The Dynamic Creation of Induction Rules Using Proof Planning

Centre for Intelligent Systems and their ApplicationsA key problem in automating proof by mathematical induction is choosing an induction rule suitable for a given conjecture. Since Boyer & Moore’s NQTHM system the standard approach has been based on recursion analysis, which uses a combination of induction rules based on the relevant recursive function definitions. However, there are practical examples on which such techniques are known to fail. Recent research has tried to improve automation by delaying the choice of inductive rule until later in the proof, but these techniques suffer from two serious problems. Firstly, a lack of search control: specifically, in controlling the application of ‘speculative’ proof steps that partially commit to a choice of induction rule. Secondly, a lack of generality: they place significant restrictions on the form of induction rule that can be chosen. In this thesis we describe a new delayed commitment strategy for inductive proof that addresses these problems. The strategy dynamically creates an appropriate induction rule by proving schematic proof goals, where unknown rule structure is represented by meta-variables which become instantiated during the proof. This is accompanied by a proof that the generated rule is valid. The strategy achieves improved control over speculative proof steps via a novel speculation critic. It also generates a wider range of useful induction rules than other delayed commitment techniques, partly because it removes unnecessary restrictions on the individual proof cases, and partly because of a new technique for generating the rule’s overall case structure. The basic version of the strategy has been implemented using the lamdaClam proof planner. The system was extended with a novel proof critics architecture for this purpose. An evaluation shows the strategy is a useful and practical technique, and demonstrates its advantages

Supporting dependently typed functional programming with proof automation and testing

Dependent types can be used to capture useful properties about programs at compile time. However, developing dependently typed programs can be difficult in current systems. Capturing interesting program properties usually requires the user to write proofs, where constructing the latter can be both a difficult and tedious process. Additionally, finding and fixing errors in program scripts can be challenging. This thesis concerns ways in which functional programming with dependent types can be made easier. In particular, we focus on providing help for developing programs that incorporate user-defined types and user-defined functions. For the purpose of supporting dependently typed programming, we have designed a framework that provides improved proof automation and error feedback. Proof automation is provided with the use of heuristic based tactics that automate common patterns of proofs that arise when programming with dependent types. In particular, we use heuristics for generalising goals and employ the rippling heuristic for guiding inductive and non-inductive proofs. The automation we describe includes features for caching and reusing lemmas proven during proof search and, whenever proof search fails, the user can assist the prover by providing high-level hints. We concentrate on providing improved feedback for the errors that occur when there is a mismatch between the specification of a program, described with the use of dependent types, and the behaviour of the program. We employ a QuickCheck-like testing tool for automatically identifying these forms of errors, where the counter examples generated are used as error messages. To demonstrate the effectiveness of our framework for supporting dependently typed programming, we have developed a prototype based around the Coq theorem prover. We demonstrate that the framework as a whole makes program development easier by conducting a series of case studies. In these case studies, which involved verifying properties of tail recursive functions, sorting functions and a binary adder, a significant number of the proofs required were automated

Knowledge Modelling and Learning through Cognitive Networks

One of the most promising developments in modelling knowledge is cognitive network science, which aims to investigate cognitive phenomena driven by the networked, associative organization of knowledge. For example, investigating the structure of semantic memory via semantic networks has illuminated how memory recall patterns influence phenomena such as creativity, memory search, learning, and more generally, knowledge acquisition, exploration, and exploitation. In parallel, neural network models for artificial intelligence (AI) are also becoming more widespread as inferential models for understanding which features drive language-related phenomena such as meaning reconstruction, stance detection, and emotional profiling. Whereas cognitive networks map explicitly which entities engage in associative relationships, neural networks perform an implicit mapping of correlations in cognitive data as weights, obtained after training over labelled data and whose interpretation is not immediately evident to the experimenter. This book aims to bring together quantitative, innovative research that focuses on modelling knowledge through cognitive and neural networks to gain insight into mechanisms driving cognitive processes related to knowledge structuring, exploration, and learning. The book comprises a variety of publication types, including reviews and theoretical papers, empirical research, computational modelling, and big data analysis. All papers here share a commonality: they demonstrate how the application of network science and AI can extend and broaden cognitive science in ways that traditional approaches cannot

Input and Output in Oral Reading in English : the Interaction of Syntax, Semantico-pragmatics and Intonation

