Multi-focused Proofs with Different Polarity Assignments

We introduce new proof systems for propositional logic, simple deduction Frege systems, general deduction Frege systems, and nested deduction Frege systems, which augment Frege systems with variants of the deduction rule. We give upper bounds on the lengths of proofs in Frege proof systems compared to lengths in these new systems. As applications we give near-linear simulations of the propositional Gentzen sequent calculus and the natural deduction calculus by Frege proofs. The length of a proof is the number of lines (or formulas) in the proof.A general deduction Frege proof system provides at most quadratic speedup over Frege proof systems. A nested deduction Frege proof system provides at most a nearly linear speedup over Frege system where by “nearly linear” is meant the ratio of proof lengths is O(α(n)) where α is the inverse Ackermann function. A nested deduction Frege system can linearly simulate the propositional sequent calculus, the tree-like general deduction Frege calculus, and the natural deduction calculus. Hence a Frege proof system can simulate all those proof systems with proof lengths bounded by O(n . α(n)). Also we show that a Frege proof of n lines can be transformed into a tree-like Frege proof of O(n log n) lines and of height O(log n). As a corollary of this fact we can prove that natural deduction and sequent calculus tree-like systems simulate Frege systems with proof lengths bounded by O(n log n).

Summary form only given. We present here the results of a series of experiments comparing the operation of an X-pinch in positive and negative polarity. Of particular interest are the X-ray yield, timing, radiating spot size, and the number of radiating spots in a given X-pinch. Conventionally, an X-pinch is operated in negative polarity resulting in electric field lines that terminate on the wires. This choice of polarity for the generator is due to the fact that breakdown in these machines is easier to prevent when they are operated in negative polarity. Previous experiments involving single wire explosions at low current (1-5 kA) have shown that more energy can be deposited in the wire cores when they are driven in positive as opposed to negative polarity. These results raised the question of what happens when pinch-type experiments are driven in positive polarity. Recently, it has become possible to use the 450 kA XP pulser at Cornell to drive X-pinches in positive polarity. The positive polarity condition is established by inserting a convolute before the load and this results in electric field lines that originate on the wires of the X-pinch. This arrangement added complexity and inductance to the positive polarity shots, making it difficult to directly compare results from positive and negative shots. More recently, the entire pulser was switched to positive polarity. This allows a more direct comparison between positive and negative polarity X-pinch operation

This paper tackles the problem of formulating and proving the completeness of\nfocused-like proof systems in an automated fashion. Focusing is a discipline on\nproofs which structures them into phases in order to reduce proof search\nnon-determinism. We demonstrate that it is possible to construct a complete\nfocused proof system from a given un-focused proof system if it satisfies some\nconditions. Our key idea is to generalize the completeness proof based on\npermutation lemmas given by Miller and Saurin for the focused linear logic\nproof system. This is done by building a graph from the rule permutation\nrelation of a proof system, called permutation graph. We then show that from\nthe permutation graph of a given proof system, it is possible to construct a\ncomplete focused proof system, and additionally infer for which formulas\ncontraction is admissible. An implementation for building the permutation graph\nof a system is provided. We apply our technique to generate the focused proof\nsystems MALLF, LJF and LKF for linear, intuitionistic and classical logics,\nrespectively.\n

To test the display luminance hypothesis of the positive polarity advantage and gain insights for display design, the joint effects of display polarity and character size were assessed with a proofreading task Studies have shown that dark characters on light background (positive polarity) lead to better legibility than do light characters on dark background (negative polarity), presumably due to the typically higher display luminance of positive polarity presentations. Participants performed a proofreading task with black text on white background or white text on black background. Texts were presented in four character sizes (8, 10, 12, and 14 pt; corresponding to 0.22 degrees, 0.25 degrees, 0.31 degrees, and 0.34 degrees of vertical visual angle). A positive polarity advantage was observed in proofreading performance. Importantly, the positive polarity advantage linearly increased with decreasing character size. The findings are in line with the assumption that the typically higher luminance of positive polarity displays leads to an improved perception of detail. Application: The implications seem important for the design of text on such displays as those of computers, automotive control and entertainment systems, and smartphones that are increasingly used for the consumption of text-based media and communication. The sizes of these displays are limited, and it is tempting to use small font sizes to convey as much information as possible. Especially with small font sizes, negative polarity displays should be avoided.

