Strategic Issues, Problems and Challenges in Inductive Theorem Proving

Abstract(Automated) Inductive Theorem Proving (ITP) is a challenging field in automated reasoning and theorem proving. Typically, (Automated) Theorem Proving (TP) refers to methods, techniques and tools for automatically proving general (most often first-order) theorems. Nowadays, the field of TP has reached a certain degree of maturity and powerful TP systems are widely available and used. The situation with ITP is strikingly different, in the sense that proving inductive theorems in an essentially automatic way still is a very challenging task, even for the most advanced existing ITP systems. Both in general TP and in ITP, strategies for guiding the proof search process are of fundamental importance, in automated as well as in interactive or mixed settings. In the paper we will analyze and discuss the most important strategic and proof search issues in ITP, compare ITP with TP, and argue why ITP is in a sense much more challenging. More generally, we will systematically isolate, investigate and classify the main problems and challenges in ITP w.r.t. automation, on different levels and from different points of views. Finally, based on this analysis we will present some theses about the state of the art in the field, possible criteria for what could be considered as substantial progress, and promising lines of research for the future, towards (more) automated ITP

Core foundations, algorithms, and language design for symbolic computation in physics

This thesis presents three contributions to the field of symbolic computation, followed by their application to symbolic physics computations. The first contribution is to interfacing systems. The Notation package, which is developed in this thesis, allows the entry and the creation of advanced notations in the Mathematica symbolic computation system. In particular, a complete and functioning notation for both Dirac's BraKet notation as well as a full tensorial notation, are given herein. The second part of the thesis introduces a prototype based rule inheritance language paradigm that is applicable to certain advanced pattern matching rewrite rule language models. In particular, an implementation is presented for Mathematica. After detailing this language extension, it is adopted throughout the rest of the thesis. Finally, the third major contribution is a highly efficient algorithm to canonicalize tensorial expressions. By an innovative technique this algorithm avoids the dummy index relabeling problem. Further algorithmic optimizations are then presented. The complete algorithm handles linear symmetries such as the Bianchi identities. It also fully accommodates partial derivatives as well as mixed index classes. These advances in language and notations are extensively demonstrated on problems in quantum mechanics, angular momentum, general relativity, and quasi-spin. It is shown that the developments in this thesis lead to an extremely flexible, extensible, and powerful working environment for the expression and ensuing calculation of symbolic physics computations

Computer algebra techniques in object-oriented mathematical modelling.

This thesis proposes a rigorous object-oriented methodology, supported by computer algebra software, to generate and relate features in a mathematical model. Evidence shows that there is little heuristic or theoretical research into this problem from any of the three principal modelling methodologies: 'case study’, ‘scenario’ and ‘generic’. This thesis comprises two other major strands: applications of computer algebra software and the efficacy of symbolic computation in teaching and learning. Developing the principal algorithms in computer algebra has sometimes been done at the expense of ease of use. Developers have also not concentrated on integrating an algebra engine into other software. A thorough review of quantitative studies in teaching and learning mathematics highlights a serious difficulty in measuring the effect of using computer algebra. This arises because of the disparate nature of learning with and without a computer. This research tackles relationship formulation by casting the problem domain into object-oriented terms and building an appropriate class hierarchy. This capitalises on the fact that specific problems are instances of generic problems involving prototype physical objects. The computer algebra facilitates calculus operations and algebraic manipulation. In conjunction, I develop an object-oriented design methodology applicable to small-scale mathematical modelling. An object model modifies the generic modelling cycle. This allows relationships between features in the mathematical model to be generated automatically. The software is validated by quantifying the benefits of using the object-oriented techniques, and the results are statistically significant. The principal problem domain considered is Newtonian particle mechanics. Although the Newtonian axioms form a firm basis for a mathematical description of interactions between physical objects, applying them within a particular modelling context can cause problems. The goal is to produce an equation of motion. Applications to other contexts are also demonstrated. This research is significant because it formalises feature and equation-generation in a novel way. A new modelling methodology ensures that this crucial stage in the modelling cycle is given priority and automated

Remote Sensing and Geosciences for Archaeology

This book collects more than 20 papers, written by renowned experts and scientists from across the globe, that showcase the state-of-the-art and forefront research in archaeological remote sensing and the use of geoscientific techniques to investigate archaeological records and cultural heritage. Very high resolution satellite images from optical and radar space-borne sensors, airborne multi-spectral images, ground penetrating radar, terrestrial laser scanning, 3D modelling, Geographyc Information Systems (GIS) are among the techniques used in the archaeological studies published in this book. The reader can learn how to use these instruments and sensors, also in combination, to investigate cultural landscapes, discover new sites, reconstruct paleo-landscapes, augment the knowledge of monuments, and assess the condition of heritage at risk. Case studies scattered across Europe, Asia and America are presented: from the World UNESCO World Heritage Site of Lines and Geoglyphs of Nasca and Palpa to heritage under threat in the Middle East and North Africa, from coastal heritage in the intertidal flats of the German North Sea to Early and Neolithic settlements in Thessaly. Beginners will learn robust research methodologies and take inspiration; mature scholars will for sure derive inputs for new research and applications

Anales del XIII Congreso Argentino de Ciencias de la Computación (CACIC)

Contenido: Arquitecturas de computadoras Sistemas embebidos Arquitecturas orientadas a servicios (SOA) Redes de comunicaciones Redes heterogéneas Redes de Avanzada Redes inalámbricas Redes móviles Redes activas Administración y monitoreo de redes y servicios Calidad de Servicio (QoS, SLAs) Seguridad informática y autenticación, privacidad Infraestructura para firma digital y certificados digitales Análisis y detección de vulnerabilidades Sistemas operativos Sistemas P2P Middleware Infraestructura para grid Servicios de integración (Web Services o .Net)Red de Universidades con Carreras en Informática (RedUNCI

Anales del XIII Congreso Argentino de Ciencias de la Computación (CACIC)

Contenido: Arquitecturas de computadoras Sistemas embebidos Arquitecturas orientadas a servicios (SOA) Redes de comunicaciones Redes heterogéneas Redes de Avanzada Redes inalámbricas Redes móviles Redes activas Administración y monitoreo de redes y servicios Calidad de Servicio (QoS, SLAs) Seguridad informática y autenticación, privacidad Infraestructura para firma digital y certificados digitales Análisis y detección de vulnerabilidades Sistemas operativos Sistemas P2P Middleware Infraestructura para grid Servicios de integración (Web Services o .Net)Red de Universidades con Carreras en Informática (RedUNCI

Trinity College Bulletin, 2016-2017 (Catalogue)

https://digitalrepository.trincoll.edu/bulletin/1483/thumbnail.jp