Transreal proof of the existence of universal possible worlds

Transreal arithmetic is total, in the sense that the fundamental operations of addition, subtraction, multiplication and division can be applied to any transreal numbers with the result being a transreal number [1]. In particular division by zero is allowed. It is proved, in [3], that transreal arithmetic is consistent and contains real arithmetic. The entire set of transreal numbers is a total semantics that models all of the semantic values, that is truth values, commonly used in logics, such as the classical, dialetheaic, fuzzy and gap values [2]. By virtue of the totality of transreal arithmetic, these logics can be implemented using total, arithmetical functions, specifically operators, whose domain and counterdomain is the entire set of transreal numbers

Transreal arithmetic as a consistent basis for paraconsistent logics

Paraconsistent logics are non-classical logics which allow non-trivial and consistent reasoning about inconsistent axioms. They have been pro- posed as a formal basis for handling inconsistent data, as commonly arise in human enterprises, and as methods for fuzzy reasoning, with applica- tions in Artificial Intelligence and the control of complex systems. Formalisations of paraconsistent logics usually require heroic mathe- matical efforts to provide a consistent axiomatisation of an inconsistent system. Here we use transreal arithmetic, which is known to be consis- tent, to arithmetise a paraconsistent logic. This is theoretically simple and should lead to efficient computer implementations. We introduce the metalogical principle of monotonicity which is a very simple way of making logics paraconsistent. Our logic has dialetheaic truth values which are both False and True. It allows contradictory propositions, allows variable contradictions, but blocks literal contradictions. Thus literal reasoning, in this logic, forms an on-the- y, syntactic partition of the propositions into internally consistent sets. We show how the set of all paraconsistent, possible worlds can be represented in a transreal space. During the development of our logic we discuss how other paraconsistent logics could be arithmetised in transreal arithmetic.

Transreal logical space of all propositions

Transreal numbers provide a total semantics containing classical truth values, dialetheaic, fuzzy and gap values. A paraconsistent Sheffer Stroke generalises all classical logics to a paraconsistent form. We introduce logical spaces of all possible worlds and all propositions. We operate on a proposition, in all possible worlds, at the same time. We define logical transformations, possibility and necessity relations, in proposition space, and give a criterion to determine whether a proposition is classical. We show that proofs, based on the conditional, infer gaps only from gaps and that negative and positive infinity operate as bottom and top values.

A Possible Influence of Equatorial Winds on the September 2002 Southern Hemisphere Sudden Warming Event

The stratospheric sudden warming in the Southern Hemisphere (SH) in September 2002 was unexpected for two reasons. First, planetary wave activity in the Southern Hemisphere is very weak, and midwinter warmings have never been observed, at least not since observations of the upper stratosphere became regularly available. Second, the warming occurred in a west phase of the quasi-biennial oscillation (QBO) in the lower stratosphere. This is unexpected because warmings are usually considered to be more likely in the east phase of the QBO, when a zero wind line is present in the winter subtropics and hence confines planetary wave propagation to higher latitudes closer to the polar vortex. At first, this evidence suggests that the sudden warming must therefore be simply a result of anomalously strong planetary wave forcing from the troposphere. However, recent model studies have suggested that the midwinter polar vortex may also be sensitive to the equatorial winds in the upper stratosphere, the region dominated by the semiannual oscillation. In this paper, the time series of equatorial zonal winds from two different data sources, the 40-yr ECMWF Re-Analysis (ERA) and the Met Office assimilated dataset, are reviewed. Both suggest that the equatorial winds in the upper stratosphere above 10 hPa were anomalously easterly in 2002. Idealized model experiments are described in which the modeled equatorial winds were relaxed toward these observations for various years to examine whether the anomalous easterlies in 2002 could influence the timing of a warming event. It is found that the 2002 equatorial winds speed up the evolution of a warming event in the model. Therefore, this study suggests that the anomalous easterlies in the 1–10-hPa region may have been a contributory factor in the development of the observed SH warming. However, it is concluded that it is unlikely that the anomalous equatorial winds alone can explain the 2002 warming event.

Microbial perchlorate reduction: A precise laboratory determination of the chlorine isotope fractionation and its possible biochemical basis

Perchlorate-reducing bacteria fractionate chlorine stable isotopes giving a powerful approach to monitor the extent of microbial consumption of perchlorate in contaminated sites undergoing remediation or natural perchlorate containing sites. This study reports the full experimental data and methodology used to re-evaluate the chlorine isotope fractionation of perchlorate reduction in duplicate culture experiments of Azospira suillum strain PS at 37 degrees C (Delta Cl-37(Cr)--ClO4-) previously reported, without a supporting data set by Coleman et al. [Coleman, M.L., Ader, M., Chaudhuri, S., Coates,J.D., 2003. Microbial Isotopic Fractionation of Perchlorate Chlorine. Appl. Environ. Microbiol. 69, 4997-5000] in a reconnaissance study, with the goal of increasing the accuracy and precision of the isotopic fractionation determination. The method fully described here for the first time, allows the determination of a higher precision Delta Cl-37(Cl)--ClO4- value, either from accumulated chloride content and isotopic composition or from the residual perchlorate content and isotopic composition. The result sets agree perfectly, within error, giving average Delta Cl-37(Cl)--ClO4- = -14.94 +/- 0.15%omicron. Complementary use of chloride and perchlorate data allowed the identification and rejection of poor quality data by applying mass and isotopic balance checks. This precise Delta Cl-37(Cl)--ClO4-, value can serve as a reference point for comparison with future in situ or microcosm studies but we also note its similarity to the theoretical equilibrium isotopic fractionation between a hypothetical chlorine species of redox state +6 and perchlorate at 37 degrees C and suggest that the first electron transfer during perchlorate reduction may occur at isotopic equilibrium between art enzyme-bound chlorine and perchlorate. (C) 2008 Elsevier B.V. All rights reserved.

Ibergirhynchia contraria (F. A. Roemer, 1850), an Early Carboniferous seep-related rhynchonellide brachiopod from the Harz Mountains, Germany - A possible successor to Dzieduszyckia?

A new genus Ibergirhynchia, a member of the rhynchonellide superfamily Dimerelloidea, is described for the species Terebratula contraria Roemer, 1850, from Early Carboniferous deposits of the Harz Mountains, Germany. Ibergirhynchia contraria is from a monospecific brachiopod limestone that formed on top of the drowned Devonian Iberg Reef which persisted as a seamount during Famennian and Early Carboniferous times. Ibergirhynchia contraria is considered a cold seep-related brachiopod based on this locality. Such seep associations have been observed for Mesozoic representatives of the rhynchonellide superfamily Dimerelloidea. Ibergirhynchia is considered the first Paleozoic representative of the family Rhynchonellinidae. Ibergirhynchia resembles Dzieduszyckia externally and may be derived from this dimerelloid.