CONTINUOUS L-DOMAINS

61.IntroductionConiinuousDCPOisoneofthemostimportantstructuresin-domaintheory.Unfor-tunatelythecategoryofcolltinuousDCPOandtheScottcontinuousfunctionsfailstobeCartesianclosed,soitisaverysignificantproblemtofinditsmakimalCartesianclosedfullsubcategories.ThecategoryofL-domain'swasdiscoveredbyA.JungwhilesolvingtheproblemoffindingmtalmalCartesianclosedcategoriesofalgebraicDCPO's[1l,andrecentworksbyA.JungandG.Gund.r[2]showsthatthecategoryofL-domain'sisaninterestingcategoryOntheotherhand,i…     

代数L-domain和强core紧空间的刻画

给出代数L-domain和强core紧空间以及连续L-domain和core紧空间的刻画。     

连续Domain的遗传性及其不变性

引入Domain子空间的概念,得到Scott开集和闭集都是Domain的子空间。证明连续Domain或代数Domain对开子空间和闭子空间都是可遗传的。证明连续Domain或代数Domain在保Waybelow序的Scott连续映射下保持不变。     

相容连续Domain的遗传性

定义相容Domain的子Domain与子空间等概念,得到Scott开集和Scott闭集都是相容Domain的子Domain与子空间的结论,证明了相容连续Domain或相容代数Domain对开子空间和闭子空间都是可遗传的。     

连续信息基

D.Scott在20世纪60年代引入了domain理论,并给出了两种等价形式——信息系统和邻域系。在型论(typetheory)基础上,G.Sambin提出了形式拓扑(Formal topology)理论,并证明了一元形式拓扑与代数Scott domain等价,从而推出代数信息基的概念,同时作为信息系统与邻域系的推广。本文从信息基的观点出发,提出了连续信息基的概念,证明了它与连续Scott domain的等价性。     

相容连续Domain上的序同态

首先给出相客定向极小集的概念,讨论它的性质及与相客连续Domain的关系;其次蛤出相客连续Domain基的概念,得到它的等价刻画.最后,引入了相客连续Domain上的序同态,同时研究了它的性质,并得出相应的扩张定理.     

连续偏序集及其Smyth幂的几个等权定理

推广连续D om a in的权的概念到连续偏序集上,探讨连续偏序集的权、相应内蕴拓扑的权、定向完备化的权以及Sm yth幂D om a in的权间的关系。得到了几个等权定理:(1)连续偏序集的权与其上Scott拓扑、L aw son拓扑的权相等;(2)连续偏序集的权与其定向完备化的权相等;(3)无穷连续D om a in的权与其Sm yth幂D om a in的权相等;(4)有限D om a in的权小于或等于它的Sm yth幂D om a in的权。     

关于连续Domain权的进一步结果

在连续格理论的基础上探索连续Domain的权与相应Scott拓扑空间的权之间的关系,并进一步讨论其与相应的Lawson拓扑空间的权之间的关系,最后给出在连续Domain中W（P）＝W（∑P）=W（AP）的结论。     

半格与Domain的表示

引入一种半格———Ｄ 半格，建立了Ｄ－半格的表示理论，利用它得到了Ｌ ｄｏｍａｉｎ（即局部代数格）的表示理论；证明了Ｌ ｄｏｍａｉｎ与稳定映射范畴对偶等价于稳定Ｄ 半格与Ｄ－半格同态范畴．     

相容Domain间Scott连续自映射的不动点

研究相容连续L-dom a in之间的稳定映射以及相容FS-dom a in之间的一致交换映射的不动点之集的性质。     

A case study in logical deconstruction: Formalizing J.D. Thompson's Organizations in Action in a multi-agent action logic

Logic is a popular word in the social sciences, but it is rarely used as a formal tool. In the past, the logical formalisms were cumbersome and difficult to apply to domains of purposeful action. Recent years, however, have seen the advance of new logics specially designed for representing actions. We present such a logic and apply it to a classical organization theory, J.D. Thompson's Organizations in Action. The working hypothesis is that formal logic draws attention to some finer points in the logical structure of a theory, points that are easily neglected in the discursive reasoning typical for the social sciences. Examining Organizations in Action we find various problems in its logical structure that should, and, as we argue, could be addressed.     

