The predicative Frege hierarchy

In this paper, we characterize the strength of the predicative Frege hierarchy, , introduced by John Burgess in his book [J. Burgess, Fixing frege, in: Princeton Monographs in Philosophy, Princeton University Press, Princeton, 2005]. We show that and are mutually interpretable. It follows that is mutually interpretable with Q. This fact was proved earlier by Mihai Ganea in [M. Ganea, Burgess’ PV is Robinson’s Q, The Journal of Symbolic Logic 72 (2) (2007) 619–624] using a different proof. Another consequence of the our main result is that is mutually interpretable with Kalmar Arithmetic (a.k.a. EA, EFA, , Q3). The fact that interprets EA was proved earlier by Burgess. We provide a different proof.Each of the theories is finitely axiomatizable. Our main result implies that the whole hierarchy taken together, , is not finitely axiomatizable. What is more: no theory that is mutually locally interpretable with is finitely axiomatizable.     

指数多项式在半带形中的闭包

该文对一类复指数多项式组成的线性空间$M(\Lambda )$ 在Banach 空间 H_α中的不完备性给出了充分必要条件, 其中 H_α为在半带形 I_α={z=x+iy: x≥ 0, |y|≤α} (α > 0 )中连续, 在I_α的内部解析且当 x→∞时, f(x+ iy)在I_α中关于 y 一致地 趋向 0 的函数 f(x+ iy)全体, 其范数为上确界范数. 同时指出, 如果$M(\Lambda )$ 在 H_α中不完备, 则它的闭包cl$(M(\Lambda ))$中所有的函数都可以延拓为由Dirichlet级数表示的解析函数.     

Incompleteness of exponential system in the weighted Banach space

We take a new approach to obtain necessary and sufficient condition for the incompleteness of exponential system in C_α, where C_α is the weighted Banach space of complex continuous functions f defined on the real axis with f(t)exp(-α(t)) vanishing at infinity, in the uniform norm.     

A multiplicative model for volume and volatility

We first present prima facie evidence for the predictions generated by the mixture of distributions hypothesis, using daily German stock returns and their corresponding daily trading volumes and number of trades. These last two variables are used as proxies for the stochastic rate of information arrival when one wishes to explain GARCH effects by adhering to the mixture of distributions hypothesis. We show that there is no need for these proxies when the stochastic rate of information arrival follows an inverted gamma distribution. Daily trading volume and the daily number of trades, however, empirically provide an explanation for the occurrence of conditional heteroskedasticity of the GARCH form. We estimate several specifications where daily trading volume is included in the conditional variance equation additively and multiplicatively. The new multiplicative specification clearly outperforms the additive specification.     

蕴含G?del定理抽象形式的集合论引理

本文证明了—个集合论性质的引理,由它可直接得出G?del不完全性定理的抽象形式. 文中还述及该引理的有关诸推论.     

基于集合论语言的三门问题的解法

强调了用集合论语言准确表示概率论语言的重要性,利用准确的集合论语言给出了关于三门问题的一种简单的分析方法.     

The consistency index in reciprocal matrices: Comparison of deterministic and statistical approaches

When checking the inconsistency level of a positive reciprocal matrix Saaty uses a deterministic criterion based on two parameters, a benchmark (the average), and a consistency level, usually 10%. Using results from a simulation experiment with 100,000 positive random reciprocal matrices of size varying from 3 to 15, we developed a probabilistic criterion and compare it to Saaty’s index. We found that if a positive reciprocal matrix is consistent according to the deterministic criterion is also consistent according to the probabilistic criterion only if we accept a higher than usual probability of Type I error. Reducing this error implies that the benchmark must be a small percentile of the probability distribution of the consistency index.     

蕴含Gdel定理抽象形式的集合论引理(英文)

本文证明了—个集合论性质的引理,由它可直接得出Godel不完全性定理的抽象形式. 文中还述及该引理的有关诸推论.     

Predicate Modal Logics Do Not Mix Very Well

The problem of completeness for predicate modal logics is still under investigation, although some results have been obtained in the last few years (cf. [2, 3, 4, 7]). As far as we know, the case of multimodal logics has not been addressed at all. In this paper, we study the combination of modal logics in terms of combining their semantics. We demonstrate by a simple example that in this sense predicate modal logics are not so easily manipulated as propositional ones: mixing two Kripke-complete predicate modal logics (one with the Barcan formula, and the other without) results in a Kripke-incomplete system.     

一种校正模糊判断矩阵一致性的新方法

给出一种校正模糊判断矩阵一致性的新方法。首先 ,给出关于模糊判断矩阵满意一致性的定义及判定方法 ,然后通过构造和分析能够反映完全一致性矩阵和原判断矩阵之间关系的偏差矩阵 ,给出校正模糊判断矩阵一致性的计算步骤 ,最后给出了一个算例。     

Conference structures and consistency

In this work we analyze consistency for allocation rules in communication situations. More precisely we characterize the rules proposed by Myerson [R.B. Myerson, Graphs and cooperation in games, Math. Oper. Res. 2, 1977, 225-229; R.B. Myerson, Conference structures and fair allocation rules, Internat J. Game Theory 9 (1980) 169-182] by means of this property.     

