forall x: Calgary. An Introduction to Formal Logic

forall x: Calgary is a full-featured textbook on formal logic. It covers key notions of logic such as consequence and validity of arguments, the syntax of truth-functional propositional logic TFL and truth-table semantics, the syntax of first-order (predicate) logic FOL with identity (first-order interpretations), translating (formalizing) English in TFL and FOL, and Fitch-style natural deduction proof systems for both TFL and FOL. It also deals with some advanced topics such as truth-functional completeness and modal logic. Exercises with solutions are available. It is provided in PDF (for screen reading, printing, and a special version for dyslexics) and in LaTeX source code

Substitution in a sense

The Reference Principle (RP) states that co-referring expressions are everywhere intersubstitutable salva congruitate. On first glance, (RP) looks like a truism, but a truism with some bite: (RP) transforms difficult philosophical questions about co-reference into easy grammatical questions about substitutability. This has led a number of philosophers to think that we can use (RP) to make short work of certain longstanding metaphysical debates. For example, it has been suggested that all we need to do to show that the predicate ‘( ) is a horse’ does not refer to a property is point out that ‘( ) is a horse’ and ‘the property of being a horse’ are not everywhere intersubstitutable salva congruitate. However, when we understand ‘substitution’ in the simplest and most straightforward way, (RP) is no truism; in fact, natural languages are full of counterexamples to the principle. In this paper, I introduce a new notion of substitution, and then develop and argue for a version of (RP) that is immune to these counterexamples. Along the way I touch on the following topics: the relation between argument forms and their natural language instances; the reification of sense; the difference between terms and predicates; and the relation between reference and disquotation. I end by arguing that my new version of (RP) cannot be used to settle metaphysical debates quite as easily as some philosophers would like

Lickometry: A novel and sensitive method for assessing functional deficits in rats after stroke

The need for sensitive, easy to administer assessments of long-term functional deficits is crucial in pre-clinical stroke research. In the present study, we introduce lickometry (lick microstructure analysis) as a precise method to assess sensorimotor deficits up to 40 days after middle cerebral artery occlusion in rats. Impairments in drinking efficiency compared to controls, and a compensatory increase in the number of drinking clusters were observed. This highlights the utility of this easy to administer task in assessing subtle, long-term deficits, which could be likened to oral deficits in patients

Hadronic Atoms and Effective Interactions

We examine the problem of hadronic atom energy shifts using the technique of effective interactions and demonstrate equivalence with the conventional quantum mechanical approach.Comment: 22 page latex file with 2 figure

Perturbative framework for the pi(+)pi(-) atom

The perturbative framework is developed for the calculation of the pi(+)pi(-) atom characteristics on the basis of the field-theoretical Bethe-Salpeter approach. A closed expression for the first-order correction to the pi(+)pi(-) atom lifetime has been obtained.Comment: 8 pages, LaTeX-fil

Historical changes in the phenology of British Odonata are related to climate

Responses of biota to climate change take a number of forms including distributional shifts, behavioural changes and life history changes. This study examined an extensive set of biological records to investigate changes in the timing of life history transitions (specifically emergence) in British Odonata between 1960 and 2004. The results show that there has been a significant, consistent advance in phenology in the taxon as a whole over the period of warming that is mediated by life history traits. British odonates significantly advanced the leading edge (first quartile date) of the flight period by a mean of 1.51 ±0.060 (SEM, n=17) days per decade or 3.08±1.16 (SEM, n=17) days per degree rise in temperature when phylogeny is controlled for. This study represents the first review of changes in odonate phenology in relation to climate change. The results suggest that the damped temperature oscillations experienced by aquatic organisms compared with terrestrial organisms are sufficient to evoke phenological responses similar to those of purely terrestrial taxa

A calculation of the Lepage-Mackenzie scale for the lattice axial and vector currents

