Defining and assessing spiritual health : a comparative study among 13- to 15-year-old pupils attending secular schools, Anglican schools, and private Christian schools in England and Wales

This article argues that the nation's commitment to young people involves proper concern for their physical health, their psychological health, and their spiritual health. In this context the notion of spiritual health is clarified by a critique of John Fisher's model of spiritual health. Fisher developed a relational model of spiritual health, which defines good spiritual health in terms of an individual's relationship to four domains: the personal, the communal, the environmental, and the transcendental. In the present analysis, we make comparisons between pupils educated in three types of schools: publicly funded schools without religious foundation, publicly funded schools with an Anglican foundation, and new independent Christian schools (not publicly funded). Our findings draw attention to significant differences in the levels of spiritual health experienced by pupils within these three types of schools

Connector algebras for C/E and P/T nets interactions

A quite fourishing research thread in the recent literature on component based system is concerned with the algebraic properties of different classes of connectors. In a recent paper, an algebra of stateless connectors was presented that consists of five kinds of basic connectors, namely symmetry, synchronization, mutual exclusion, hiding and inaction, plus their duals and it was shown how they can be freely composed in series and in parallel to model sophisticated "glues". In this paper we explore the expressiveness of stateful connectors obtained by adding one-place buffers or unbounded buffers to the stateless connectors. The main results are: i) we show how different classes of connectors exactly correspond to suitable classes of Petri nets equipped with compositional interfaces, called nets with boundaries; ii) we show that the difference between strong and weak semantics in stateful connectors is reflected in the semantics of nets with boundaries by moving from the classic step semantics (strong case) to a novel banking semantics (weak case), where a step can be executed by taking some "debit" tokens to be given back during the same step; iii) we show that the corresponding bisimilarities are congruences (w.r.t. composition of connectors in series and in parallel); iv) we show that suitable monoidality laws, like those arising when representing stateful connectors in the tile model, can nicely capture concurrency aspects; and v) as a side result, we provide a basic algebra, with a finite set of symbols, out of which we can compose all P/T nets, fulfilling a long standing quest

Enumerating Independent Linear Inferences

A linear inference is a valid inequality of Boolean algebra in which each variable occurs at most once on each side. Equivalently, it is a linear rewrite rule on Boolean terms that constitutes a valid implication. Linear inferences have played a significant role in structural proof theory, in particular in models of substructural logics and in normalisation arguments for deep inference proof systems. In this work we leverage recently developed graphical representations of linear formulae to build an implementation that is capable of more efficiently searching for switch-medial-independent inferences. We use it to find four `minimal' 8-variable independent inferences and also prove that no smaller ones exist; in contrast, a previous approach based directly on formulae reached computational limits already at 7 variables. Two of these new inferences derive some previously found independent linear inferences. The other two (which are dual) exhibit structure seemingly beyond the scope of previous approaches we are aware of; in particular, their existence contradicts a conjecture of Das and Strassburger. We were also able to identify 10 minimal 9-variable linear inferences independent of all the aforementioned inferences, comprising 5 dual pairs, and present applications of our implementation to recent `graph logics'.Comment: 33 pages, 3 figure

Multi-amalgamation of rules with application conditions in M-adhesive categories

Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.Amalgamation is a well-known concept for graph transformations that is used to model synchronised parallelism of rules with shared subrules and corresponding transformations. This concept is especially important for an adequate formalisation of the operational semantics of statecharts and other visual modelling languages, where typed attributed graphs are used for multiple rules with nested application conditions. However, the theory of amalgamation for the double-pushout approach has so far only been developed on a set-theoretical basis for pairs of standard graph rules without any application conditions. For this reason, in the current paper we present the theory of amalgamation for M-adhesive categories, which form a slightly more general framework than (weak) adhesive HLR categories, for a bundle of rules with (nested) application conditions. The two main results are the Complement Rule Theorem, which shows how to construct a minimal complement rule for each subrule, and the Multi-Amalgamation Theorem, which generalises the well-known Parallelism and Amalgamation Theorems to the case of multiple synchronised parallelism. In order to apply the largest amalgamated rule, we use maximal matchings, which are computed according to the actual instance graph. The constructions are illustrated by a small but meaningful running example, while a more complex case study concerning the firing semantics of Petri nets is presented as an introductory example and to provide motivation

A Stronger Bell Argument for (Some Kind of) Parameter Dependence

It is widely accepted that the violation of Bell inequalities excludes local theories of the quantum realm. This paper presents a new derivation of the inequalities from non-trivial non-local theories and formulates a stronger Bell argument excluding also these non-local theories. Taking into account all possible theories, the conclusion of this stronger argument provably is the strongest possible consequence from the violation of Bell inequalities on a qualitative probabilistic level (given usual background assumptions). Among the forbidden theories is a subset of outcome dependent theories showing that outcome dependence is not sufficient for explaining a violation of Bell inequalities. Non-local theories which can violate Bell inequalities (among them quantum theory) are rather characterised by the fact that at least one of the measurement outcomes in some sense (which is made precise) probabilistically depends both on its local as well as on its distant measurement setting ('parameter'). When Bell inequalities are found to be violated, the true choice is not 'outcome dependence or parameter dependence' but between two kinds of parameter dependences, one of them being what is usually called 'parameter dependence'. Against the received view established by Jarrett and Shimony that on a probabilistic level quantum non-locality amounts to outcome dependence, this result confirms and makes precise Maudlin's claim that some kind of parameter dependence is required.Comment: forthcoming in: Studies in the History and Philosophy of Modern Physic

Multi-amalgamation of rules with application conditions in M-adhesive categories

Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.Amalgamation is a well-known concept for graph transformations that is used to model synchronised parallelism of rules with shared subrules and corresponding transformations. This concept is especially important for an adequate formalisation of the operational semantics of statecharts and other visual modelling languages, where typed attributed graphs are used for multiple rules with nested application conditions. However, the theory of amalgamation for the double-pushout approach has so far only been developed on a set-theoretical basis for pairs of standard graph rules without any application conditions. For this reason, in the current paper we present the theory of amalgamation for M-adhesive categories, which form a slightly more general framework than (weak) adhesive HLR categories, for a bundle of rules with (nested) application conditions. The two main results are the Complement Rule Theorem, which shows how to construct a minimal complement rule for each subrule, and the Multi-Amalgamation Theorem, which generalises the well-known Parallelism and Amalgamation Theorems to the case of multiple synchronised parallelism. In order to apply the largest amalgamated rule, we use maximal matchings, which are computed according to the actual instance graph. The constructions are illustrated by a small but meaningful running example, while a more complex case study concerning the firing semantics of Petri nets is presented as an introductory example and to provide motivation