394 research outputs found
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
TRX: A Formally Verified Parser Interpreter
Parsing is an important problem in computer science and yet surprisingly
little attention has been devoted to its formal verification. In this paper, we
present TRX: a parser interpreter formally developed in the proof assistant
Coq, capable of producing formally correct parsers. We are using parsing
expression grammars (PEGs), a formalism essentially representing recursive
descent parsing, which we consider an attractive alternative to context-free
grammars (CFGs). From this formalization we can extract a parser for an
arbitrary PEG grammar with the warranty of total correctness, i.e., the
resulting parser is terminating and correct with respect to its grammar and the
semantics of PEGs; both properties formally proven in Coq.Comment: 26 pages, LMC
A Paraconsistent Higher Order Logic
Classical logic predicts that everything (thus nothing useful at all) follows
from inconsistency. A paraconsistent logic is a logic where an inconsistency
does not lead to such an explosion, and since in practice consistency is
difficult to achieve there are many potential applications of paraconsistent
logics in knowledge-based systems, logical semantics of natural language, etc.
Higher order logics have the advantages of being expressive and with several
automated theorem provers available. Also the type system can be helpful. We
present a concise description of a paraconsistent higher order logic with
countable infinite indeterminacy, where each basic formula can get its own
indeterminate truth value (or as we prefer: truth code). The meaning of the
logical operators is new and rather different from traditional many-valued
logics as well as from logics based on bilattices. The adequacy of the logic is
examined by a case study in the domain of medicine. Thus we try to build a
bridge between the HOL and MVL communities. A sequent calculus is proposed
based on recent work by Muskens.Comment: Originally in the proceedings of PCL 2002, editors Hendrik Decker,
Joergen Villadsen, Toshiharu Waragai (http://floc02.diku.dk/PCL/). Correcte
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Unsupervised Formal Grammar Induction with Confidence
I present a novel algorithm for minimally supervised formal grammar induction using a linguistically-motivated grammar formalism. This algorithm, called the Missing Link algorithm (ML), is built off of classic chart parsing methods, but makes use of a probabilistic confidence measure to keep track of potentially ambiguous lexical items. Because ML uses a structured grammar formalism, each step of the algorithm can be easily understood by linguists, making it ideal for studying the learnability of different linguistic phenomena. The algorithm requires minimal annotation in its training data, but is capable of learning nuanced data from relatively small training sets and can be applied to a variety of grammar formalisms. Though evaluating an unsupervised syntactic model is difficult, I present an evaluation using the Corpus of Linguistic Acceptability and show state-of-the-art performance
Montague Grammar Induction
We propose a computational model for inducing full-fledged combinatory categorial grammars from behavioral data. This model contrasts with prior computational models of selection in representing syntactic and semantic types as structured (rather than atomic) objects, enabling direct interpretation of the modeling results relative to standard formal frameworks. We investigate the grammar our model induces when fit to a lexicon-scale acceptability judgment dataset – Mega Acceptability – focusing in particular on the types our model assigns to clausal complements and the predicates that select them
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
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