Inductive Construction of Repletion

The aim of this paper is to give a purely logical construction of repletion, i.e. the reflection of an arbitrary set to a replete one. Replete sets within constructive logic were introduced independently by M. Hyland and P. Taylor as the most restrictive but sufficiently general notion of predomain suitable for the purposes of denotational semantics à la Scott.For any set A its repletion R(A) appears as an inductively defined subset of S²(A) (A S) S which can be expressed within the internal language of a model of type theory. More explicitly, R(A) is the least subset of S²(A) containing all point filters and closed under a class of generalised limit processes. Improvements of our construction arise from several results saying that it suffices for the purpose of repletion to consider more restrictive classes of generalised limit processes.     

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.     

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.     

包络半群与拓扑动力学中的接近关系

运用包络半群的理论，对接近关系中一个重要定理给出了一个简单证明．作为这一定理的应用，我们得到接近关系可乘性的一个结果．并且对另一种接近关系，也得到一个结果．这两个定理减弱了Ｃｌａｙ在这一领域中两个定理的条件．     

2—Harmonic Totally Real Submanifolds in a Complex Projective Space

２－ＨａｒｍｏｎｉｃＴｏｔａｌｌｙＲｅａｌＳｕｂｍａｎｉｆｏｌｄｓｉｎａＣｏｍｐｌｅｘ　Ｐｒｏｊｅｃｔｉｖｅ　ＳｐａｃｅＳｕｎＨｏｎｇａｎ（孙弘安）（ＳｏｕｔｈｅｒｎＩｎｓｔｉｔｕｔｅｏｆＭｅｔａｌｌｕｒｇｙ）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａｐｅｒ...     

Intuitionistic ϵ- and τ-calculi

There are several open problems in the study of the calculi which result from adding either of Hilbert's ?- or τ-operators to the first order intuitionistic predicate calculus. This paper provides answers to several of them. In particular, the first complete and sound semantics for these calculi are presented, in both a “quasi-extensional” version which uses choice functions in a straightforward way to interpret the ?- or τ-terms, and in a form which does not require extensionality assumptions. Unlike the classical case, the addition of either operator to intuitionistic logic is non-conservative. Several interesting consequences of the addition of each operator are proved. Finally, the independence of several other schemes in either calculus are also proved, making use of the semantics supplied earlier in the paper.     

Regular Subgraphs in Graphs and Rooted Graphs and Definability in Monadic Second - Order Logic

We investigate the definability in monadic ∑₁¹ and monadic Π₁¹ of the problems REG_k, of whether there is a regular subgraph of degree k in some given graph, and XREG_k, of whether, for a given rooted graph, there is a regular subgraph of degree k in which the root has degree k, and their restrictions to graphs in which every vertex has degree at most k, namely REG_k^k and XREG_k^k, respectively, for k ≥ 2 (all our graphs are undirected). Our motivation partly stems from the fact (which we prove here) that REG_k^k and XREG_k^k are logspace equivalent to CONN and REACH, respectively, for k ≥ 3, where CONN is the problem of whether a given graph is connected and REACH is the problem of whether a given graph has a path joining two given vertices. We use monadic first - order reductions, monadic ∑₁¹ games and a recent technique due to Fagin, Stockmeyer and Vardi to almost completely classify whether these problems are definable in monadic ∑₁¹ and monadic Π₁¹, and we compare the definability of these problems (in monadic ∑₁¹ and monadic Π₁¹ with their computational complexity (which varies from solvable using logspace to NP - complete).     

Karl Menger's contributions to social thought

The work of Karl Menger in social science is briefly surveyed, in particular in the areas of marginal utility and diminishing value, utility, and uncertainty, a logic of imperatives based on deterrence, and a theory of voluntary associations in which cohesive groups are studied combinatorially.     

About membership functions estimation

A logical approach to fuzzy sets method originated by Giles is developed. The infinitely many-valued logic t_ω is taken as basic. We accept, it is correct to use the strong conjunction by the logical analysis of the summation of fuzzy items. Under some broad conditions it is proved. that the sum of many fuzzy variables is a variable whose membership function is approximately equal to $\text{?(x) =}\text{max}\text{{1 ?}\text{1}\text{2}\text{c(x ? α)}{}^2\text{, 0}}$, where a and c are some constant parameters. A method of estimation of the unknown parameters is developed in a general case. The proposed fuzzy method coincides with the method of maximum likelihood if used in problems of classical mathematical statistics.