Fuzzy Topology Based on Residuated Lattice-Valued Logic

We use a semantical method of complete residuated lattice-valued logic to give a generalization of fuzzy topology as a partial answer to a problem by Roser and Turquette. This work is supported by the National Foundation for Distinguished Young Scholars (Grant No: 69725004), Research and Development Project of High-Technology (Grant No: 863-306-ZT06-04-3) and Foundation of Natural Sciences (Grant No: 69823001) of China and Fok Ying-Tung Education Foundation     

A Modal Logic Based on Linearly Ordered f-Spaces

A modal logic associated with the -spaces introduced by Ershov is examined. We construct a modal calculus that is complete w.r.t. the class of all strictly linearly ordered -frames, and the class of all strictly linearly ordered -frames.     

基于交换作用的纳磁逻辑电路片上时钟结构研究

纳磁逻辑电路具有低功耗、非易失和可常温下制备等优点, 实现低功耗片上时钟是其集成化的必备条件. 本文提出了一种基于交换作用的纳磁逻辑电路片上时钟结构, 用载流铜导线产生的奥斯特场将铁磁体薄膜覆层进行磁化, 然后依靠铁磁体层与纳磁体界面存在的交换作用场使后者磁化方向发生翻转. 与轭式铁磁体时钟用外磁场控制纳磁体磁化方向相比, 该方案在功耗方面降低了5/6, 时钟边界杂散场强度降低了2/3, 达到降低功耗、减轻串扰的目的. 此外, 采用微磁仿真进一步验证了该时钟结构上的纳磁体逻辑阵列可以实现逻辑功能. 关键词： 纳磁逻辑 片上时钟 交换作用     

Parallelizing Tabu Search on a Cluster of Heterogeneous Workstations

In this paper, we present the parallelization of tabu search on a network of workstations using PVM. Two parallelization strategies are integrated: functional decomposition strategy and multi-search threads strategy. In addition, domain decomposition strategy is implemented probabilistically. The performance of each strategy is observed and analyzed. The goal of parallelization is to speedup the search in finding better quality solutions. Observations support that both parallelization strategies are beneficial, with functional decomposition producing slightly better results. Experiments were conducted for the VLSI cell placement, an NP-hard problem, and the objective was to achieve the best possible solution in terms of interconnection length, timing performance (circuit speed), and area. The multiobjective nature of this problem is addressed using a fuzzy goal-based cost computation.     

Soft Constraint Logic Programming and Generalized Shortest Path Problems

In this paper we study the relationship between Constraint Programming (CP) and Shortest Path (SP) problems. In particular, we show that classical, multicriteria, partially ordered, and modality-based SP problems can be naturally modeled and solved within the Soft Constraint Logic Programming (SCLP) framework, where logic programming is coupled with soft constraints. In this way we provide this large class of SP problems with a high-level and declarative linguistic support whose semantics takes care of both finding the cost of the shortest path(s) and also of actually finding the path(s). On the other hand, some efficient algorithms for certain classes of SP problems can be exploited to provide some classes of SCLP programs with an efficient way to compute their semantics.     

剩余格与正则剩余格的特征定理

本文进一步研究了具有广泛应用的一类模糊逻辑代数系统——剩余格，并引入了正则剩余格的概念，对剩余格与正则剩余格的定义进行了讨论，给出了剩余格与正则剩余格的特征定理，其中包含剩余格与正则剩余格的等式特征，从而这两个格类都构成簇．本文还讨论了剩余格与正则剩余格公理系统的独立性，以及它们与相近代数结构的关系．     

Pr值逻辑函数相关免疫的等价判别条件

本文首先基于环Zpr中的元的padic分解并结合概率论的思想,给出了pr值随机变量的分解性质及pr值随机变量独立性的等价描述,然后在对pr值逻辑函数及其变元都进行padic分解的基础上,直接通过p值逻辑函数的Chrestenson谱给出了padic分解意义下pr值逻辑函数k阶相关免疫的线性组合引理和谱判别定理.     

The Σ1-provability logic of HA

In this paper we introduce a modal theory ${\mathsf{iH}}_{\sigma }$ which is sound and complete for arithmetical ${\mathrm{\Sigma }}_1$-interpretations in $\mathsf{HA}$, in other words, we will show that ${\mathsf{iH}}_{\sigma }$ is the ${\mathrm{\Sigma }}_1$-provability logic of $\mathsf{HA}$. Moreover we will show that ${\mathsf{iH}}_{\sigma }$ is decidable. As a by-product of these results, we show that $\mathsf{HA}+\square \perp$ has de Jongh property.     

基于错误逻辑分解转化联结词的生态文明指标知识表达模型研究

研究错误逻辑的知识表达模型,以错误逻辑理论结合生态文明"五位一体"所构建的生态文明建设指标体系,进行基于对象识别的知识表达.指标体系内的各元素分别被定义为错误逻辑模型中的事物、特征、函数和规则.建模时,首先进行事物分解,第二步进行特定事物下对应的特性及规则分解,最后根据判别规则G对错误函数f形式的影响,对各项指标所适用的错误函数类型进行分类.对象的生成可以为用矩阵这样的数据结构对逻辑知识进行系统化组织做前期准备.     

Reasoning about proof and knowledge

In previous work [15], we presented a hierarchy of classical modal systems, along with algebraic semantics, for the reasoning about intuitionistic truth, belief and knowledge. Deviating from Gödel's interpretation of IPC in S4, our modal systems contain IPC in the way established in [13]. The modal operator can be viewed as a predicate for intuitionistic truth, i.e. proof. Epistemic principles are partially adopted from Intuitionistic Epistemic Logic IEL [4]. In the present paper, we show that the S5-style systems of our hierarchy correspond to an extended Brouwer–Heyting–Kolmogorov interpretation and are complete w.r.t. a relational semantics based on intuitionistic general frames. In this sense, our S5-style logics are adequate and complete systems for the reasoning about proof combined with belief or knowledge. The proposed relational semantics is a uniform framework in which also IEL can be modeled. Verification-based intuitionistic knowledge formalized in IEL turns out to be a special case of the kind of knowledge described by our S5-style systems.