On the unity of logic

AbstractNous présentons un calcul des séquents unifié, commun aux logiques classique, intuitionniste et linéaire. La principale nouveautéest que les logiques classique, intuitionniste et linéaire apparaissent comme des fragments, c'estádire comme des classes particuliéres de formules et de séquents. Par exemple la démonstration d'unénoncéintuitionniste pourra utiliser des lemmes classiques ou intuitionnistes sans limitation: simplement aprèsélimination des coupures, la démonstration se fera entièrement dans le fragment intuitionniste, ce qui est superficiellement assurépar la propriétéde la sous-formule (seulement des formules intuitionnistes sont utilisées) et plus profondément par un traitement très rigoureux des règles structurelles. Cette approche est radicalement différente de l'approche habituelle qui consiste tout bonnementàchanger la règle du jeu quand on veut changer de logique, c'estàdire de style de séquent: ici il n'y a plus qu'une seule logique, qui au grédes utilisation peut apparaître classique, intuitionniste ou linéaire

The Effects of IFRS on Financial Ratios: Early Evidence in Canada

This paper provides preliminary evidence of the impact on financial ratios caused by the transition to International Financial Reporting Standards (IFRS) in Canada. The main features of IFRS are explained in the context of a shift from Canadian Generally Accepted Accounting Principles (GAAP) while the main differences between the two sets of rules are underscored – heavier reliance of IFRS on fair value accounting and comprehensive income, and the use of the entity theory for consolidation. The effects of IFRS on financial ratios in the areas of liquidity, leverage, coverage and profitability are discussed and verified using a sample cohort of early adopters in Canada. The preliminary evidence reveals significantly higher volatility to most of the ratios under IFRS when compared to those derived under pre-changeover Canadian GAAP. While the means and medians of IFRS ratios differ from the means and medians of the same ratios under pre-changeover Canadian GAAP, the differences are not statistically significant overall. However, important individual discrepancies are in some cases observed. Naturally, analysts using ratios for analytical purposes during the transition period need to be vigilant as ratios computed under IFRS are not directly comparable with those derived under pre-changeover Canadian GAAP. It is recommended that heightened attention be directed to the new feature – comprehensive income – which incorporates unrealized gains and losses that bypass the income statement. The suggested analytical tools best suited to mitigate the contributing effect include reliance on comprehensive-Return on Assets (ROA) and comprehensive-Return on Equity (ROE).IFRS, financial ratios, first application of IFRS

The three dimensions of proofs

In this document, we study a 3-polygraphic translation for the proofs of SKS, a formal system for classical propositional logic. We prove that the free 3-category generated by this 3-polygraph describes the proofs of classical propositional logic modulo structural bureaucracy. We give a 3-dimensional generalization of Penrose diagrams and use it to provide several pictures of a proof. We sketch how local transformations of proofs yield a non contrived example of 4-dimensional rewriting.Comment: 38 pages, 50 figure

Study of Geographical Variation in Kiln-Drying Behavior of Plantation-Grown White Spruce

White spruce (Picea glauca |Moench| Voss) is one of the most important tree species for reforestation in Canada. Over the past 30 years, hundreds of thousands of hectares were planted. Plantation-grown wood will become an important source of supply for the lumber industry in the near future. Plantation wood is generally known to have a greater proportion of juvenile wood than that from natural stands. For this reason, quality attributes of lumber from plantations might be considerably reduced, especially after kiln-drying. However, these quality attributes might be influenced by the origin of the seed sources used for the reforestation program. The main purpose of this study was to investigate the genetic variation in the effect of kiln-drying under restraint on shrinkage and warp of dimension lumber processed from 26 provenances originating from the Great Lakes and St. Lawrence Region. Two drying treatments were applied, i.e. conventional and high-temperature drying. Analyses of variance showed no significant differences among provenances for any type of shrinkage (longitudinal shrinkage, shrinkage in thickness, shrinkage in width) or warp (bow, crook, twist) measurements. For the effect of the drying treatment, it was significant only in the case of shrinkage in width

A System of Interaction and Structure II: The Need for Deep Inference

This paper studies properties of the logic BV, which is an extension of multiplicative linear logic (MLL) with a self-dual non-commutative operator. BV is presented in the calculus of structures, a proof theoretic formalism that supports deep inference, in which inference rules can be applied anywhere inside logical expressions. The use of deep inference results in a simple logical system for MLL extended with the self-dual non-commutative operator, which has been to date not known to be expressible in sequent calculus. In this paper, deep inference is shown to be crucial for the logic BV, that is, any restriction on the ``depth'' of the inference rules of BV would result in a strictly less expressive logical system