This dissertation provides an integrated linguistic description of reading intonation, in which input and output are equally considered. There are therefore two main points of interest. On the one hand, there are the medium-independent abstract presentation structures of words and syntactic structures, and their medium-dependent presentation via orthography and punctuation. On the other hand, there is a consideration of different reading performances, and of the fact that the written text can be orally presented in different ways. It is the aim of this thesis to compile these different modes of presentation and to pin down their assessment in a linguistic model. For this purpose, the presentation structural device of the ‘talk unit’ is modified and used for a systematic investigation of the interaction of syntax, semantico-pragmatics and discourse intonation (placement of tone unit boundaries, of nuclei as well as choice of tone movements and their situation in a speaker’s pitch range) in a corpus comprising typical domains of oral reading (Speech, News, Commentary, Fiction). This thesis also deals with the use of obtrusive pauses (segmentation, anticipation, hesitation) as well as with the respective influence of medium-independent presentation structures and punctuation on a reader’s own presentation in the spoken medium.In dieser Dissertation geht es um eine integrierte linguistische Beschreibung von Leseintonation, bei der Input und Output gleichermaßen berücksichtigt werden. Gegenstand der Untersuchung ist daher einmal die mediumunabhängige abstrakte sprachliche Kette von Wörtern und Strukturen und deren mediumabhängige Präsentation durch Orthographie und Interpunktion. Zum anderen wird berücksichtigt, dass es unterschiedliche Leseleistungen gibt, dass also die intonatorische Präsentation der geschriebenen Vorlage auf unterschiedliche Weise geschehen kann. Diese Variationsmöglichkeiten sowie deren Bewertung in einem linguistischen Modell zu erfassen hat sich die vorliegende Arbeit zum Ziel gesetzt. Hierzu wird das präsentationsstrukturelle Mittel der Redeeinheit (’talk unit’) modifiziert und eingesetzt für eine systematische Untersuchung der Interaktion von Syntax, Semantiko-Pragmatik und der Diskurs-Intonation (Platzierung der Sprechtaktgrenzen, der Nuklei sowie Wahl der Tonbewegungen und deren Platzierung im Stimmumfang eines Sprechers) anhand eines Korpus, das sich aus typischen Anwendungsbereichen des lauten Lesens zusammensetzt (Rede, Nachrichtentexte, Kommentare, fiktive Texte). Zusätzlich wird der Einsatz von auffälligen Pausen (Segmentierung, Antizipation, Zögern) untersucht sowie das Ausmaß des Einflusses von mediumunabhängigen Strukturen einerseits und mediumabhängigen graphischen Strukturen (Interpunktion) andererseits auf die Umsetzung im gesprochenen Medium

Deep learning for fast and robust medical image reconstruction and analysis

Medical imaging is an indispensable component of modern medical research as well as clinical practice. Nevertheless, imaging techniques such as magnetic resonance imaging (MRI) and computational tomography (CT) are costly and are less accessible to the majority of the world. To make medical devices more accessible, affordable and efficient, it is crucial to re-calibrate our current imaging paradigm for smarter imaging. In particular, as medical imaging techniques have highly structured forms in the way they acquire data, they provide us with an opportunity to optimise the imaging techniques holistically by leveraging data. The central theme of this thesis is to explore different opportunities where we can exploit data and deep learning to improve the way we extract information for better, faster and smarter imaging. This thesis explores three distinct problems. The first problem is the time-consuming nature of dynamic MR data acquisition and reconstruction. We propose deep learning methods for accelerated dynamic MR image reconstruction, resulting in up to 10-fold reduction in imaging time. The second problem is the redundancy in our current imaging pipeline. Traditionally, imaging pipeline treated acquisition, reconstruction and analysis as separate steps. However, we argue that one can approach them holistically and optimise the entire pipeline jointly for a specific target goal. To this end, we propose deep learning approaches for obtaining high fidelity cardiac MR segmentation directly from significantly undersampled data, greatly exceeding the undersampling limit for image reconstruction. The final part of this thesis tackles the problem of interpretability of the deep learning algorithms. We propose attention-models that can implicitly focus on salient regions in an image to improve accuracy for ultrasound scan plane detection and CT segmentation. More crucially, these models can provide explainability, which is a crucial stepping stone for the harmonisation of smart imaging and current clinical practice.Open Acces

Automated Deduction – CADE 28

This open access book constitutes the proceeding of the 28th International Conference on Automated Deduction, CADE 28, held virtually in July 2021. The 29 full papers and 7 system descriptions presented together with 2 invited papers were carefully reviewed and selected from 76 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations, and practical experience. The papers are organized in the following topics: Logical foundations; theory and principles; implementation and application; ATP and AI; and system descriptions

Proceedings of the 21st Conference on Formal Methods in Computer-Aided Design – FMCAD 2021

The Conference on Formal Methods in Computer-Aided Design (FMCAD) is an annual conference on the theory and applications of formal methods in hardware and system verification. FMCAD provides a leading forum to researchers in academia and industry for presenting and discussing groundbreaking methods, technologies, theoretical results, and tools for reasoning formally about computing systems. FMCAD covers formal aspects of computer-aided system design including verification, specification, synthesis, and testing