Birkhoff-like sheaf representation for varieties of lattice expansions

Given a variety we study the existence of a class such that S1 every A can be represented as a global subdirect product with factors in and S2 every non-trivial A is globally indecomposable. We show that the following varieties (and its subvarieties) have a class satisfying properties S1 and S2: p-algebras, distributive double p-algebras of a finite range, semisimple varieties of lattice expansions such that the simple members form a universal class (bounded distributive lattices, De Morgan algebras, etc) and arithmetical varieties in which the finitely subdirectly irreducible algebras form a universal class (f-rings, vector groups, Wajsberg algebras, discriminator varieties, Heyting algebras, etc). As an application we obtain results analogous to that of Nachbin saying that if every chain of prime filters of a bounded distributive lattice has at most length 1, then the lattice is Boolean.We wish to thank Lic. Alfredo Guerin and Dr. Daniel Penazzi for helping us with linguistics aspects. We are indebted to the referee for several helpful suggestions. We also wish to thank Professor Mick Adams for providing us with several reprints and useful e-mail information on the subject.Suported by CONICOR and SECyT (UNC).     

Refuting the unfolding-argument on the irrelevance of causal structure to consciousness

The unfolding argument (UA) was advanced as a refutation of prominent theories, which posit that phenomenal experience is determined by patterns of neural activation in a recurrent (neural) network (RN) structure. The argument is based on the statement that any input–output function of an RN can be approximated by an “equivalent” feedforward-network (FFN). According to UA, if consciousness depends on causal structure, its presence is unfalsifiable (thus non-scientific), as an equivalent FFN structure is behaviorally indistinguishable with regards to any behavioral test. Here I refute UA by appealing to computational theory and cognitive-neuroscience. I argue that a robust functional equivalence between FFN and RN is not supported by the mathematical work on the Universal Approximator theorem, and is also unlikely to hold, as a conjecture, given data in cognitive neuroscience; I argue that an equivalence of RN and FFN can only apply to static functions between input/output layers and not to the temporal patterns or to the network’s reactions to structural perturbations. Finally, I review data indicating that consciousness has functional characteristics, such as a flexible control of behavior, and that cognitive/brain dynamics reveal interacting top-down and bottom-up processes, which are necessary for the mediation of such control processes.     

共享概念的性质对拥有关系句子情景模型建立的影响

应用扇效应技术探讨共享概念的性质对建构拥有关系情境模型的影响。共包括2个实验,探讨在将“多人买1物”句式中的所购“物品”改变为隐含共同地点信息的“物品”条件下,被试对“多人买1物”拥有行为句式的学习是否表现出扇效应。结果表明,当所购物品隐含的相同地点信息的情况下,“多人买1物”的拥有行为句式无论是否具有明确的地点状语,都如同“1人买多物”的句式一样,没有表现出扇效应,与Radvanskv的研究结果不同。据此认为,只有在共享概念是属于情景模型建构的维度信息的情况下,有共享概念的信息才能整合为同一个情景模型。     

Admissibility of Cut in <Emphasis Type="Italic">LC</Emphasis> with Fixed Point Combinator

The fixed point combinator (Y) is an important non-proper combinator, which is defhable from a combinatorially complete base. This combinator guarantees that recursive equations have a solution. Structurally free logics (LC) turn combinators into formulas and replace structural rules by combinatory ones. This paper introduces the fixed point and the dual fixed point combinator into structurally free logics. The admissibility of (multiple) cut in the resulting calculus is not provable by a simple adaptation of the similar proof for LC with proper combinators. The novelty of our proof—beyond proving the cut for a newly extended calculus–is that we add a fourth induction to the by-and-large Gentzen-style proof. Presented by Robert Goldblatt     

