基于消点法的几何自动推理系统实现

为了实现几何自动推理的可读性证明,并提高推理效率,介绍了一个基于消点法的可构造性几何命题自动推理系统的设计与实现。该系统提供作图的方式接受用户的几何命题前提条件的输入,可以对初等几何中的大部分可构造性几何问题进行自动证明和求解,并生成可读的证明步骤,大大方便了初高等几何教育和相关研究者的需要。     

.NET平台下故障树分析技术的实现及应用

故障树分析是一种自上而下的方法,通过对可能造成系统故障的硬件、软件、环境、人为因素进行分析,分析得出故障原因的各种可能组合方式,由总体至部分,按树状结构,逐层细化的一种分析方法.开发了故障树分析工具,提供了对规范化故障树定性的割集计算、简化等功能,提出了基于容斥定理的定量化顶事件概率简化计算方法,可满足企业对部件级元件进行故障详细分析的需求.还给出了所开发的系统实现界面,系统已在某企业中得到了具体的应用.     

An auxiliary theorem for stability analysis in the presence of interval-valued parameters

A theorem which helps to determine the boundary of the image of an interval inR ⁿ under a differentiable mapping,F:R ⁿ C, is expounded. Examples illustrating the application of the theorem are given.     

The liberalized δ-rule in free variable semantic tableaux

In this paper we have a closer look at one of the rules of the tableau calculus presented by Fitting [4], called the -rule. We prove that a modification of this rule, called the ⁺-rule, which uses fewer free variables, is also sound and complete. We examine the relationship between the ⁺-rule and variations of the -rule presented by Smullyan [9]. This leads to a second proof of the soundness of the ⁺-rule. An example shows the relevance of this modification for building tableau-based theorem provers.     

A new methodology for query answering in default logics via structure-oriented theorem proving

We present a new approach to query answering in default logics. The basic idea is to treat default rules as classical implications along with some qualifying conditions restricting the use of such rules while query answering. We accomplish this by taking advantage of the conception of structure-oriented theorem proving provided by Bibel's connection method. We show that the structure-sensitive nature of the connection method allows for an elegant characterization of proofs in default logic. After introducing our basic method for query answering in default logics, we present a corresponding algorithm and describe its implementation. Both the algorithm and its implementation are obtained by slightly modifying an existing algorithm and an existing implementation of the standard connection method. In turn, we give a couple of refinements of the basic method that lead to conceptually different algorithms. The approach turns out to be extraordinarily qualified for implementations by means of existing automated theorem proving techniques. We substantiate this claim by presenting implementations of the various algorithms along with some experimental analysis.Even though our method has a general nature, we introduce it in the first part of this paper with the example of constrained default logic. This default logic is tantamount to a variant due to Brewka, and it coincides with Reiter's default logic and a variant due to ukaszewicz on a large fragment of default logic. Accordingly, our exposition applies to these instances of default logic without any modifications.     

SATCHMORE: SATCHMO with RElevancy

We introduce a relevancy detection algorithm to be used in conjunction with the SATCHMO prover. The version of SATCHMO considered here is essentially a bidirectional prover, utilizing Prolog (back chaining) on Horn clauses and forward chaining on non-Horn clauses. Our extension, SATCHMORE (SATCHMO with RElevancy), addresses the major weakness of SATCHMO: the uncontrolled use of forward chaining. By marking potentially relevant clause head literals, and then requiring that all the head literals be marked relevant (be totally relevant) before a clause is used for forward chaining, SATCHMORE is able to guide the use of these rules. Furthermore, the relevancy testing is performed without extending the proof search beyond what is done in SATCHMO. A simple implementation of the extended SATCHMO can be written in Prolog. We describe our relevancy testing approach, present the implementation, prove soundness and completeness, and provide examples that demonstrate the power of relevancy testing.This research was partially supported by NSF Grants IRI-8805696 and CCR-9116203. This paper is a major revision of Wilson and Loveland (1989).     

A Ramsey theorem in Boyer-Moore logic

We use the Boyer-Moore Prover, Nqthm, to verify the Paris-Harrington version of Ramsey's theorem. The proof we verify is a modification of the one given by Ketonen and Solovay. The theorem is not provable in Peano Arithmetic, and one key step in the proof requires ₀ induction.Author supported by NSF Grant DMS-9100665.     

基于特勒根定理的风场送出线路新型纵联保护

双馈风机和永磁直驱风机广泛应用于陆上风电场。受控制策略影响,送出线路故障时风场侧故障特性与同步机电源差异显著,使传统纵联保护性能下降。特勒根定理建立于基尔霍夫电压、电流定律,仅与电路拓扑结构有关,对含线性/非线性、时变/时不变元件的电路均能适用。将特勒根定理应用到陆上风场送出系统,建立了满足定理应用要求的线路故障拓扑结构图。以此为基础,分析了能够区分内、外部故障的特征量,提出了一种基于故障前后线路两端电压电流的新型纵联保护动作判据。利用风场多个故障案例的录波数据和基于PSCAD的仿真数据对所提判据进行验证及对比分析,证明了所提纵联保护方法的优越性和可行性。     

分数阶时滞非线性多智能体系统的自适应控制

针对分数阶多智能体系统中存在时滞和非线性特性, 时滞往往会引起控制系统的性能下降甚至出现系统 不稳定等问题, 提出了一种含时滞非线性的分数阶多智能体系统自适应控制方法. 对于多智能体系统的控制协议, 设计了基于领导者和相邻智能体状态信息的自适应控制协议, 减小了过大常数控制增益带来的能源浪费. 对于一 致性, 利用图论基础、分数阶Halanay不等式稳定性定理、Kronecker积和Schur补引理, 获得了分数阶时滞非线性多 智能体系统的LMI一致性条件. 仿真结果验证了本文算法的正确性和有效性. 由于整数阶系统是分数阶系统的特殊 形式, 本文结论可以直接推广到整数阶多智能体系统中.