Glue TAG semantics for binary branching syntactic structures

This thesis presents Gl-TAG, a new semantics for a fragment of natural language including simple in/transitive sentences with quantifiers. Gl-TAG utilises glue semantics, a proof-theoretic semantics based on linear logic, and TAG, a tree-based syntactic theory. We demonstrate that Gl-TAG is compositional, and bears interesting similarities to other approaches to the semantics of quantifiers. Chapter 1, rather than discussing the arguments of the thesis as a whole, outlines the global picture of language and semantic theory we adopt, introducing different semantics for quantification, so that Gl-TAG is understood in the proper context. Chapter 2, the heart of the thesis, introduces Gl-TAG, illustrating its application to quantifier scope ambiguity (Qscope ambiguity) and binding. Ways of constricting quantifier scope where necessary are suggested, but their full development is a topic of future research. Chapter 3 demonstrates that our semantics is compositional in certain formal senses there distinguished. Our account of quantification bears striking similarities to that proposed in Heim and Kratzer (1998), and also to Cooper storage (Cooper ((1983))); in fact, we can set up a form of Cooper storage within Gl-TAG. We suggest in conclusion that the features in common between frameworks highlight the possible formal similarities between the approaches. One philosophically interesting aspect of our semantics left aside is that it depends on proof theoretic methods; glue semantics combines semantic values both by harnessing the inferential power of linear logic and by exploiting the Curry-Howard isomorphism (CHI) familiar from proof theory (see chapter 2 for a brief explanation of the CHI). The semantic value of a proposition is thus a proof, as some proof theorists have desired (see Martin-Lof (1996). This raises a question for future research; namely, whether Gl-TAG is an inferential semantics in the sense that some philosophers have discussed (Murzi and Steinberger (2015))

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

Towards a constraint parser for categorial type logics

This thesis shows how constraint programming can be applied to the processing of Categorial Type Logics(CTL). It presents a novel formalisation of the parsing task for categorial grammars as a tree configuration problem, and demonstrates how a recent proposal for emph{structural constraints} on CTL parse trees can be integrated into this framework. The resulting processing model has been implemented using the Mozart programming environment. It appears to be a promising starting point for further research on the application of constraint parsing to CTL and the investigation of the practical processing complexity of CTL grammar fragments.}