Constructive linear-time temporal logic: Proof systems and Kripke semantics

Electrical breakdown of a gap between a wire (modeled as a hyperboloid) and a plane has been investigated numerically by solving the two-dimensional form of the diffusion flux equations for the charged particle number densities and Poisson’s equation for the self-consistent electric field. Electron impact ionization, thermal ionization, and three-body recombination have been considered as the charged particle production and loss mechanisms. The electrode surfaces are considered to be absorbing and the initial density of the particles is small, but nonzero. A gap length of 0.5 mm is investigated and the gas medium is air or argon at atmospheric pressure. The temporal development of the profiles of ion and electron number densities, potential and electric field, and current growth on both the electrodes are presented when the applied voltage is 1500 and 2500 V for both positive and negative wires. When the wire is negatively biased, the peaks in the radial distribution of both of the charged particle densities near the wire occur off the axis except during the very early part of the breakdown. With positive polarity, the electron density maximum always occurs on the discharge axis, while for ions it moves away from the axis, later in the transient, due to the reverse particle drift in the electric field from the negative polarity case. The discharge spreads farther out into the ambient (almost two times the gap length) when the wire is negatively biased than with positive polarity. The effect of charge separation on the externally applied electric field is significant at voltages 2500 V and higher. Ionization is greater in argon than in air for a fixed potential difference between the electrodes.

It is commonly assumed that comparative coherence relations (e.g., Peter is tall but his brother is short) can be analyzed in terms of semantic contrast. In this article it is claimed that comparative relations need to be understood in a context containing a similarity assumption. This assumption may be con®rmed (positive polarity) or denied (negative polarity) by the comparative text passage. When two entities are characterized in terms of a common variable without a similarity assumption being present (e. g., Peter's favorite color is red. His brother prefers green), the coherence relation is merely additive. Additive relations are not de®ned for polarity. While comparative relations may be linguistically marked by connectives like but, by contrast, or and in English or maar, daarentegen, or en in Dutch, additive relations remain unmarked. The distinction between comparative and additive relations is empirically supported by a corpus-based study of the linguistic marking of similarities and di€erences between the price movements of shares, using 400 fragments from stock-market reports in a Dutch daily newspaper. Some of these fragments clearly invoke similarity assumptions, for instance because of the fact that two companies are in the same branch of industry or because the fragment is preceded by an announcement of the general trend in share prices on a particular day. It was found that the overwhelming majority of linguistic markers of similarities and di€erences in share price movements occurred in contexts containing similarity assumptions. For instance, similarities that were to be expected may be marked by en `and' (e.g., Elsevier gained 1.10 [en] Kluwer went up forty cents), while unexpected di€erences are often marked by daarentegen `by contrast' (e.g., Elsevier gained 1.10 (new price 67.80). [Daarentegen] Kluwer lost forty cents (new price 50.70)). Some apparent counterexamples, in which two companies from the same branch of industry show di€erent share price movements while this di€erence remains unmarked, in fact do not invalidate the similarity assumption framework but Cognitive Linguistics 10±2 (1999), 147±184 0936±5907/99/0010±0147 # Walter de Gruyter support it. In the majority of these cases the similarity assumption has been eliminated or weakened by earlier announcements of di€erences within a certain branch. A closer analysis of ®ve Dutch comparative connectives reveals that two dimensions of comparative polarity need to be distinguished: a propositional polarity parameter with the values ``di€erence'' and ``similarity'', and an assumptional polarity parameter distinguishing between con®rmations and denials of the relevant assumption. Di€erent linguistic elements may be characterized in terms of di€erent polarity dimensions. For instance, ook `also' expresses positive propositional polarity, while maar `but' is an indication of negative assumptional polarity.

