Ordered Tree Decomposition for HRG Rule Extraction

We present algorithms for extracting Hyperedge Replacement Grammar (HRG) rules from a graph along with a vertex order. Our algorithms are based on finding a tree decomposition of smallest width, relative to the vertex order, and then extracting one rule for each node in this structure. The assumption of a fixed order for the vertices of the input graph makes it possible to solve the problem in polynomial time, in contrast to the fact that the problem of finding optimal tree decompositions for a graph is NP-hard. We also present polynomial-time algorithms for parsing based on our HRGs, where the input is a vertex sequence and the output is a graph structure. The intended application of our algorithms is grammar extraction and parsing for semantic representation of natural language. We apply our algorithms to data annotated with Abstract Meaning Representations and report on the characteristics of the resulting grammars

Probabilistic graph formalisms for meaning representations

In recent years, many datasets have become available that represent natural language semantics as graphs. To use these datasets in natural language processing (NLP), we require probabilistic models of graphs. Finite-state models have been very successful for NLP tasks on strings and trees because they are probabilistic and composable. Are there equivalent models for graphs? In this thesis, we survey several graph formalisms, focusing on whether they are probabilistic and composable, and we contribute several new results. In particular, we study the directed acyclic graph automata languages (DAGAL), the monadic second-order graph languages (MSOGL), and the hyperedge replacement languages (HRL). We prove that DAGAL cannot be made probabilistic, we explain why MSOGL also most likely cannot be made probabilistic, and we review the fact that HRL are not composable. We then review a subfamily of HRL and MSOGL: the regular graph languages (RGL; Courcelle 1991), which have not been widely studied, and particularly have not been studied in an NLP context. Although Courcelle (1991) only sketches a proof, we present a full, more NLP-accessible proof that RGL are a subfamily of MSOGL. We prove that RGL are probabilistic and composable, and we provide a novel Earley-style parsing algorithm for them that runs in time linear in the size of the input graph. We compare RGL to two other new formalisms: the restricted DAG languages (RDL; Bj¨orklund et al. 2016) and the tree-like languages (TLL; Matheja et al. 2015). We show that RGL and RDL are incomparable; TLL and RDL are incomparable; and either RGL are incomparable to TLL, or RGL are contained within TLL. This thesis provides a clearer picture of this field from an NLP perspective, and suggests new theoretical and empirical research directions

Object-oriented engineering of visual languages

Visual languages are notations that employ graphics (icons, diagrams) to present information in a two or more dimensional space. This work focuses on diagrammatic visual languages, as found in software engineering, and their computer implementations. Implementation means the development of processors to automatically analyze diagrams and the development of graphical editors for constructing the diagrams. We propose a rigorous implementation technique that uses a formal grammar to specify the syntax of a visual language and that uses parsing to automatically analyze the visual sentences generated by the grammar. The theoretical contributions of our work are an original treatment of error handling (error detection, reporting, and recovery) in off-line visual language parsing, and the source-to-source translation of visual languages. We have also substantially extended an existing grammatical model for multidimensional languages, called atomic relational grammars. We have added support for meta-language expressions that denote optional and repetitive right-hand-side elements. We hav

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

Graphical Models with Structured Factors, Neural Factors, and Approximation-aware Training

This thesis broadens the space of rich yet practical models for structured prediction. We introduce a general framework for modeling with four ingredients: (1) latent variables, (2) structural constraints, (3) learned (neural) feature representations of the inputs, and (4) training that takes the approximations made during inference into account. The thesis builds up to this framework through an empirical study of three NLP tasks: semantic role labeling, relation extraction, and dependency parsing -- obtaining state-of-the-art results on the former two. We apply the resulting graphical models with structured and neural factors, and approximation-aware learning to jointly model part-of-speech tags, a syntactic dependency parse, and semantic roles in a low-resource setting where the syntax is unobserved. We present an alternative view of these models as neural networks with a topology inspired by inference on graphical models that encode our intuitions about the data

Graph-based broad-coverage semantic parsing

Many broad-coverage meaning representations can be characterized as directed graphs, where nodes represent semantic concepts and directed edges represent semantic relations among the concepts. The task of semantic parsing is to generate such a meaning representation from a sentence. It is quite natural to adopt a graph-based approach for parsing, where nodes are identified conditioning on the individual words, and edges are labeled conditioning on the pairs of nodes. However, there are two issues with applying this simple and interpretable graph-based approach for semantic parsing: first, the anchoring of nodes to words can be implicit and non-injective in several formalisms (Oepen et al., 2019, 2020). This means we do not know which nodes should be generated from which individual word and how many of them. Consequently, it makes a probabilistic formulation of the training objective problematical; second, graph-based parsers typically predict edge labels independent from each other. Such an independence assumption, while being sensible from an algorithmic point of view, could limit the expressiveness of statistical modeling. Consequently, it might fail to capture the true distribution of semantic graphs. In this thesis, instead of a pipeline approach to obtain the anchoring, we propose to model the implicit anchoring as a latent variable in a probabilistic model. We induce such a latent variable jointly with the graph-based parser in an end-to-end differentiable training. In particular, we test our method on Abstract Meaning Representation (AMR) parsing (Banarescu et al., 2013). AMR represents sentence meaning with a directed acyclic graph, where the anchoring of nodes to words is implicit and could be many-to-one. Initially, we propose a rule-based system that circumvents the many-to-one anchoring by combing nodes in some pre-specified subgraphs in AMR and treats the alignment as a latent variable. Next, we remove the need for such a rule-based system by treating both graph segmentation and alignment as latent variables. Still, our graph-based parsers are parameterized by neural modules that require gradient-based optimization. Consequently, training graph-based parsers with our discrete latent variables can be challenging. By combing deep variational inference and differentiable sampling, our models can be trained end-to-end. To overcome the limitation of graph-based parsing and capture interdependency in the output, we further adopt iterative refinement. Starting with an output whose parts are independently predicted, we iteratively refine it conditioning on the previous prediction. We test this method on semantic role labeling (Gildea and Jurafsky, 2000). Semantic role labeling is the task of predicting the predicate-argument structure. In particular, semantic roles between the predicate and its arguments need to be labeled, and those semantic roles are interdependent. Overall, our refinement strategy results in an effective model, outperforming strong factorized baseline models