固定设计下半参数回归模型估计的相合性

对于固定设计下的半参数模型yi=x1β g(ti)┬ei=1，2……，n本文综合最小二乘法和一般的非参数权估计方法，定义了β，g的估计量-βn，-gn及误差方差口α^2=Ee^21的估计量-α^2n，并在适当条件下，证明了它们的强相合性与P(≥2)阶平均相合性．     

An axiomatization of minimal curb sets

Norde et al. [Games Econ. Behav. 12 (1996) 219] proved that none of the equilibrium concepts in the literature on equilibrium selection in finite strategic games satisfying existence is consistent. A transition to set-valued solution concepts overcomes the inconsistency problem: there is a multiplicity of consistent set-valued solution concepts that satisfy nonemptiness and recommend utility maximization in one-player games. The minimal curb sets of Basu and Weibull [Econ. Letters 36 (1991) 141] constitute one such solution concept; this solution concept is axiomatized in this article.     

蕴含G(o)del定理抽象形式的集合论引理

本文证明了一个集合论性质的引理,由它可直接得出G(o)del不完全性定理的抽象形式.文中还述及该引理的有关诸推论.     

An interpretability improvement for fuzzy rule bases obtained by the iterative rule learning approach

Interpretability is one of the key concepts in many of the applications using the fuzzy rule-based approach. It is well known that there are many different criteria around this concept, the complexity being one of them. In this paper, we focus our efforts in reducing the complexity of the fuzzy rule sets. One of the most interesting approaches for learning fuzzy rules is the iterative rule learning approach. It is mainly characterized by obtaining rules covering few examples in final stages, being in most cases useless to represent the knowledge. This behavior is due to the specificity of the extracted rules, which eventually creates more complex set of rules. Thus, we propose a modified version of the iterative rule learning algorithm in order to extract simple rules relaxing this natural trend. The main idea is to change the rule extraction process to be able to obtain more general rules, using pruned searching spaces together with a knowledge simplification scheme able to replace learned rules. The experimental results prove that this purpose is achieved. The new proposal reduces the complexity at both, the rule and rule base levels, maintaining the accuracy regarding to previous versions of the algorithm.     

Asymptotic Properties of a Modified Semi-Parametric MLE in Linear Regression with Right-Censored Data

Consider a linear regression model, Y=β′X+ε where Y may be right censored and the cdf F _o of ε is unknown. We show that a modified semi-parametric MLE, denoted by is strongly consistent under certain regularity conditions. Moreover, if F _o is discontinuous, then P(≠β i.o.)=0, which means that P(=β if the sample size is large)=1. The latter property has not been reported for the existing estimators. By contrast, most estimators, such as the Buckley-James estimator and M-estimators , satisfy that P(≠β i.o.)=1. Received April 23, 2001, Accepted November 13, 2001     

A geometric averaging procedure for constructing supertransitive approximation to binary comparison matrices

The usefulness of encoding the fuzzy evaluations of alternatives and the importance weights of criteria, in a multiple objective decision problem through binary comparison matrices (or pairwise judgment matrices) is receiving considerable attention. The methodology for identifying the best alternative in a given decision problem involves the computation of the principal eigenvectors of the binary comparison matrices. The eigenvectors transform the fuzzy evaluations of the importance of the criteria and the ratings of the alternatives into a ratio scale. A difficulty that is often experienced in using this approach in practice, is the inconsistency of the binary evaluations. This paper proposes a simple averaging procedure to construct a supertransitive approximation to a binary comparison matrix, where inconsistency is a problem. It is further suggested that such an adjustment might be necessary to more closely reflect the inherent fuzziness of the evaluations contained in a binary comparison matrix. The procedure is illustrated by means of examples.     

一种改进的半参数极大似然法估计量的渐近性质

本文研究线性回归模型, Y=β'X+∈,并假设Y可被右删失,∈的分布函 数F0未知.本文证明,在某些条件下, β的一种改进的半参数极大似然法估计量β 有相合性. 同时证明,如果F0不连续,则P{β≠βi.o.}=0.这意味着以概率为一, 当样本很大时, β=β.文献中的现有估计量未见有关于这一性质的报道.相反,包括 Buckley-James估计量及M-估计量在内的大多数的估计量,都不满足这一性质.     

模糊k-强传递阵

推广强传递阵 ,给出 k-强传递阵的概念 ,讨论它的等价刻画、与截阵性质一致问题 ,证明文献中几种传递性概念与强传递的等价性 ,丰富了模糊矩阵传递性的研究内容。