Theorem proving procedures for the propositional calculus have traditionally relied on syntactic manipulations of the formula to derive a proof. In particular, clausal theorem provers sometimes lose some of the obvious semantics present in the theorem, in the process of converting the theorem into an unnatural normal form. Most existing propositional theorem provers do not incorporate substitution of equals for equals as an inference rule. In this paper we develop a “natural” proof system for the propositional calculus, with the goal that most succinct mathematical proofs should be encodable as short formal proofs within the proof system. The main distinctive features of NPS are: We show that from a complexity theoretic viewpoint NPS is at least as powerful as the resolution procedure. We further demonstrate formulas on which NPS fares better than resolution. Finally, since proofs in NPS usually resemble manual proofs, we feel that NPS is easily amenable to an interactive theorem prover.

A normalization procedure is presented for a classical natural deduction (ND) proof system. This proof system, called N-Graphs, has a multiple conclusion proof structure, where cycles are allowed. With this, we have developed a thorough treatment of cycles, including cycles normalization via an algorithm. We also demonstrate the usefulness of the graphical framework of N-Graphs, where derivations are seen as digraphs. We use geometric perspective techniques to establish the normalization mechanism, thus giving a direct normalization proof. Moreover, the subformula and separation properties are determined.

One of the main advantages of the MIG/MAG process is its high productivity. In most of the applications, positive polarity is used, due to its greater arc stability, generation of less splatter and formation of weld beads with suitable geometry. However, in some applications, there is a need for greater production capacity than that offered by conventional MIG/MAG welding. In the literature, it is stated that negative polarity provides a higher fusion rate than positive, despite leading to a high level of splatter and unsuitable formation of the weld bead. Unfortunately, there is not much information available on the effects of the process variables in this polarity, much less justification for such. Therefore, this work is an attempt to try to understand the reason why there is a higher deposit rate in negative polarity, as well as the related effect on the geometry of the weld beads. To do this, comparative MIG/MAG welds were produced in both positive and negative polarities, using two compositions of shielding gases at two current values. The transfer mode and the behaviour of the arc were analysed by synchronized profiling. The geometric profile of the weld bead was evaluated by means of metallographic procedures. From the results, which disagree in part with the current literature, it was seen that both the transfer mode as well as the morphology and the appearance of the weld bead are dependent on the composition of the shielding gas. To explain the phenomena inherent in the greater fusion rate of wire in DC − , the suggestion is that the fact that arc scales the sides of the wire in this polarity may be the governing factor.

Matrix effect is the effect on an analytical method caused by all other components of the sample except the specific compound to be quantified. Matrix effects and selectivity issues have long been associated with bioanalytical techniques. A number of approaches have been investigated to improve reproducibility and robustness of LC-MS-MS methods that are subjected to matrix effects. In the present research work the role of ionization polarity on matrix effect was studied. Enalapril and its metabolite were analyzed in positive and negative polarity by using ESI-LC-MS/MS. Matrix factor (MF) was determined to evaluate the matrix effects in different polarities. Two different concentration levels of each analyte were used to determine the MF. In positive polarity the MF at two different concentration levels were 0.6353 & 0.6496 for enalapril and 0.6885 & 0.6770 for enalaprilat, whereas, the MF in negative polarity at two different concentration levels were 0.8203 & 0.7717 for enalapril and 1.1124 & 1.0915 for enalaprilat. These data showed approximately 30-35% ion suppression in positive polarity for both the analyte, but approximately 20% ion suppression for enalapril and 10% ion enhancement for enalaprilat in negative polarity. So, matrix effects depend on the ionization polarity also.

Gentzen's systems of natural deduction and sequent calculus were byproducts in his program of proving the consistency of arithmetic and analysis. It is suggested that the central component in his results on logical calculi was the use of a tree form for derivations. It allows the composition of derivations and the permutation of the order of application of rules, with a full control over the structure of derivations as a result. Recently found documents shed new light on the discovery of these calculi. In particular, Gentzen set up five different forms of natural calculi and gave a detailed proof of normalization for intuitionistic natural deduction. An early handwritten manuscript of his thesis shows that a direct translation from natural deduction to the axiomatic logic of Hilbert and Ackermann was, in addition to the influence of Paul Hertz, the second component in the discovery of sequent calculus. A system intermediate between the sequent calculus LI and axiomatic logic, denoted LIG in unpublished sources, is implicit in Gentzen's published thesis of 1934–35. The calculus has half rules, half “groundsequents,” and does not allow full cut elimination. Nevertheless, a translation from LI to LIG in the published thesis gives a subformula property for a complete class of derivations in LIG. After the thesis, Gentzen continued to work on variants of sequent calculi for ten more years, in the hope to find a consistency proof for arithmetic within an intuitionistic calculus.

