45,057 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
On the Relation between Context-Free Grammars and Parsing Expression Grammars
Context-Free Grammars (CFGs) and Parsing Expression Grammars (PEGs) have
several similarities and a few differences in both their syntax and semantics,
but they are usually presented through formalisms that hinder a proper
comparison. In this paper we present a new formalism for CFGs that highlights
the similarities and differences between them. The new formalism borrows from
PEGs the use of parsing expressions and the recognition-based semantics. We
show how one way of removing non-determinism from this formalism yields a
formalism with the semantics of PEGs. We also prove, based on these new
formalisms, how LL(1) grammars define the same language whether interpreted as
CFGs or as PEGs, and also show how strong-LL(k), right-linear, and LL-regular
grammars have simple language-preserving translations from CFGs to PEGs
Implicit learning of recursive context-free grammars
Context-free grammars are fundamental for the description of linguistic syntax. However, most artificial grammar learning
experiments have explored learning of simpler finite-state grammars, while studies exploring context-free grammars have
not assessed awareness and implicitness. This paper explores the implicit learning of context-free grammars employing
features of hierarchical organization, recursive embedding and long-distance dependencies. The grammars also featured
the distinction between left- and right-branching structures, as well as between centre- and tail-embedding, both
distinctions found in natural languages. People acquired unconscious knowledge of relations between grammatical classes
even for dependencies over long distances, in ways that went beyond learning simpler relations (e.g. n-grams) between
individual words. The structural distinctions drawn from linguistics also proved important as performance was greater for
tail-embedding than centre-embedding structures. The results suggest the plausibility of implicit learning of complex
context-free structures, which model some features of natural languages. They support the relevance of artificial grammar
learning for probing mechanisms of language learning and challenge existing theories and computational models of
implicit learning
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
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
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