The Basic Algebra of Game Equivalences

We give a complete axiomatization of the identities of the basic game algebra valid with respect to the abstract game board semantics. We also show that the additional conditions of termination and determinacy of game boards do not introduce new valid identities.En route we introduce a simple translation of game terms into plain modal logic and thus translate, while preserving validity both ways, game identities into modal formulae.The completeness proof is based on reduction of game terms to a certain minimal canonical form, by using only the axiomatic identities, and on showing that the equivalence of two minimal canonical terms can be established from these identities.     

A Coalgebraic View of Heyting Duality

We give a coalgebraic view of the restricted Priestley duality between Heyting algebras and Heyting spaces. More precisely, we show that the category of Heyting spaces is isomorphic to a full subcategory of the category of all -coalgebras, based on Boolean spaces, where is the functor which maps a Boolean space to its hyperspace of nonempty closed subsets. As an appendix, we include a proof of the characterization of Heyting spaces and the morphisms between them.     

On subdirectly irreducible OMAs

In this paper some properties of epi-representations and Schmidt-congruence relations of orthomodular partial algebras are investigated and an infinite list of OMA-epi-subdirectly irreducible orthomodular partial algebras will be constructed.Special issue of Studia Logica: Algebraic Theory of Quasivarieties Presented by M. E. Adams, K. V. Adaricheva, W. Dziobiak, and A. V. Kravchenko     

A Generalization of the Łukasiewicz Algebras

We introduce the variety _n ^m , m 1 and n 2, of m-generalized ukasiewicz algebras of order n and characterize its subdirectly irreducible algebras. The variety _n ^m is semisimple, locally finite and has equationally definable principal congruences. Furthermore, the variety _n ^m contains the variety of ukasiewicz algebras of order n.     

Intuitive physics and cognitive algebra: A review

IntroductionIntuitive physics explores how people without a formal instruction in physics intuitively understand physical phenomena. After a general overview of the topics of current research in intuitive physics and a discussion of current debates, this paper provides an introduction to Information Integration Theory (IIT).ObjectiveBy means of examples, it is shown how IIT can be used to directly compare the algebraic structure of physical laws and the algebraic structure of cognitive representations of these laws.MethodThe review considers about 40 years of research on the application of IIT in the field of intuitive physics. Occasionally, reference is also made to intuitive physics studies outside this theoretical framework.ResultsThe reviewed studies highlight four main factors that affect the degree of consistency between physical laws and cognitive algebraic laws: the participants’ age, their familiarity with the event under study, the type of task, and possible learning processes.ConclusionThe last part of the article discusses the implications of the results of the reviewed studies for the two main current hypotheses on the nature of intuitive physics, namely, that intuitive physics may be based on sub-optimal heuristics or may be based on the internalization of physical laws.     

New measures of political attitudes in Northern Ireland: a social identity perspective

Twenty‐eight measures of political attitudes were validated on a sample of 388 undergraduate students from Northern Ireland. Confirmatory factor analysis showed the scales to be unidimensional, discriminantly valid, with generally excellent reliabilities. The pattern of intergroup differentiation between Catholics and Protestants conformed to Social Identity Theory, with maximum differentiation on important issues, Catholics adopting a social change ideology and Protestants defending the status quo. Catholics and Protestants resolved their respective group associations with violence by condemning both it and terrorism, and also reported interdenominational friendships. The utility of these new measures of political attitudes in terms of measuring changes due to political initiatives, cross‐community reconciliation programmes and in assessing changes in attitudes as a result of integrated or segregated denominational schooling within the Province is outlined. Copyright © 2000 John Wiley & Sons, Ltd.     

TIME AND ETERNITY: HYMNIC,BIBLICAL, SCIENTIFIC,AND THEOLOGICAL VIEWS

The book Time and Eternity, the English version of Zeit und Ewigkeit, by Antje Jackelén, contains scientific and theological treatments of these two topics, starting with the usage of such ideas in German, Swedish, and English hymns. This essay describes her work and explains how the scientific ideas provide a coherent framework for understanding the place of time.     

Motivational dynamics in the development of career attitudes among adolescents

Super (1990) proposed that the psychological determinants of career development attitudes are time perspective, self-esteem, and causal attributions. The present study analyzed the effects of these determinants on the career development attitudes of 320 students from grade 9 and 300 students from grade 12. The analysis of the data using structural equations modeling (LISREL) showed both similarities and differences in the effects of the determinants of career attitudes between the two grade levels. The results are discussed in the context of the career maturity model.     

Illumination-invariance of Plateau's midgray

In a classical experiment Plateau [(1872). Sur la mesure des sensations physiques, et sur la loi qui lie l’intensité de la cause excitante. Bulletins de L’Academie Royale des Sciences, des Lettres et des Beaux-Arts de Belgique, 2me Série, 33, 376-388] found that the midgray operation is illumination-invariant. Falmagne [(1985). Elements of psychophysical theory. New York: Oxford University Press] provided a formalization of this finding that gives rise to two functional equations, the solutions of which determine the possible forms of the psychophysical function. This approach is generalized so that it explicitly refers to the illuminance, and can be applied to the experimentally well-studied class of center-surround stimuli. It is shown that the illumination-invariance of both cross-context matches and Plateau's midgray specify the psychophysical function up to an increasing function of the relative luminance of stimulus/illumination and center/surround, respectively. Relating this result to that implied by Wallach's ratio principle clarifies the role of Plateau's midgray in experimental research on achromatic color perception. Further generalizing the framework extends its scope to more complex experimental settings and the therein observed invariances.