We calculate the perturbative scales (q*) for the axial and vector currents for the Wilson action, with and without tadpole improvement, using Lepage and Mackenzie's formalism. The scale for the pseudoscalar density (times the mass) is computed as well. Contrary to naive expectation, tadpole improvement reduces q* by only a small amount for the operators we consider. We also discuss the use of a nonperturbative coupling to calculate the perturbative scale.Comment: 13 pages. One postscript figur

Separable potential model for K−NK^{-}N interactions at low energies

The effective separable meson-baryon potentials are constructed to match the equivalent chiral amplitudes up to the second order in external meson momenta. We fit the model parameters (low energy constants) to the threshold and low energy $K^{-}p$ data. In the process, the $K^{-}$-proton bound state problem is solved exactly in the momentum space and the 1s level characteristics of the kaonic hydrogen are computed simultaneously with the available low energy $K^{-}p$ cross sections. The model is also used to describe the $\pi \Sigma$ mass spectrum and the energy dependence of the $K^{-}n$ amplitude.Comment: 31 pages, v2 - added corrections to make it compatible with the published versio

The analytical singlet αs4\alpha_s^4 QCD contributions into the e+e−e^+e^--annihilation Adler function and the generalized Crewther relations

The generalized Crewther relations in the channels of the non-singlet and vector quark currents are considered. They follow from the double application of the operator product expansion approach to the same axial vector-vector-vector triangle amplitude in two regions, adjoining to the angle sides $(x,y)$ (or $p^2,q^2$). We assume that the generalized Crewther relations in these two kinematic regimes result in the existence of the same perturbation expression for two products of the coefficient functions of annihilation and deep-inelastic scattering processes in the non-singlet and vector channels. Taking into account the 4-th order result for $S_{GLS}$ and the perturbative effects of the violation of the conformal symmetry in the generalized Crewther relation, we obtain the analytical contribution to the singlet $\alpha_s^4$ correction to the $D_A^{V}$-function. Its a-posteriori comparison with the recent result of direct diagram-by-diagram evaluation of the singlet 4-th order corrections to $D_A^{V}$- function demonstrates the coincidence of the predicted and obtained $\zeta_3^2$-contributions to the singlet term. They can be obtained in the conformal invariant limit from the original Crewther relation. On the contrary to previous belief, the appearance of $zeta_3$-terms in perturbative series in gauge models does not contradict to the property of conformal symmetry and can be considered as ragular feature. The Banks-Zaks motivated relation between our predicted and obtained 4-th order corrections is mentioned. This confirms Baikov-Chetyrkin-Kuhn expectation that the generalized Crewther relation in the channel of vector currents receives additional singlet contribution, which in this order of perturbation theory is proportional to the first coefficient of the QCD $\beta$-function.Comment: Concrete new foundations explained, abstract updated, presentation improved, 2 references added, extra acknowledgements added. This work is dedicated to K. G. Chetyrkin on the occasion of his 60th anniversary, to be published in Jetp. Lett supposedly in vol.94, issue 1

Systematic and detailed analysis of behavioural tests in the rat Middle Cerebral Artery Occlusion (MCAO) model of stroke: tests for long-term assessment

In order to test therapeutics, functional assessments are required. In pre-clinical stroke research, there is little consensus regarding the most appropriate behavioural tasks to assess deficits; especially when testing over extended times in milder models with short occlusion times and small lesion volumes. In this study we comprehensively assessed 16 different behavioural tests, with the aim of identifying those that show robust, reliable and stable deficits for up to 2 months. These tasks are regularly used in stroke research, as well as being useful for examining striatal dysfunction in models of Huntington’s and Parkinson’s disease. Two cohorts of male Wistar rats underwent the intraluminal filament model of MCAO (30min) and were imaged 24hrs later. This resulted in primarily subcortical infarcts, with a small amount of cortical damage. Animals were tested, along with sham and naïve groups at 24hrs, 7 days, and 1 and 2 months. Following behavioural testing, brains were processed and striatal neuronal counts were performed alongside measurements of total brain and white matter atrophy. The staircase, adjusting steps, rotarod and apomorphine induced rotations were the most reliable for assessing long-term deficits in the 30 min transient MCAO model of stroke