277 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
Efficient Normal-Form Parsing for Combinatory Categorial Grammar
Under categorial grammars that have powerful rules like composition, a simple
n-word sentence can have exponentially many parses. Generating all parses is
inefficient and obscures whatever true semantic ambiguities are in the input.
This paper addresses the problem for a fairly general form of Combinatory
Categorial Grammar, by means of an efficient, correct, and easy to implement
normal-form parsing technique. The parser is proved to find exactly one parse
in each semantic equivalence class of allowable parses; that is, spurious
ambiguity (as carefully defined) is shown to be both safely and completely
eliminated.Comment: 8 pages, LaTeX packaged with three .sty files, also uses cgloss4e.st
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
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
Parsing Combinatory Categorial Grammar with Answer Set Programming: Preliminary Report
Combinatory categorial grammar (CCG) is a grammar formalism used for natural
language parsing. CCG assigns structured lexical categories to words and uses a
small set of combinatory rules to combine these categories to parse a sentence.
In this work we propose and implement a new approach to CCG parsing that relies
on a prominent knowledge representation formalism, answer set programming (ASP)
- a declarative programming paradigm. We formulate the task of CCG parsing as a
planning problem and use an ASP computational tool to compute solutions that
correspond to valid parses. Compared to other approaches, there is no need to
implement a specific parsing algorithm using such a declarative method. Our
approach aims at producing all semantically distinct parse trees for a given
sentence. From this goal, normalization and efficiency issues arise, and we
deal with them by combining and extending existing strategies. We have
implemented a CCG parsing tool kit - AspCcgTk - that uses ASP as its main
computational means. The C&C supertagger can be used as a preprocessor within
AspCcgTk, which allows us to achieve wide-coverage natural language parsing.Comment: 12 pages, 2 figures, Proceedings of the 25th Workshop on Logic
Programming (WLP 2011
\u3ci\u3eCorrect Reasoning: Essays on Logic-Based AI in Honour of Vladimir Lifschitz\u3c/i\u3e
Co-edited by Yuliya Lierler, UNO faculty member.
Essay, Parsing Combinatory Categorial Grammar via Planning in Answer Set Programming, co-authored by Yuliya Lierler, UNO faculty member.
This Festschrift published in honor of Vladimir Lifschitz on the occasion of his 65th birthday presents 39 articles by colleagues from all over the world with whom Vladimir Lifschitz had cooperation in various respects. The 39 contributions reflect the breadth and the depth of the work of Vladimir Lifschitz in logic programming, circumscription, default logic, action theory, causal reasoning and answer set programming.https://digitalcommons.unomaha.edu/facultybooks/1231/thumbnail.jp
Efficient Parsing for French
International audienceParsing with categorial grammars often leads to problems such as proliferating lexical ambiguity, spurious parses and overgeneration. This paper presents a parser for French developed on an unification based categorial grammar (FG) which avoids these problems. This parser is a bottom-up chart parser augmented with a heuristic eliminating spurious parses. The unicity and completeness of parsing are proved
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
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
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