This paper presents the research results on the effect of internal impurity of palm oil and needle electrode polarity on the breakdown voltage. The electrodes used in this research were in an arrangement of needle-plate with the needle sharpness angles used were 45° and 60°. A DC high voltage has been used as the testing voltage during experiment with the spark gap between the needle and plate electrodes was 2.5mm and 5mm. Breakdown testing has been done using two polarities on the needle electrodes, which were positive and negative polarities. Before the exposure to electric field, microscopically an unused palm oil looked clear and did not reveal any impurity. The solid impurities started to appear in the oil once it was exposed to electric field. It was originated from the fat contained in the palm oil. Under the influence of electric field, the impurities were moving and gathering around the tip of the needle electrode, the part with the highest field intensity. The largest amount of internal impurities around the needle tip has been found during the experiment with the needle sharpness angle of 60°, meaning that sharper the needle point, larger would be the amount of impurities gathered around. Considering the two spark-gap distances and the two needle sharpness angles used in the research, it was found that the level of breakdown voltage at positive polarity is smaller than the breakdown voltage level at negative polarity.

In the present paper some numerical results, based on the theory developed in double and third scattering approximation are presented. The influences of microphysical and morphological properties of discrete random medium on photometric and polarimetric characteristics of backscattered radiation are discussed. If the effective refractive index of the medium is kept the same, the differences in the features of the opposition effects are caused by differences in the microscopic characteristics of the scatterers. From theoretical observations, it is concluded that the results demonstrate that the state of polarization of the back scattered radiation is controlled by the state of polarization of singly scattered radiation. It is well known that the positive polarization of light scattered by isolated particle leads to a negative polarization feature in the backscattering direction. The angular dependence of the polarization state for wavelength sized spherical particles is much more complex and oscillatory. The interference may lead to a more complex dependence of polarization on the scattering angle, with positive and negative polarization regions appearing simultaneously. The resulting interference of doubly scattered waves can result in positive polarization as well as negative polarization.

The object of research is a circuit that simulates a lightning strike to a tower of 220 kV power transmission line, taking into consideration the reflection of a current wave from 10 nearest towers. Computation of the voltage arising at the top of the struck tower is necessary further to determine the lightning performance of transmission line by various methods. The lightning current has several maxima, in the case of a positive impulse polarity and, accordingly, several minima, in the case of a negative polarity, which are generally being called peaks. In addition, the lightning current impulse has a non-constant steepness in the entire area of current rise up to the first peak. The approximation of the real lightning current by simplified mathematical expressions cannot take into account all its real features. For a more detailed study of transient processes caused by thunderstorm activity, there is a need to use oscillograms of real lightning currents when modeling. The problem of determining the voltage at the top of the stricken transmission line tower was solved using circuit simulation. For an in-depth study of how the shape of the lightning current impulse affects the shape of the voltage at the top of the tower struck, digitized oscillograms of real lightning currents were used. The simulation was carried out for 7 negative lightning impulses with the first peak varying from –33.380 kA to –74.188 kA. In the case of positive lightning, 3 oscillograms were used with the first peak varying from +38.461 kA to +41.012 kA. The article shows that the shape of the front of the lightning current impulse and the amplitude of the first peak of the lightning current have a decisive effect on the maximum voltage value at the top of a power transmission line tower struck by lightning. The maximum voltage occurs precisely at the front of the current wave before the first peak of the lightning current. Therefore, the back flashover of the insulation from the tower to the phase conductor is most likely at a moment in time at the front of the current wave. By the time the maximum current is reached, the voltage at the top of the tower will be reduced by several tens of percent, compared to the maximum voltage at the tower, which occurs much earlier at the front of the current wave. The conducted research contributes to the development of methods for calculating the lightning performance of power lines and extends the scope of application of circuit simulation programs.