The Variety of Lattice-Ordered Monoids Generated by the Natural Numbers

We study the variety Var() of lattice-ordered monoids generated by the natural numbers. In particular, we show that it contains all 2-generated positively ordered lattice-ordered monoids satisfying appropriate distributive laws. Moreover, we establish that the cancellative totally ordered members of Var() are submonoids of ultrapowers of and can be embedded into ordered fields. In addition, the structure of ultrapowers relevant to the finitely generated case is analyzed. Finally, we provide a complete isomorphy invariant in the two-generated case.     

The Variety of Lattice Effect Algebras Generated by MV-algebras and the Horizontal Sum of Two 3-element Chains

It has been recently shown [4] that the lattice effect algebras can be treated as a subvariety of the variety of so-called basic algebras. The open problem whether all subdirectly irreducible distributive lattice effect algebras are just subdirectly irreducible MV-chains and the horizontal sum of two 3-element chains is in the paper transferred into a more tractable one. We prove that modulo distributive lattice effect algebras, the variety generated by MV-algebras and is definable by three simple identities and the problem now is to check if these identities are satisfied by all distributive lattice effect algebras or not. Presented by Daniele Mundici     

《长春真人西游记》的艺术特征

李志常所撰写的《长春真人西游记》是道教史上具有重要代表意义的一篇经典游记作品。本文在对其进行认真分析、研究的基础上,指出该游记具有“两种视角的独特写法”、“与政治同行的宗教游记”以及风俗人情的记载、科学不盲从的态度、语言简洁、优美,结构前后照应等艺术特征。     

The Necessities of Perfect Freedom

This article is a reflection on Augustine's suggestion that Christians have significant theological reasons to accept that freedom need not be correlated with having choices. Following his lead, I explore questions about freedom and agency raised by the perfect freedom of the saints in heaven, Jesus' sinless earthly life and the freedom with which the triune God is eternally blessed. My thesis is that those who worship the triune God and praise the sinless perfection of Christ and the heavenly saints have reason to accept a ‘normative’ conception of freedom, according to which certain kinds of necessity are not merely compatible with perfect freedom but intrinsic to it.     

Ordinal judgments of numerical symbols by macaques (Macaca mulatta)

Two rhesus monkeys (Macaca mulatta) learned that the arabic numerals 0 through 9 represented corresponding quantities of food pellets. By manipulating a joystick, the monkeys were able to make a selection of paired numerals presented on a computer screen. Although the monkeys received a corresponding number of pellets even if the lesser of the two numerals was selected, they learned generally to choose the numeral of greatest value even when pellet delivery was made arrhythmic. In subsequent tests, they chose the numerals of greater value when presented in novel combinations or in random arrays of up to five numerals. Thus, the monkeys made ordinal judgments of numerical symbols in accordance with their absolute or relative values.     

Mathematical Proof Theory in the Light of Ordinal Analysis

We give an overview of recent results in ordinal analysis. Therefore,we discuss the different frameworks used in mathematical proof-theory, namely subsystem of analysis including reversemathematics, Kripke–Platek set theory, explicitmathematics, theories of inductive definitions,constructive set theory, and Martin-Löfs typetheory.     

The Short Form of the Revised Almost Perfect Scale

We created a shorter and more refined item set from the Almost Perfect Scale–Revised (APS–R; Slaney, Mobley, Trippi, Ashby, & Johnson, 1996; Slaney, Rice, Mobley, Trippi, & Ashby, 2001) to measure 2 major dimensions of perfectionism: standards (high performance expectations) and discrepancy (self-critical performance evaluations). In Study 1, after testing the internal structure of the measure (N = 749), a subset of the current APS–R items was derived (Short Almost Perfect Scale [SAPS]) that possessed good psychometric features, such as strong item–factor loadings, score reliability, measurement invariance between women and men, and criterion-related validity through associations with neuroticism, conscientiousness, academic performance, and depression. Controlling for neuroticism and conscientiousness, factor mixture modeling supported a 2-factor, 3-class model of perfectionism, and results were consistent with labeling the classes as nonperfectionists and adaptive and maladaptive perfectionists. Measurement results were cross-validated in a separate sample (N = 335). Study 2 also provided substantial evidence for the convergent, discriminant, and criterion-related validity of SAPS scores. Both studies supported the SAPS as a brief and psychometrically strong measure of major perfectionism factors and classes of perfectionists.     

Equational Characterization of the Subvarieties of BL Generated by t-norm Algebras

In this paper we show that the subvarieties of BL, the variety of BL-algebras, generated by single BL-chains on [0, 1], determined by continous t-norms, are finitely axiomatizable. An algorithm to check the subsethood relation between these subvarieties is provided, as well as another procedure to effectively find the equations of each subvariety. From a logical point of view, the latter corresponds to find the axiomatization of every residuated many-valued calculus defined by a continuous t-norm and its residuum. Actually, the paper proves the results for a more general class than t-norm BL-chains, the so-called regular BL-chains.     

Ordinal representation of numeric quantities by brown capuchin monkeys (Cebus apella)

Using techniques established by E. M. Brannon and H. S. Terrace (2000) with rhesus macaques (Macaca mulatta), the authors tested the ability of brown capuchins (Cebus apella) to order arrays of items ranging in quantity from 1 to 9. Three monkeys were trained on a touch screen to select the quantities 1-4 in ascending order. The monkeys exhibited successful transfer of this ability to novel representations of the quantities 1-4 and to pairs of the novel quantities 5-9. Patterns of responding with respect to numeric distance and magnitude were similar to those seen in human subjects, suggesting the use of similar psychological processes. The capuchins demonstrated an ordinal representation of quantity equivalent to that shown in Old World monkeys.     

