7,672 research outputs found
Hybrid Type-Logical Grammars, First-Order Linear Logic and the Descriptive Inadequacy of Lambda Grammars
In this article we show that hybrid type-logical grammars are a fragment of
first-order linear logic. This embedding result has several important
consequences: it not only provides a simple new proof theory for the calculus,
thereby clarifying the proof-theoretic foundations of hybrid type-logical
grammars, but, since the translation is simple and direct, it also provides
several new parsing strategies for hybrid type-logical grammars. Second,
NP-completeness of hybrid type-logical grammars follows immediately. The main
embedding result also sheds new light on problems with lambda grammars/abstract
categorial grammars and shows lambda grammars/abstract categorial grammars
suffer from problems of over-generation and from problems at the
syntax-semantics interface unlike any other categorial grammar
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
A Compositional Treatment of Polysemous Arguments in Categorial Grammar
We discuss an extension of the standard logical rules (functional application
and abstraction) in Categorial Grammar (CG), in order to deal with some
specific cases of polysemy. We borrow from Generative Lexicon theory which
proposes the mechanism of {\em coercion}, next to a rich nominal lexical
semantic structure called {\em qualia structure}.
In a previous paper we introduced coercion into the framework of {\em
sign-based} Categorial Grammar and investigated its impact on traditional
Fregean compositionality. In this paper we will elaborate on this idea, mostly
working towards the introduction of a new semantic dimension. Where in current
versions of sign-based Categorial Grammar only two representations are derived:
a prosodic one (form) and a logical one (modelling), here we introduce also a
more detaled representation of the lexical semantics. This extra knowledge will
serve to account for linguistic phenomena like {\em metonymy\/}.Comment: LaTeX file, 19 pages, uses pubsmacs, pubsbib, pubsarticle, leqn
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
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