Optimal natural dualities for varieties of Heyting algebras

The techniques of natural duality theory are applied to certain finitely generated varieties of Heyting algebras to obtain optimal dualities for these varieties, and thereby to address algebraic questions about them. In particular, a complete characterisation is given of the endodualisable finite subdirectly irreducible Heyting algebras. The procedures involved rely heavily on Priestley duality for Heyting algebras.     

Loglinear multidimensional IRT models for polytomously scored items

A loglinear IRT model is proposed that relates polytomously scored item responses to a multidimensional latent space. The analyst may specify a response function for each response, indicating which latent abilities are necessary to arrive at that response. Each item may have a different number of response categories, so that free response items are more easily analyzed. Conditional maximum likelihood estimates are derived and the models may be tested generally or against alternative loglinear IRT models.Hank Kelderman is currently affiliated with Vrije Universiteit, Amsterdam.We thank Linda Vodegel-Matzen of the Division of Developmental Psychology of the University of Amsterdam for making available the data used in the example in this article.     

The conjunctive model of hierarchical classes

This paper describes the conjunctive counterpart of De Boeck and Rosenberg's hierarchical classes model. Both the original model and its conjunctive counterpart represent the set-theoretical structure of a two-way two-mode binary matrix. However, unlike the original model, the new model represents the row-column association as a conjunctive function of a set of hypothetical binary variables. The conjunctive nature of the new model further implies that it may represent some conjunctive higher order dependencies among rows and columns. The substantive significance of the conjunctive model is illustrated with empirical applications. Finally, it is shown how conjunctive and disjunctive hierarchical classes models relate to Galois lattices, and how hierarchical classes analysis can be useful to construct lattice models of empirical data.The research reported in this paper was supported by NATO (Grant CRG.921321 to Iven Van Mechelen and Seymour Rosenberg) and by the Research Fund of Katholieke Universiteit Leuven (Grants PDM92/19 and POR93/3 to Iven Van Mechelen; Grants OT89/9 and F91/56 to Paul De Boeck).     

模糊偏序关系在心理学研究中的应用

本文首次给出建立模糊偏序关系矩阵的可行途径。以大学生的颜色爱好实验为例,论证了采用本文所建立的模糊偏序关系矩阵进行排序的方法是制作顺序量表的一种较佳方法。     

Item information and discrimination functions for trinary pcm items

For trinary partial credit items the shape of the item information and the item discrimination function is examined in relation to the item parameters. In particular, it is shown that these functions are unimodal if ₂ – ₁ < 4 ln 2 and bimodal otherwi The locations and values of the maxima are derived. Furthermore, it is demonstrated that the value of the maximum is decreasing in ₂ – ₁. Consequently, the maximum of a unimodal item information function is always larger than the maximum of a bimodal one, and similarly for the item discrimination function.The work reported herein was partially supported under the National Assessment of Educational Progress (Grant No. R999G30002; CFDA No. 84.999G) as administered by the Office of Educational Research and Improvement, US Department of Education.     

ON THE INABILITY OF INTERVAL TIME SAMPLING TO REFLECT FREQUENCY OF OCCURRENCE DATA1

Interval time sampling yields the result, percentage of intervals scored. It is rudimentary to note that this measure per se does not constitute a response dimension. It is a useful behavioral measure, therefore, only to the extent that it accurately reflects the nature and degree of the fundamental dimensions from which it is drawn i.e., frequency and duration. The correspondence between scored intervals and response duration is fairly well understood (Journal of Applied Behavior Analysis, 1975, 8 , 463–469; 1977, 10 , 325–332). This study determined the correspondence between scored intervals and response frequency. Eleven, 30-minute experimental sessions that differed along the variables of frequency of occurrence and time per response (the average length of a response per session) were computer simulated. In the first group of four sessions, the frequencies were 45, 100, 150, and 300; in these sessions, all responses ranged from one to three seconds. In the second group of four sessions, the frequencies were 31, 61, 101, and 152; in these sessions, all responses ranged from three to nine seconds. In the last group of three sessions, the frequencies were 25, 34, and 50; here, all responses ranged from nine to 27 seconds. The response distribution within the above ranges was rectangular, with each whole second represented once. The responses were selected by a random number generator, and on each trial every number in the distribution had an equal probability of occurrence. These provisions produced a linear pattern of responding. The time per response in the three groups of sessions were 2, 6, and 18 seconds. For all sessions, event recordings were made and analyzed. The analysis consisted of using partial interval time sampling to determine the percentage of intervals scored; this total was subdivided into intervals containing (1) single responses, (2) multiple responses, (3) continuing responses, and (4) response initiations or terminations. The analysis was performed when the length of the observation interval was 5, 10, 20, 30, 60, and 120 seconds. An additional session drawn from a study that contained real-life data was subjected to this same analysis. The most significant results were derived by finding the ratio of scored intervals containing single responses to the total intervals scored. If every scored interval contained a single response, this ratio would equal 1.0; if no scored interval contained a single response, the ratio would be 0.0. It can be seen that this ratio is an objective expression of the validity of interval time sampling as a measure of response frequency. Of 66 data points (11 sessions × six observation lengths per session), only five were equal to or greater than 0.80. These five points were all found in just two sessions (f = 45, 100). A validity index of less than 0.50 was observed in 49 of the 66 points. Also, the validity index increased, peaked, and then decreased within sessions as the length of the observation interval was increased. The results from the real-life session were in close agreement with those obtained from the simulations. The importance of these and previous findings lies in the demonstration that changes in scored intervals need not represent true behavior change. The data indicate that there are many combinations of behavioral frequency and duration where interval time sampling cannot produce valid measurement results.     

某些影响儿童视觉写实绘画因素的实验研究

与Brenmer等(1997)的实验对照,对4～7岁的儿童考察观察角度的变化方式、模型状态、年龄等与其绘画简单深度关系中视觉写实水平的关系。实验结果表明：年龄是影响儿童绘画简单深度关系中视觉写实水平的重要因素;观察角度变化的两种方式在6～7岁组有显著差异;模型状态对不同性别儿童的绘画成绩影响显著。     

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     

Structural Realism, Scientific Change, and Partial Structures

Scientific change has two important dimensions: conceptual change and structural change. In this paper, I argue that the existence of conceptual change brings serious difficulties for scientific realism, and the existence of structural change makes structural realism look quite implausible. I then sketch an alternative account of scientific change, in terms of partial structures, that accommodates both conceptual and structural changes. The proposal, however, is not realist, and supports a structuralist version of van Fraassen’s constructive empiricism (structural empiricism).