The Discrimination of Patient-Generated and Randomly Generated MMPIs

A discriminant analysis was applied to 34 randomly generated and 34 patient-generated Minnesota Multiphasic Personality inventory (MMPI) profiles. The discriminant was able to differentiate the two sets at greater than 97% accuracy. A cross validation based on derived unstandardized canonical discriminant functions was carried out on an additional 10 random and l0 patient MMPIs, It attained 95% accuracy. Eight experienced clinical psychologists attained tess than 70% accuracy–six of the eight did no better than chance. The importance of including actuarial data in validity judgments was discussed.     

The best of all possibleworlds

The Argument from Inferiority holds that our world cannot be the creation of an omnipotent and omnibenevolent being; for if it were, it would be the best of all possible worlds, which evidently it is not. We argue that this argument rests on an implausible principle concerning which worlds it is permissible for an omnipotent being to create: roughly, the principle that such a being ought not to create a non-best world. More specifically, we argue that this principle is plausible only if we assume that there is a best element in the set of all possible worlds. However, as we show, there are conceivable scenarios in which that assumption does not hold.     

The Font of all Wisdom

Can Religion be Explained Away ? D. Z. Phillips (ed.) Atheism and Theism , J. J.C. Smart and J. J. Haldane Arguing for Atheism: An Introduction to the Philosophy of Religion , Robin Le Poidevin     

模态逻辑典范框架的生成子框架

模态逻辑的典范性由“局部”典范性拼接而成。本文讨论了“局部”典范性问题,即一个模态逻辑的典范框架的什么样的生成子框架是该逻辑的框架。主要的结果是证明了一个逻辑的典范框架的有界宽的生成子框架都是该逻辑的框架,并且典范框架内嵌了所有该逻辑的有穷宽框架。     

A Unified Framework for the Comparison of Treatments with Ordinal Responses

Different latent variable models have been used to analyze ordinal categorical data which can be conceptualized as manifestations of an unobserved continuous variable. In this paper, we propose a unified framework based on a general latent variable model for the comparison of treatments with ordinal responses. The latent variable model is built upon the location-scale family and is rich enough to include many important existing models for analyzing ordinal categorical variables, including the proportional odds model, the ordered probit-type model, and the proportional hazards model. A flexible estimation procedure is proposed for the identification and estimation of the general latent variable model, which allows for the location and scale parameters to be freely estimated. The framework advances the existing methods by enabling many other popular models for analyzing continuous variables to be used to analyze ordinal categorical data, thus allowing for important statistical inferences such as location and/or dispersion comparisons among treatments to be conveniently drawn. Analysis on real data sets is used to illustrate the proposed methods.     

The Adequacy of Resemblance Nominalism about Perfect Naturalness

Resemblance Nominalism About Perfect Naturalness (RNPN) is the view that perfect naturalness of classes is best defined by a conceptual primitive of resemblance between particulars. The adequacy of RNPN is defended by (part I) outlining nominalism as the strictly anti‐constitutive view that the particulars’ being the fundamental ways they are is not constituted by anything further, (part II) supplying a doubly plural contrastive and graded resemblance predicate that allows for a definition of perfect naturalness on an actualist basis, and (part III) proving a representation and a uniqueness theorem on the basis of a formal constraint on resemblance called “the Principle”, thereby revealing that bodies of nominalist resemblance facts are guaranteed to behave as if they were grounded in patterns of universals distributed over particulars.     

Ordinal process dissociation and the measurement of automatic and controlled processes

The process-dissociation equations (L. Jacoby, 1991) have been applied to results from inclusion and exclusion tasks to derive quantitative estimates of the influence of controlled and automatic processes on memory. This research has provoked controversies (e.g., T. Curran & D. Hintzman, 1995) regarding the validity of specific assumptions underlying the process-dissociation equations. In this article, the author explores the conclusions one can draw about the ordinal relations between automatic and controlled processes across experimental conditions from results in the inclusion and exclusion tasks. Given relatively neutral assumptions, this article presents and proves 6 theorems that allow investigators to draw conclusions about the ordinal relations between automatic and/or controlled processes across experimental conditions. An illustrative example is presented, and the current approach is compared with the original process-dissociation framework.     

Ordinal structure in the visual perception and cognition of smoothly curved surfaces

In theoretical analyses of visual form perception, it is often assumed that the 3-dimensional structures of smoothly curved surfaces are perceptually represented as point-by-point mappings of metric depth and/or orientation relative to the observer. This article describes an alternative theory in which it is argued that our visual knowledge of smoothly curved surfaces can also be defined in terms of local, nonmetric order relations. A fundamental prediction of this analysis is that relative depth judgments between any two surface regions should be dramatically influenced by monotonicity of depth change (or lack of it) along the intervening portions of the surface through which they are separated. This prediction is confirmed in a series of experiments using surfaces depicted with either shading or texture. Additional experiments are reported, moreover, that demonstrate that smooth occlusion contours are a primary source of information about the ordinal structure of a surface and that the depth extrema in between contours can be optically specified by differences in luminance at the points of occlusion.