Declarative theorem proving for operational semantics

iAbstract The aim of this Masters Thesis is to propose to SYSteam Nät AB, a local Internet Service Provider (ISP) in Uppsala, Sweden, how to implement IP telephony in their existing IT-infrastructure as a service to their customers. Thus the perspective of the thesis will be that of a local Internet Service Provider. Three general areas are covered in the thesis: Market and Business Model, Technology, and Economics. Important issues for SYSteam Nät AB as an established local broadband Internet Service Provider are to both retain present customers and to attract new customers. Some believe that offering value added services such as IP telephony could do this. Implementation of IP telephony can be done in different ways to fulfil SYSteam Nät’s requirements. The analysis leads to a proposal of how SYSteam Nät could implement IP telephony. This involves many multi-faceted business, technical, and financial issues; each aspect is examined in this thesis. ii Sammanfattnin

Joule heat effects on reliability of RF MEMS switches

Microelectromechanical systems (MEMS) technology has been evolving for about two decades and, now it is integrated in many designs, including radio frequency (RF) switches characterized by µm dimensions. Today, designers are attempting o develop the ideal RF MEMS switch, yet electro-thermo-mechanical (ETM) effects still limit the design possibilities and adversely affect reliability of these microswitches. The ETM effects are a result of Joule heat generated at the microswitch contact areas. This heat is due to the current passing through the microswitch, characteristics of the contact interfaces, and other parameters characterizing a particular design. It significantly raises temperature of the microswitch, thus affecting the mechanical and electrical properties of the contacts, which may lead to welding, causing a major reliability issue. Advanced research was performed, in this thesis, to minimize the Joule heat effects on the contact areas, thus improving performance of the microswitch. Thermal analyses done computationally on a cantilever-type RF MEMS switch indicate heat-effected zones and the influences that various design parameters have on these zones. Uncertainty analyses were also performed to ensure accuracy of the computational results, which indicate contact temperatures on the order of 700˚C, for the cases considered in this thesis. Although these temperatures are well below the melting temperatures of the materials used, new designs of the microswitches will have to be developed, in order to lower their maximum operating temperatures and reduce temporal effects they cause, to increase reliability of the RF MEMS switches

ONTIC: A Knowledge Representation System for Mathematics

Ontic is an interactive system for developing and verifying mathematics. Ontic's verification mechanism is capable of automatically finding and applying information from a library containing hundreds of mathematical facts. Starting with only the axioms of Zermelo-Fraenkel set theory, the Ontic system has been used to build a data base of definitions and lemmas leading to a proof of the Stone representation theorem for Boolean lattices. The Ontic system has been used to explore issues in knowledge representation, automated deduction, and the automatic use of large data bases

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

Proof-theoretic Semantics for Intuitionistic Multiplicative Linear Logic

This work is the first exploration of proof-theoretic semantics for a substructural logic. It focuses on the base-extension semantics (B-eS) for intuitionistic multiplicative linear logic (IMLL). The starting point is a review of Sandqvist’s B-eS for intuitionistic propositional logic (IPL), for which we propose an alternative treatment of conjunction that takes the form of the generalized elimination rule for the connective. The resulting semantics is shown to be sound and complete. This motivates our main contribution, a B-eS for IMLL , in which the definitions of the logical constants all take the form of their elimination rule and for which soundness and completeness are established

Influence of snow properties on directional surface reflectance in Antarctica

The significance of the polar regions for the Earth’s climate system and their observed amplified response to climate change indicate the necessity for high temporal and spatial coverage for the monitoring of the reflective properties of snow surfaces and their influencing factors. Therefore, the specific surface area (SSA, as a proxy for snow grain size) and the hemispherical directional reflectance factor (HDRF) of snow were measured for a 2-month period in central Antarctica (Kohnen research station) during austral summer 2013/14. The SSA data were retrieved on the basis of ground-based spectral surface albedo measurements collected by the COmpact RAdiation measurement System (CORAS) and airborne observations with the Spectral Modular Airborne Radiation measurement sysTem (SMART). The snow grain size and pollution amount (SGSP) algorithm, originally developed to analyze spaceborne reflectance measurements by the MODerate Resolution Imaging Spectroradiometer (MODIS), was modified in order to reduce the impact of the solar zenith angle on the retrieval results and to cover measurements in overcast conditions. Spectral ratios of surface albedo at 1280 and 1100 nm wavelength were used to reduce the retrieval uncertainty. The retrieval was applied to the ground-based and airborne observations and validated against optical in situ observations of SSA utilizing an IceCube device. The SSA retrieved from CORAS observations varied between 29 and 96 m2 kg-1. Snowfall events caused distinct relative maxima of the SSA which were followed by a gradual decrease in SSA due to snow metamorphism and wind-induced transport of freshly fallen ice crystals. The ability of the modified algorithm to include measurements in overcast conditions improved the data coverage, in particular at times when precipitation events occurred and the SSA changed quickly. SSA retrieved from measurements with CORAS and MODIS agree with the in situ observations within the ranges given by the measurement uncertainties. However, SSA retrieved from the airborne SMART data underestimated the ground-based results. The spatial variability of SSA in Dronning Maud Land ranged in the same order of magnitude as the temporal variability revealing differences between coastal areas and regions in interior Antarctica. The validation presented in this study provided an unique test bed for retrievals of SSA under Antarctic conditions where in situ data are scarce and can be used for testing prognostic snowpack models in Antarctic conditions. The HDRF of snow was derived from airborne measurements of a digital 180° fish-eye camera for a variety of conditions with different surface roughness, snow grain size, and solar zenith angle. The camera provides radiance measurements with high angular resolution utilizing detailed radiometric and geometric calibrations. The comparison between smooth and rough surfaces (sastrugi) showed significant differences in the HDRF of snow, which are superimposed on the diurnal cycle. By inverting a semi-empirical kernel-driven model for the bidirectional reflectance distribution function (BRDF), the snow HDRF was parameterized with respect to surface roughness, snow grain size, and solar zenith angle. This allows a direct comparison of the HDRF measurements with BRDF products from satellite remote sensing

Proof, rigour and informality : a virtue account of mathematical knowledge

This thesis is about the nature of proofs in mathematics as it is practiced, contrasting the informal proofs found in practice with formal proofs in formal systems. In the first chapter I present a new argument against the Formalist-Reductionist view that informal proofs are justified as rigorous and correct by corresponding to formal counterparts. The second chapter builds on this to reject arguments from Gödel's paradox and incompleteness theorems to the claim that mathematics is inherently inconsistent, basing my objections on the complexities of the process of formalisation. Chapter 3 looks into the relationship between proofs and the development of the mathematical concepts that feature in them. I deploy Waismann's notion of open texture in the case of mathematical concepts, and discuss both Lakatos and Kneebone's dialectical philosophies of mathematics. I then argue that we can apply work from conceptual engineering to the relationship between formal and informal mathematics. The fourth chapter argues for the importance of mathematical knowledge-how and emphasises the primary role of the activity of proving in securing mathematical knowledge. In the final chapter I develop an account of mathematical knowledge based on virtue epistemology, which I argue provides a better view of proofs and mathematical rigour.Funded by the Caroline Elder PG Scholarship and a SASP scholarship, and with travel funded by the Indo-European Research Training Network in Logic and the Arché Travel Fund