逻辑系统UL的广义H-赋值

研究了Schweizer-Sklar T-范数（本文讨论p〈0的情况）及其刺佘蕴涵的性质。以此为基础,对泛逻辑基本形式系统UL中的H-g值进行了拓广,引入了广义H-赋值概念,证明了UL在广义H-赋值之下可靠性定理成立。     

逻辑系统RDP中子代数的广义重言式理论

将RDP逻辑系统中的广义重言式理论进行推广,给出RDP逻辑系统中子代数的广义重言式概念,并讨论其序稠密子代数的广义重言式理论     

修正的RDP逻辑系统中的广义矛盾式

讨论了修正的RDP逻辑系统中的广义矛盾式,并对该系统中的广义矛盾式进行了分划;给出了修正的RDP逻辑系统中的广义矛盾式之间的一种降级算法并讨论了它的性质。     

逻辑系统L*中基于Г-演绎真度的近似推理

在逻辑系统L*中引入了公式Γ-演绎真度的概念,在Γ-演绎真度的基础上,定义了Γ-演绎相似度与伪距离,并讨论了它的一些基本性质。接着在逻辑系统L*中定义了3种不同类型的近似推理模式,对Γ-演绎真度的3种不同类型的近似推理模式之间的关系进行了详细的研究,结果表明这3种不同类型近似推理模式是等价的。通过对这些理论的研究,为进一步研究基于Γ-演绎真度的发散度、相容度和近似推理奠定了良好的基础。     

Gödel逻辑系统中1/2-子代数上的广义重言式理论

将Gödel逻辑系统中的广义重言式理论进行推广,讨论了逻辑系统G中具有1/2聚点的三类无限子代数上的广义重言式理论,并利用可达广义重言式的概念在G的三类子代数中给出F（S）关于¬同余的一个分划。     

Gdel逻辑系统中1/2-子代数上的广义重言式理论

将Gdel逻辑系统中的广义重言式理论进行推广,讨论了逻辑系统-G中具有1/2聚点的三类无限子代数上的广义重言式理论,并利用可达广义重言式的概念在-G的三类子代数中给出F(S)关于同余的一个分划。     

修正的Gdel逻辑系统中子代数的广义重言式理论

将修正的Gdel逻辑系统中的广义重言式理论进行推广,讨论其序稠密子代数的广义重言式理论,并利用可达广义重言式概念和α-矛盾式概念在G的序稠密子代数中给出F(S)关于┐同余的一个分划.     

修正的RDP逻辑系统中子代数的广义重言式理论

讨论了修正的RDP逻辑系统中序稠密子代数的广义重言式理论,并利用可达广义重言式概念和[α-]矛盾式概念在[RDP]的序稠密子代数中给出[F(S)]关于[～]同余的一个分划。     

逻辑系统L*中公式的Γ-演绎真度理论

在命题逻辑系统L*中引入了公式的Γ-演绎真度概念,研究了Γ-演绎真度的若干特征性质,并给出了真度推理规则。     

修正的Gödel逻辑系统中子代数的广义重言式理论

将修正的Gödel逻辑系统中的广义重言式理论进行推广,讨论其序稠密子代数的广义重言式理论,并利用可达广义重言式概念和α-矛盾式概念在G的序稠密子代数中给出F（S）关于┐同余的一个分划.     

A semantically complete extension sequence of the system L

In this paper, the method of well-combined semantics and syntax proposed by Pavelka is applied to the research of the propositional calculus formal system L*. The partial constant values are taken as formulas, formulas are fuzzified in two manners of semantics and syntax, and inferring processes are fuzzified. A sequence of new extensions {Ln*} of the system L* is proposed, and the completeness of Ln* is proved.     

Constructing the real numbers in HOL

This paper describes a construction of the real numbers in the HOL theorem-prover by strictly definitional means using a version of Dedekind's method. It also outlines the theory of mathematical analysis that has been built on top of it and discusses current and potential applications in verification and computer algebra.     

命题演算两个推理系统的等价性

首先介绍命题演算的Gentzen型系统G,然后给出一个命题演算的永真推理系统H,最后证明一个命题在G中可证当且仅当它在H中可证,从而G与H是等价的.     

Exploitation of parallel processing for implementing high-performance deduction systems

We describe a scheme for parallelizing first-order logic deduction systems. This scheme has been successfully used for parallelizing OTTER, which is a sequential deduction system developed at Argonne National Laboratory. This parallel deduction system, called PARRallel OTter-II (PARROT-II) has attained real speedups in excess of 20 over the best results of current sequential deduction systems. We believe that our results are of interest for two distinct reasons: (1) this is (as far as we know) the first case in which a system has successfully exploited parallelism to outperform the best sequential deduction systems on difficult problems, and (2) we believe that our approach generalizes to other deduction paradigms (e.g., term rewriting systems).This paper discusses the motivation for developing the scheme used by PARROT-II and the implementation details of PARROT-II. It also presents timing results for PARROT-II for some benchmark problems.Work submitted as partial fulfillment of the requirements for the doctoral degree at the Graduate College of the University of Illinois at Chicago. This work was supported in part by the Applied Mathematical Sciences subprogram of the Office of Energy Research, U.S. Department of Energy, under Contract W-31-109-Eng-38.     

Reasoning about Qualitative Spatial Relationships

In this paper, we consider various spatial relationships that are of general interest in pictorial database systems and other applications. We present a set of rules that allow us to deduce new relationships from a given set of relationships. A deductive mechanism using these rules can be used in query-processing systems that retrieve pictures by content. The given set of rules is shown to be sound; that is, the deductions are logically correct. The rules are also shown to be complete for three-dimensional systems; that is, every relationship that is implied by a given consistent set of relationships F is deducible from F using the given rules. In addition, we show that the given set of rules is incomplete for two-dimensional systems. We also present efficient algorithms for the deduction and reduction problems. The deduction problem consists of computing all the relationships deducible from a given set, while the reduction problem consists of computing a minimal subset of a given set of relationships that implies all the relationships in the given set.