L’Etude détaillée des accidents (EDA ): Un outil pour la recherche

L’accès aux données est généralement une difficulté de la recherche. En matière de sécurité routière, une solution possible est le recours aux études approfondies d’accidents. Cette note expose I’Etude Détaillée des Accidents (EDA) de I’INRETS. L’objectif initial de I’EDA est d’enrichir la connaissance sur le déroulement des accidents en vue de leur prévention. La méthode de I’EDA repose sur une conception de l’accident comme symptôme de dysfonctionnement du système de circulation, sur une analyse en phase du déroulement de l’accident, et sur un modèle de l’usager comme système de traitement de l’information. Les données recueillies immédiatement sur la scène de l’accident par une équipe de spécialistes sont exploitées cliniquement cas par cas. La banque d’accidents ainsi constituée se prête à des exploitations thématiques. Au final, I’EDA apparaît comme un outil de recherche complémentaire aux autres outils classiques comme l’analyse statistique de fichiers nationaux, l’observation de terrain, ou l’expérimentation sur piste et en laboratoire.It is often difficult to collect the relevant data for scientific research. When working in the field of road safety we may have recourse to in-depth investigation of accidents. This paper deals with the Etude Détaillée des Accidents (EDA) carried out by INRETS. The initial objective of this study was to improve Our knowledge of the accident process for accident prevention purposes. From a methodological standpoint, this work is based on the premise that an accident can be defined as a symptom of a malfunction in the transport system. It uses a phase model analysis and views the road user as an information processing system. The data are collected on the scene of the accident by a qualified team, and the accidented then reconstructed and analysed case by case. The accidenty data bank is available for thematic-oriented applications. Finally, EDA would seem to be a research tool can be used as a complement to standard methods such as statistical file analysis, field investigation, laboratory experimentation and track-tests.O acesso a dados empíricos é geralmente difícil na investigação. Em segurança rodoviária uma solução possível consiste no recurso a estudos aprofundados de acidentes. Este artigo descreve O «Etude Détaillée des Accidents)) (EDA) do INRETS. O objectivo inicial do EDA é O de aumentar O conhecimento sobre os acidentes numa perspectiva de prevenção. O método do EDA assenta numa concepção do acidente como sintoma de disfuncionamento do sistema de circulação, numa análise em fase de progressão do acidente e num modelo de condutor como sistema de tratamento de informação. Os dados recolhidos imediatamente no local do acidente por uma equipa de especialistas serão explorados clinicamente, caso a caso. O banco de dados sobre acidentes assim constituído permite varias explorações temáticas. O EDA constituí pois um instrumento de investigação complementar aos outros meios classicos como a analise estatistica de ficheiros nacionais, as observações de campo ou as experiências em circuito e em laboratório

Five Conferences on Undecidability

These five lectures on undecidability were given to students with a good level in mathematics but with no special knowledge on logic. The first conference presents the formalization of mathematics with a short historical survey, the language of first order predicates and the axioms of set theory. The second and third lectures explain the incompleteness phenomena from the Hilbert program until Gödel's theorems with a presentation of the sequent calculus of Gentzen.The fourth talk deepens model theory reasoning in the case of the continuum hypothesis, and the last conference gives examples of effective computability results

Sublogarithmic uniform Boolean proof nets

Using a proofs-as-programs correspondence, Terui was able to compare two models of parallel computation: Boolean circuits and proof nets for multiplicative linear logic. Mogbil et. al. gave a logspace translation allowing us to compare their computational power as uniform complexity classes. This paper presents a novel translation in AC0 and focuses on a simpler restricted notion of uniform Boolean proof nets. We can then encode constant-depth circuits and compare complexity classes below logspace, which were out of reach with the previous translations.Comment: In Proceedings DICE 2011, arXiv:1201.034

On additive bases in infinite abelian semigroups

27 pagesIn this paper, building on previous work by Lambert, Plagne and the third author, we study various aspects of the behavior of additive bases in a class of infinite abelian semigroups, which we term \em translatable \em semigroups. These include all numerical semigroups as well as all infinite abelian groups. We show that, for every such semigroup $T$, the number of essential subsets of any additive basis is finite, and also that the number $E_T(h, k)$ of essential subsets of cardinality $k$ contained in an additive basis of order at most $h$ can be bounded in terms of $h$ and $k$ alone. These results extend the reach of two theorems, one due to Deschamps and Farhi and the other to Hegarty, bearing upon ${\mathbf{N}}$. Also, using invariant means, we address a classical problem, initiated by Erd\H{o}s and Graham and then generalized by Nash and Nathanson both in the case of ${\mathbf{N}}$, of estimating the maximal order $X_T(h, k)$ that a basis of cocardinality $k$ contained in an additive basis of order at most $h$ can have. Among other results, we prove that, whenever $T$ is a translatable semigroup, $X_T(h, k)$ is $O(h^{2k+1})$ for every integer $k \ge 1$. This result is new even in the case where $k = 1$ and $T$ is an infinite abelian group. Besides the maximal order $X_T(h, k)$, the typical order $S_T(h, k)$ is also studied

Bounded Linear Logic

A typed, modular paradigm for polynomial time computation is proposed