Introducing a Calculus of Effects and Handlers for Natural Language Semantics

In compositional model-theoretic semantics, researchers assemble truth-conditions or other kinds of denotations using the lambda calculus. It was previously observed that the lambda terms and/or the denotations studied tend to follow the same pattern: they are instances of a monad. In this paper, we present an extension of the simply-typed lambda calculus that exploits this uniformity using the recently discovered technique of effect handlers. We prove that our calculus exhibits some of the key formal properties of the lambda calculus and we use it to construct a modular semantics for a small fragment that involves multiple distinct semantic phenomena

A Labelled Analytic Theorem Proving Environment for Categorial Grammar

We present a system for the investigation of computational properties of categorial grammar parsing based on a labelled analytic tableaux theorem prover. This proof method allows us to take a modular approach, in which the basic grammar can be kept constant, while a range of categorial calculi can be captured by assigning different properties to the labelling algebra. The theorem proving strategy is particularly well suited to the treatment of categorial grammar, because it allows us to distribute the computational cost between the algorithm which deals with the grammatical types and the algebraic checker which constrains the derivation.Comment: 11 pages, LaTeX2e, uses examples.sty and a4wide.st

Morphology Within the Parallel Architecture Framework : the Centrality of the Lexicon Below the Word Level

The Parallel Architecture (PA) framework (Jackendoff 2002, 2007, Culicover & Jackendoff 2005) is one of the most complete constraint-based linguistic theories that encompasses phonology, syntax and semantics. However, it lacks a fully developed model of word formation. More recently, a theory called Relational Morphology (RM) (Jackendoff & Audring 2020) has been developed, that integrates into the PA. The current study shows how the Slot Structure model (Benavides 2003, 2009, 2010), which is compatible with the PA and is based on the dual-route model and percolation of features (Pinker 1999, 2006; Huang & Pinker 2010), can provide a better account of morphology than RM, and can also be incorporated into the PA, thus contributing to make this a more explanatory framework. Spanish data are used as the basis to demonstrate the implementation of the SSM. The current paper demonstrates two key problems for RM: inconsistent and confusing coindexation, and a proliferation of schemas, and shows that these issues do not arise in the Slot Structure model. Overall, the paper points out significant drawbacks in the RM framework, while at the same time showing how the PA's morphological component can be enriched with the Slot Structure model

Categorial Grammar

The paper is a review article comparing a number of approaches to natural language syntax and semantics that have been developed using categorial frameworks. It distinguishes two related but distinct varieties of categorial theory, one related to Natural Deduction systems and the axiomatic calculi of Lambek, and another which involves more specialized combinatory operations

Paracompositionality, MWEs and Argument Substitution

Multi-word expressions, verb-particle constructions, idiomatically combining phrases, and phrasal idioms have something in common: not all of their elements contribute to the argument structure of the predicate implicated by the expression. Radically lexicalized theories of grammar that avoid string-, term-, logical form-, and tree-writing, and categorial grammars that avoid wrap operation, make predictions about the categories involved in verb-particles and phrasal idioms. They may require singleton types, which can only substitute for one value, not just for one kind of value. These types are asymmetric: they can be arguments only. They also narrowly constrain the kind of semantic value that can correspond to such syntactic categories. Idiomatically combining phrases do not subcategorize for singleton types, and they exploit another locally computable and compositional property of a correspondence, that every syntactic expression can project its head word. Such MWEs can be seen as empirically realized categorial possibilities, rather than lacuna in a theory of lexicalizable syntactic categories.Comment: accepted version (pre-final) for 23rd Formal Grammar Conference, August 2018, Sofi

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

Gapping as Constituent Coordination

A number of coordinate constructions in natural languages conjoin sequences which do not appear to correspond to syntactic constituents in the traditional sense. One striking instance of the phenomenon is afforded by the gapping construction of English, of which the following sentence is a simple example: (1) Harry eats beans, and Fred, potatoes Since all theories agree that coordination must in fact be an operation upon constituents, most of them have dealt with the apparent paradox presented by such constructions by supposing that such sequences as the right conjunct in the above example, Fred, potatoes, should be treated in the grammar as traditional constituents, of type S, but with pieces missing or deleted