Having defined a notion of homology for paired graphs, Métayer ([Ma]) proves a homological correctness criterion for proof nets, and states that for any proof net \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $G$\end{document} there exists a Jordan-Hölder decomposition of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} ${\mathsf H}_0(G)$\end{document}. This decomposition is determined by a certain enumeration of the pairs in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $G$\end{document}. We correct his (...) proof of this fact and show that there exists a 1-1 correspondence between these Jordan-Hölder decompositions of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} ${\mathsf H}_0(G)$\end{document} and the possible ‘construction-orders’ of the par-net underlying \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $G$\end{document}. (shrink)

Bakhsh-i avval. Akhlāq-i Islāmī -- Bakhsh-i duvvum. Ādāb-i ijtimāʻī.

Having defined a notion of homology for paired graphs, Métayer ([Ma]) proves a homological correctness criterion for proof nets, and states that for any proof net $G$ there exists a Jordan-Hölder decomposition of ${\mathsf H}_0(G)$ . This decomposition is determined by a certain enumeration of the pairs in $G$ . We correct his proof of this fact and show that there exists a 1-1 correspondence between these Jordan-Hölder decompositions of ${\mathsf H}_0(G)$ and the possible ‘construction-orders’ of the par-net underlying $G$.

We present a novel way of using proof nets for the multimodal Lambek calculus, which provides a general treatment of both the unary and binary connectives. We also introduce a correctness criterion which is valid for a large class of structural rules and prove basic soundness, completeness and cut elimination results. Finally, we will present a correctness criterion for the original Lambek calculus Las an instance of our general correctness criterion.

When we cut a multiplicative proof-net of linear logic in two parts we get two modules with a certain border. We call pretype of a module the set of partitions over its border induced by Danos-Regnier switchings. The type of a module is then defined as the double orthogonal of its pretype. This is an optimal notion describing the behaviour of a module: two modules behave in the same way precisely if they have the same type.In this paper we define (...) a procedure which allows to characterize (and calculate) the type of a module only exploiting its intrinsic geometrical properties and without any explicit mention to the notion of orthogonality. This procedure is simply based on elementary graph rewriting steps, corresponding to the associativity, commutativity and weak-distributivity of the multiplicative connectives of linear logic. (shrink)

al-Juzʼ al-awwal. al-Akhlāq al-fāḍilah -- al-juzʼ al-thānī. al-Akhlāq al-sāfilah.

An enquiry into plant consciousness requires, on the one hand, taking into account recent experiments in plant biology and, on the other hand, refining the theoretical framework of behaviour and the various degrees of cognition. The main goal of this contribution is to advance such a framework by comparing classical animal and human cognition approaches with the theories of minimal cognition. This leads us to interpret more carefully the various plant activities and to highlight the limits of classical theories of (...) zoocentric cognition. In particular, the article shows that the notions of cognition and consciousness are often abusively confused, and with that of behaviour. Once this ambiguity is removed, it is possible to better distinguish several meanings of consciousness and to evaluate their relevance to plant activities. (shrink)

Collection of studies on a leading moral philosopher and his work, or dedicated to him.

Smooth function is the essence of the ε-smooth support vector regression (ε-SSVR) which is an unconstrained convex quadratic programming. In this paper, Bézier function as a new smooth function is proposed to replace the ε-insensitive loss function of ε-SSVR with tolerating a smaller error in fitting given data sets linearly and nonlinearly. The ε-Bézier function smooth support vector regression (ε-BSSVR) model is presented. Theoretical analyses show that the derived smooth function has improved approximation precision compared with other smooth approximate functions. (...) The Newton-Armijo algorithm is applied to solve the new model. Numerical results and comparisons demonstrate that the proposed method has the better regression performance and learning efficiency compared with other given models. (shrink)

A new smooth method for solving the support vector machine classification (SVC) is presented. Since the objective function of the unconstrained SVC is non-smooth, we apply the smooth technique and replace the SVC function with Bézier function and get a class of Bézier smooth support vector machines (BSSVM). The fast Newton-Armijo algorithm is used to solve the BSSVM. Theoretical analysis and numerical results illustrate that this smooth SVM model improves in efficiency and accuracy compared with other smooth methods.

Ṣadr al-Dīn Shīrāzī, Muḥammad ibn Ibrāhīm; -1641; Islamic philosophy.

On human values and norms, their different kinds and theories are discussed in historical perspective.

We show how to get canonical models from in which the nonstationary ideal on ω1 is ω1 dense and there is no P-point.

Bachelard, Gaston; criticism and interpretation; knowledge, theory of; science; philosophy.