Algebras of Intervals and a Logic of Conditional Assertions

Intervals in boolean algebras enter into the study of conditional assertions (or events) in two ways: directly, either from intuitive arguments or from Goodman, Nguyen and Walker's representation theorem, as suitable mathematical entities to bear conditional probabilities, or indirectly, via a representation theorem for the family of algebras associated with de Finetti's three-valued logic of conditional assertions/events. Further representation theorems forge a connection with rough sets. The representation theorems and an equivalent of the boolean prime ideal theorem yield an algebraic completeness theorem for the three-valued logic. This in turn leads to a Henkin-style completeness theorem. Adequacy with respect to a family of Kripke models for de Finetti's logic, ukasiewicz's three-valued logic and Priest's Logic of Paradox is demonstrated. The extension to first-order yields a short proof of adequacy for Körner's logic of inexact predicates.     

Fitts’ Theorem in Oculomotor Control: Dissociable Movement Times for Amplitude and Width Manipulations

The authors examined whether movement times (MT) for discrete saccades are constant given equivalent index of difficulty (ID) values (i.e., unitary nature of Fitts’ theorem). To that end, we contrasted ID/MT relations for saccades equated for ID but differing with respect to their target amplitudes and widths. Results showed that MT increased with increasing ID within amplitude and width conditions; however, the ID/MT slope was markedly steeper in the former condition. Thus, the amplitude condition imposed greater information processing demands than the width condition—a result indicating that the constituent elements of Fitts’ theorem are dissociable (i.e., nonunitary). Further, examination of saccade kinematics demonstrated that the optimal MT for a given target amplitude was largely independent of target width.     

Reconsidering religion and fandom: Christian fan works in My Little Pony fandom

Studies of religion and fandom have tended to explore the extent to which fan cultures might be seen as forms of surrogate religion. This article suggests that a more detailed examination of the way in which believers use their faith within their individual fandoms would offer more interesting insights into both contemporary religious practice and fandom. Conducting a case study of ‘Brony’ fandom (adult fandom of cartoon My Little Pony: Friendship is Magic), this article explores the ways in which Christian fans use fan fiction and art to promote religious literacy, explore theological issues and engage in evangelism and exegesis. Fan knowledge is used as a way to quickly impart and explore complex religious concepts in a manner which utilises the shared culture of fandom. This should not be seen as a symptom of ‘mediatisation’ but as part of a complex synthesis of faith and popular culture.     

The fan effect influences face recognition but does not moderate the own-age bias

ABSTRACT

The fan effect shows that memory is superior for information associated with few contexts relative to information associated with many contexts. The current study examined the fan effect within face recognition. Participants studied faces in which eye regions were associated with only one face (low-fan) or several faces (high-fan). Additionally, we examined whether featural fan might moderate in-group biases (i.e. in-group faces are better remembered than out-group faces). To this end, we manipulated occupation status (Experiment 1) and age (Experiment 2) of studied faces, and presented high- and low-fan faces. Results showed that low-fan faces were better remembered than high-fan faces. We did not detect an in-group bias as a function of occupation status, but there was a robust own-age bias. Fan type did not moderate the own-age bias, however. Although face recognition is sensitive to featural fan, the effect does not appear to differentially impact the own-age bias..     

The Undecidability of Grisin's Set Theory

We investigate a contractionless naive set theory, due to Grisin [11]. We prove that the theory is undecidable.     

Promoting fan engagement: An exploration of the fundamental motives for sport consumption amongst premier league football spectators

The aim of this study was to examine whether fan engagement could be predicted by the motivational dimensions of sport consumption. A sample of 806 football sport fans (African = 85%, male = 67.4%, part of an organised supporters club = 57.6%) were participants. They completed the Fan Engagement Scale (FES), the Motivation Scale for Sport Consumption (MSSC) and a biographical questionnaire. Structural equation modelling was applied to evaluate the postulated regressive paths between the motivational dimensions for sports consumption and fan engagement. The motivational dimensions for sport consumption were clustered into personal and game-related factors. Both these clusters of factors were predictive of fan engagement. Customer engagement (CE) theory appears to explain the findings.