Single axioms for odd exponent groups

With the aid of automated reasoning techniques, we show that all previously known short single axioms for odd exponent groups are special cases of one general schema. We also demonstrate how to convert the proofs generated by an automated reasoning system into proofs understandable by a human.Authors supported by NSF Grant DMS-9100665     

描述逻辑FL0概念及术语公理集的表达能力刻画

表达能力和推理复杂性是一个逻辑的两个重要特征,也是一对相互制约的关系。解释之间的互模拟关系是从语义的角度刻画逻辑表达能力的一个有效途径,其代表性的结果是命题模态逻辑表达能力的刻画定理-van Benthem刻画定理。文中给出了描述逻辑FL0(含构造子:原子概念、顶概念、概念交、全称量词约束)的模拟关系,建立了FL0中概念和术语公理集的表达能力刻画定理,即一阶逻辑公式与FL0概念和术语公理集等价的充分必要条件。上述结果为寻求表达能力与推理复杂性之间的最佳平衡提供了有效的支持。     

Lω-空间的ωS-分离性

在Lω-空间中引入了Lω-分离性的概念,主要包括ωS-1、ωS0、次ωS0分离性,讨论了它们的一些基本的拓扑性质.给出了ωS-分离性的几个等价刻划,讨论了它们之间的关系.     

On global solutions to fractional functional differential equations with infinite delay in Fréchet spaces

In this paper, we investigate global uniqueness results for fractional functional differential equations with infinite delay in Fréchet spaces. We shall rely on a nonlinear alternative of Leray-Schauder type in Fréchet spaces due to Frigon and Granas. The results are obtained by using the α-resolvent family (S_α(t))_t≥0 on a complex Banach space X combined with the above-mentioned fixed point theorem. As an application, a controllability result with one parameter is also provided to illustrate the theory.     

从中文Web网页中获取实体简称的研究

简称是自然语言词汇的重要组成部分,其获取是自然语言处理中的一个基本而又关键的问题。提出了一种根据汉语全称从Web中获取对应汉语简称的方法。该方法包括获取和验证两个步骤。获取步骤通过选择查询模式从Web上获得候选简称集合。为了验证候选简称,定义了全简称关系约束,分别定性和定量地表示全称和对应简称之间的约束,构建了全简称关系图来表示所有全称和简称之间的联系,在验证过程中,先分别用约束公理和关系图对候选简称进行过滤,再用约束函数对候选简称分类,并以分类类别、语料标记和约束函数值作为属性构建决策树,利用决策树对候选简称进行验证。实验结果表明,获取方法的最终准确率为94.63%,召回率为84.09%,验证方法的准确率为94.81%。     

Armstrong axioms and Boyce-Codd-Heath Normal Form under bag semantics

The theory of functional dependencies is based on relations, i.e. sets of tuples. Over relations, the class of functional dependencies subsumes the class of keys. Commercial database systems permit the storage of bags of tuples where duplicate tuples can occur. Over bags, keys and functional dependencies interact differently from how they interact over relations.We establish finite ground axiomatizations of keys and functional dependencies over bags, and show a strong correspondence to goal and definite clauses in classical propositional logic. We define a syntactic Boyce-Codd-Heath Normal Form condition, and show that the condition characterizes schemata that will never have any redundant data value occurrences in their instances. The results close the gap between the existing set-based theory of data dependencies and database practice where bags are permitted.     

On constitutive equations for thermoelastic dielectric continuum in terms of invariants

Electro-thermomechanical behavior of a thermoelastic dielectric body subject to external loading has been investigated theoretically in the present analysis. The theory is formulated in the context of continuum electrodynamics. The reaction of the body subject to external loads is expressed in symmetric stress, electrical polarization and heat flux. The solid medium is assumed to be linear, dielectric, isotropic, incompressible and dependent on temperature gradient. It has been observed that, as a result of thermodynamic constraints, the stress potential function is dependent on the deformation tensor, the electric field vector and the temperature, while the heat flux vector function is dependent on the deformation tensor, the electric field vector, the temperature and temperature gradient. To determine arguments of the stress potential and the heat flux vector functionals, findings of the theory of invariants have been used as a method because of that isotropy constraint is imposed on the material. As a result, constitutive equations of symmetric stress, polarization field and heat flux vector have been obtained in both material and spatial coordinates and asymmetric stress has been found using the expressions of symmetric stress and polarization field.     

Graphoid properties of epistemic irrelevance and independence

This paper investigates Walley's concepts of epistemic irrelevance and epistemic independence for imprecise probability models. We study the mathematical properties of irrelevance and independence, and their relation to the graphoid axioms. Examples are given to show that epistemic irrelevance can violate the symmetry, contraction and intersection axioms, that epistemic independence can violate contraction and intersection, and that this accords with informal notions of irrelevance and independence.     

An axiomatic approach for combining evidence from a variety of sources

Development of intelligent decision-making systems which operate in complex environments like an automated factory, needs effective procedures for combining evidence from a variety of sources. Currently there are many ad-hoc evidence combination formulae as well as those based on specific methodologies such as the Bayesian, likelihood, etc. However, the limitations of these approaches have been well documented. In this paper, we begin with the testable and desirable properties required in a special problem. These properties are termed as axioms. We then systematically develop various families of combination rules obeying subsets of these axioms. The existing combination formulae form a subset of the rules mentioned here. We discuss the appropriateness of the different families of combination formulae.Partially supported by the Office of Naval Research under the grant N00014-85K-0611 and NSF under the grant IST 8405052.