A probabilistic extension of intuitionistic logic

We introduce a probabilistic extension of propositional intuitionistic logic. The logic allows making statements such as P_≥sα, with the intended meaning “the probability of truthfulness of α is at least s”. We describe the corresponding class of models, which are Kripke models with a naturally arising notion of probability, and give a sound and complete infinitary axiomatic system. We prove that the logic is decidable.     

四值互斥变量K图及其化简

参照二值互斥变量K图的讨论,提出了四值互斥变量K图,讨论了它的特点以及在四值互斥变量逻辑函数化简中的应用,给出了四值互斥变量K图化简的规则,并用具体实例作了说明.提出的四值互斥变量K图大大地压缩了K图的规模,扩大了K图的应用范围.     

A theory,implementation and applications of human-like understanding

Operation logic is a formal logic with well-defined formulas as semantic language clauses and with modus ponens rules as a method of reasoning. Operation logic can be implemented on any database management system (as the so-called OLS) having a universal general knowledge database and enabling understanding of data stored in the database. Semantic language clauses have necessary and sufficient properties for being able to describe any process in the world. Semantic language is the deepest level of any natural language, the level of data storing, understanding and reasoning. OLS can be a tool for studying implementation possibilities of human-like consciousness, for building artificial experts and artificial encyclopedias and for constructing semantic mathematical theories of anthropoecosystems (which is such an exact theory that qualitative information can be used with meaning completely defined by the user). In the paper the theory (and complete information enabling implementation) is presented for human-like understanding, topic-focus division of clauses, for human-like problem solving (program synthesis and verification) and for semantic mathematical analyses. Many examples are presented.     

基于信息熵和回归分析的信用风险评估研究

信用风险管理一直是银行和其他金融机构最关心的问题之一。本利用信息熵与传统的统计回归对比分析的方法，对信用信息数据库中的逻辑变量进行了数值化处理，在完成属性筛选的基础上，建立多元回归模型来实现对客户特征的评估。实证研究表明，这种数值化的处理方法是可行的，利用该方法评估和预测可能发生的信用风险是有实用价值的。     

求车间最优逐月生产计划的一个算法

给出一个求车间最优逐月生产计划的数值算法，证明了算法的理论依据，并举例说明算法的应用。     

碳纳米管电子学的研究与进展

简单回顾了碳纳米管的电学性质以及各种基于碳纳米管的电子器伯,最新发现的碳纳米管的双极型性质也作了简单报道，着重讨论了由碳纳米管构成的逻辑电路，阐明了碳纳米管电子学发展过程将遇到的困难和挑战，了碳纳米管电子学的未来和应用前景。     

确定有限域上给定周期的不可约多项式的个数以及利用低次不可约多项式构造高次不可约多项式

主要利用较献[4]更为简明的方法证明了有关有限域Fq(q为一个素数幂）上的以l为周期的n次不可约多项式的个数的结论。另外，本结合结合初等数论知识得到了前面这个结论的几个推论，并对利用低次不可约多项式构造高次不可约多项式进行了研究。     

How to measure uncertainties in environmental risk assessment

Environmental risk assessment is an essential element in any decision-making process in order to minimize the effects of human activities on the environment. Unfortunately, often environmental data tends to be vague and imprecise, so uncertainty is associated with any study related with these kind of data.

Essentially, uncertainty in risk assessment may have two origins – randomness and incompleteness. There are two main ways to deal with these uncertainties – probability theory and fuzzy logic.

Probability theory is based on a stochastic approach, using probability functions to describe random variability in environmental parameters.

Fuzzy logic uses membership functions and linguistic parameters to express vagueness in environmental issues.

We discuss the best way to deal with uncertainties in the environmental field and give examples of probabilistic and fuzzy-logic approaches applied to environmental risk assessment.     

An efficient multiple-mode molecular logic system for pH, solvent polarity, and Hg ions

A novel fluorophore 1,3-bis(1,1,3-trimethyl-1H-benzo[e]indol-2(3H)-ylidene)propan-2-one (L) was synthesized and fully characterized by ¹H NMR, ¹³C NMR, HRMS, and X-ray single-crystal structural analysis. Compound L is a pH-controlled molecular switch due to its protonation. The fluorescence change in protic polar solvents means that this compound also could be used as a protic solvent polarity sensor. Among the considered metal ions, the fluorescence of compound L could be quenched completely by Hg²⁺ ions with a high selectivity. Based on these fluorescence characters, this fluorescent dye L has promising applications as a multiple-mode molecular logic system.     

Tangency sets in PG(3, q)

A tangency set of PG (d,q) is a set Q of points with the property that every point P of Q lies on a hyperplane that meets Q only in P. It is known that a tangency set of PG (3,q) has at most points with equality only if it is an ovoid. We show that a tangency set of PG (3,q) with , or points is contained in an ovoid. This implies the non‐existence of minimal blocking sets of size , , and of with respect to planes in PG (3,q), and implies the extendability of partial 1‐systems of size , , or to 1‐systems on the hyperbolic quadric . © 2007 Wiley Periodicals, Inc. J Combin Designs 16: 462–476, 2008