463 research outputs found
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
Type-driven semantic interpretation and feature dependencies in R-LFG
Once one has enriched LFG's formal machinery with the linear logic mechanisms
needed for semantic interpretation as proposed by Dalrymple et. al., it is
natural to ask whether these make any existing components of LFG redundant. As
Dalrymple and her colleagues note, LFG's f-structure completeness and coherence
constraints fall out as a by-product of the linear logic machinery they propose
for semantic interpretation, thus making those f-structure mechanisms
redundant. Given that linear logic machinery or something like it is
independently needed for semantic interpretation, it seems reasonable to
explore the extent to which it is capable of handling feature structure
constraints as well.
R-LFG represents the extreme position that all linguistically required
feature structure dependencies can be captured by the resource-accounting
machinery of a linear or similiar logic independently needed for semantic
interpretation, making LFG's unification machinery redundant. The goal is to
show that LFG linguistic analyses can be expressed as clearly and perspicuously
using the smaller set of mechanisms of R-LFG as they can using the much larger
set of unification-based mechanisms in LFG: if this is the case then we will
have shown that positing these extra f-structure mechanisms is not
linguistically warranted.Comment: 30 pages, to appear in the the ``Glue Language'' volume edited by
Dalrymple, uses tree-dvips, ipa, epic, eepic, fullnam
Grammatical structures and logical deductions
The three essays presented here concern natural connections between grammatical derivations and structures provided by certain standard grammar formalisms, on the one hand, and deductions in logical systems, on the other hand. In the first essay we analyse the adequacy of Polish notation for higher-order languages. The Ajdukiewicz algorithm (Ajdukiewicz 1935) is discussed in terms of generalized MP-deductions. We exhibit a failure in Ajdukiewicz’s original version of the algorithm and give a correct one; we prove that generalized MP-deductions have the frontier property, which is essential for the plausibility of Polish notation. The second essay deals with logical systems corresponding to different grammar formalisms, as e.g. Finite State Acceptors, Context-Free Grammars, Categorial Grammars, and others. We show how can logical methods be used to establish certain linguistically significant properties of formal grammars. The third essay discusses the interplay between Natural Deduction proofs in grammar oriented logics and semantic structures expressible by typed lambda terms and combinators
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Formalizing graphical notations
The thesis describes research into graphical notations for software engineering, with a principal interest in ways of formalizing them. The research seeks to provide a theoretical basis that will help in designing both notations and the software tools that process them.
The work starts from a survey of literature on notation, followed by a review of techniques for formal description and for computational handling of notations. The survey concentrates on collecting views of the benefits and the problems attending notation use in software development; the review covers picture description languages, grammars and tools such as generic editors and visual programming environments. The main problem of notation is found to be a lack of any coherent, rigorous description methods. The current approaches to this problem are analysed as lacking in consensus on syntax specification and also lacking a clear focus on a defined concept of notated expression.
To address these deficiencies, the thesis embarks upon an exploration of serniotic, linguistic and logical theory; this culminates in a proposed formalization of serniosis in notations, using categorial model theory as a mathematical foundation. An argument about the structure of sign systems leads to an analysis of notation into a layered system of tractable theories, spanning the gap between expressive pictorial medium and subject domain. This notion of 'tectonic' theory aims to treat both diagrams and formulae together.
The research gives details of how syntactic structure can be sketched in a mathematical sense, with examples applying to software development diagrams, offering a new solution to the problem of notation specification. Based on these methods, the thesis discusses directions for resolving the harder problems of supporting notation design, processing and computer-aided generic editing. A number of future research areas are thereby opened up. For practical trial of the ideas, the work proceeds to the development and partial implementation of a system to aid the design of notations and editors. Finally the thesis is evaluated as a contribution to theory in an area which has not attracted a standard approach
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