lim+, delta+, and Non-Permutability of beta-Steps

Using a human-oriented formal example proof of the (lim+) theorem, i.e. that the sum of limits is the limit of the sum, which is of value for reference on its own, we exhibit a non-permutability of beta-steps and delta+-steps (according to Smullyan's classification), which is not visible with non-liberalized delta-rules and not serious with further liberalized delta-rules, such as the delta++-rule. Besides a careful presentation of the search for a proof of (lim+) with several pedagogical intentions, the main subject is to explain why the order of beta-steps plays such a practically important role in some calculi.Comment: ii + 36 page

Hilbert's "Verunglueckter Beweis," the first epsilon theorem, and consistency proofs

In the 1920s, Ackermann and von Neumann, in pursuit of Hilbert's Programme, were working on consistency proofs for arithmetical systems. One proposed method of giving such proofs is Hilbert's epsilon-substitution method. There was, however, a second approach which was not reflected in the publications of the Hilbert school in the 1920s, and which is a direct precursor of Hilbert's first epsilon theorem and a certain 'general consistency result' due to Bernays. An analysis of the form of this so-called 'failed proof' sheds further light on an interpretation of Hilbert's Programme as an instrumentalist enterprise with the aim of showing that whenever a `real' proposition can be proved by 'ideal' means, it can also be proved by 'real', finitary means.Comment: 18 pages, final versio

Исследование процесса шлифования стальных кулачков инструментом из кубического нитрида бора без охлаждения

Экспериментальными исследованиями, имитирующими шлифование кулачков из закаленной легированной стали, установлено, что их обработка с минимальным нагревом обрабатываемой поверхности с охлаждением масляным туманом или без охлаждения возможна высокопористым кругом из кубического нитрида бора. Выявлено, что для минимизации термодинамической напряженности сухого шлифования целесообразно назначать режим обработки с максимальной возможной глубиной врезания круга и минимальной скоростью вращения детали.Експериментальними дослідженнями, які імітують шліфування кулачків із загартованої легованої сталі, встановлено, що їх обробка з мінімальним нагрівом оброблюваної поверхні з охолодженням масляним туманом або без охолодження можлива високопористим кругом з кубічного нітриду бору. Виявлено, що для мінімізації термодинамічної напруженості сухого шліфування доцільно призначати режим обробки з максимальною можливою глибиною врізання круга і мінімальною швидкістю обертання деталі.Experimental studies simulating grinding of Cams of hardened alloy steel, determined that their treatment with the lowest heating of the surface cooled oil mist or without cooling are possible by using highly porous grinding wheels from cubic boron nitride. Also identified that to minimize the thermodynamic tension dry sanding it is advisable to appoint a mode of processing with the maximum possible depth plunging grinding wheel and a minimum speed of rotation of the part

Experimental Detection and Quantitative Interrogation of Damage in a Jointed Composite Structure

The aerospace field has concentrated substantial attention toward the development of structural health monitoring (SHM) systems for multidisciplinary applications. Research is motivated by catastrophic failures of operational systems which may have been avoided with the prior implementation of a successful damage prediction method. This research utilizes a smart sensor array to collect sensing information over a variety of damaged scenarios on a composite lap-joint assembly. Damage was implemented as bolt torque loss within the joint. A damage index was used as the key diagnostic feature to interrogate damage within the structure. Pattern recognition of the damage index, in addition to a rule-based, statistical discrimination method was employed to detect, localize and quantify damage due to bolt torque loss in the structure. The methodology accurately detected the presence of damage within the joint, localized the damage within the structures four quadrants, and assessed the level of torque loss

Experimental Detection and Quantitative Interrogation of Damage in a Jointed Composite Structure

The aerospace field has concentrated substantial attention toward the development of structural health monitoring (SHM) systems for multidisciplinary applications. Research is motivated by catastrophic failures of operational systems which may have been avoided with the prior implementation of a successful damage prediction method. This research utilizes a smart sensor array to collect sensing information over a variety of damaged scenarios on a composite lap-joint assembly. Damage was implemented as bolt torque loss within the joint. A damage index was used as the key diagnostic feature to interrogate damage within the structure. Pattern recognition of the damage index, in addition to a rule-based, statistical discrimination method was employed to detect, localize and quantify damage due to bolt torque loss in the structure. The methodology accurately detected the presence of damage within the joint, localized the damage within the structures four quadrants, and assessed the level of torque loss

Basic Logic and Quantum Entanglement

As it is well known, quantum entanglement is one of the most important features of quantum computing, as it leads to massive quantum parallelism, hence to exponential computational speed-up. In a sense, quantum entanglement is considered as an implicit property of quantum computation itself. But...can it be made explicit? In other words, is it possible to find the connective "entanglement" in a logical sequent calculus for the machine language? And also, is it possible to "teach" the quantum computer to "mimic" the EPR "paradox"? The answer is in the affirmative, if the logical sequent calculus is that of the weakest possible logic, namely Basic logic. A weak logic has few structural rules. But in logic, a weak structure leaves more room for connectives (for example the connective "entanglement"). Furthermore, the absence in Basic logic of the two structural rules of contraction and weakening corresponds to the validity of the no-cloning and no-erase theorems, respectively, in quantum computing.Comment: 10 pages, 1 figure,LaTeX. Shorter version for proceedings requirements. Contributed paper at DICE2006, Piombino, Ital

Polarizing Double Negation Translations

Double-negation translations are used to encode and decode classical proofs in intuitionistic logic. We show that, in the cut-free fragment, we can simplify the translations and introduce fewer negations. To achieve this, we consider the polarization of the formul{\ae}{} and adapt those translation to the different connectives and quantifiers. We show that the embedding results still hold, using a customized version of the focused classical sequent calculus. We also prove the latter equivalent to more usual versions of the sequent calculus. This polarization process allows lighter embeddings, and sheds some light on the relationship between intuitionistic and classical connectives

An order-theoretic analysis of interpretations among propositional deductive systems

In this paper we study interpretations and equivalences of propositional deductive systems by using a quantale-theoretic approach introduced by Galatos and Tsinakis. Our aim is to provide a general order-theoretic framework which is able to describe and characterize both strong and weak forms of interpretations among propositional deductive systems also in the cases where the systems have different underlying languages