structural facilitation’ for nonlinearity and we give an account of relativisation including islands and parasitic gaps and their interaction.Peer ReviewedPostprint (published version

Linguistic explanation and domain specialization: a case study in bound variable anaphora

The core question behind this Frontiers research topic is whether explaining linguistic phenomena requires appeal to properties of human cognition that are specialised to language. We argue here that investigating this issue requires taking linguistic research results seriously, and evaluating these for domain-specificity. We present a particular empirical phenomenon, bound variable interpretations of pronouns dependent on a quantifier phrase, and argue for a particular theory of this empirical domain that is couched at a level of theoretical depth which allows its principles to be evaluated for domain-specialisation. We argue that the relevant principles are specialised when they apply in the domain of language, even if analogues of them are plausibly at work elsewhere in cognition or the natural world more generally. So certain principles may be specialised to language, though not, ultimately, unique to it. Such specialisation is underpinned by ultimately biological factors, hence part of UG

Overtly anaphoric control in type logical grammar

In this paper we analyse anaphoric pronouns in control sentences and we investigate the implications of these kinds of sentences in relation to the Propositional Theory versus Property Theory question. For these purposes, we invoke the categorial calculus with limited contraction, a conservative extension of Lambek calculus that builds contraction into the logical rules for a customized slash type-constructor.Peer ReviewedPostprint (author's final draft

The Grail theorem prover: Type theory for syntax and semantics

As the name suggests, type-logical grammars are a grammar formalism based on logic and type theory. From the prespective of grammar design, type-logical grammars develop the syntactic and semantic aspects of linguistic phenomena hand-in-hand, letting the desired semantics of an expression inform the syntactic type and vice versa. Prototypical examples of the successful application of type-logical grammars to the syntax-semantics interface include coordination, quantifier scope and extraction.This chapter describes the Grail theorem prover, a series of tools for designing and testing grammars in various modern type-logical grammars which functions as a tool . All tools described in this chapter are freely available