Applications of the duality method to generalizations of the Jordan canonical form

The Jordan normal form for a matrix over an arbitrary field and the canonical form for a pair of matrices under contragredient equivalence are derived using Pták's duality method.     

Metric spaces are universal for bi-interpretation with metric structures

In the context of metric structures introduced by Ben Yaacov, Berenstein, Henson, and Usvyatsov [3], we exhibit an explicit encoding of metric structures in countable signatures as pure metric spaces in the empty signature, showing that such structures are universal for bi-interpretation among metric structures with positive diameter. This is analogous to the classical encoding of arbitrary discrete structures in finite signatures as graphs, but is stronger in certain ways and weaker in others. There are also certain fine grained topological concerns with no analog in the discrete setting.     

Domain理论中的映射

Domain理论的目的是为程序设计语言提供数学语义的模型,信息状态域的指标称为Domain,而程序的指称是Domain间的映射。本文主要介绍Domain理论中的三类重要映射－Scott连续映射,Berry的稳定映射以及CM映射的定义以及等价刻画和表示。     

Interpreting Intuitionistic Propositional Logic in Terms of Intuitionistic Protothetics

An algebra of sentences of the quite intuitionistic protothetics, that is, an intuitionistic propositional logic with quantifiers augmented by the negation of the excluded middle, is a faithful model of intuitionistic propositional logic.     

基于函数凸性的变换区域舍选法在连续分布随机数中的应用

本文提出了基于函数凸性的变换区域舍选法算法 ,该方法可应用于产生具有凸性区间的密度函数随机数 .与一般舍选法相比 ,变换区域舍选法有较大的接受概率 ,能有效地提高舍选法效率 .     

n值逻辑系统中条件随机真度理论

在n值命题逻辑系统中命题的随机真度、随机逻辑度量空间的基础上,给出了修正的n值G¨odel命题逻辑系统中命题的条件真度、条件相似度的概念并讨论了其性质,建立了条件随机逻辑度量空间。     

Computational adequacy for recursive types in models of intuitionistic set theory

This paper provides a unifying axiomatic account of the interpretation of recursive types that incorporates both domain-theoretic and realizability models as concrete instances. Our approach is to view such models as full subcategories of categorical models of intuitionistic set theory. It is shown that the existence of solutions to recursive domain equations depends upon the strength of the set theory. We observe that the internal set theory of an elementary topos is not strong enough to guarantee their existence. In contrast, as our first main result, we establish that solutions to recursive domain equations do exist when the category of sets is a model of full intuitionistic Zermelo–Fraenkel set theory. We then apply this result to obtain a denotational interpretation of FPC, a recursively typed lambda-calculus with call-by-value operational semantics. By exploiting the intuitionistic logic of the ambient model of intuitionistic set theory, we analyse the relationship between operational and denotational semantics. We first prove an “internal” computational adequacy theorem: the model always believes that the operational and denotational notions of termination agree. This allows us to identify, as our second main result, a necessary and sufficient condition for genuine “external” computational adequacy to hold, i.e. for the operational and denotational notions of termination to coincide in the real world. The condition is formulated as a simple property of the internal logic, related to the logical notion of 1-consistency. We provide useful sufficient conditions for establishing that the logical property holds in practice. Finally, we outline how the methods of the paper may be applied to concrete models of FPC. In doing so, we obtain computational adequacy results for an extensive range of realizability and domain-theoretic models.     

Mining information from time series in the form of sentences of natural language

The goal of this paper is to provide a more detailed explanation of the principles how special formulas that characterize properties of trend of time series can be formed and how they are interpreted. Then we show how these formulas can be used in a tectogrammatical tree that construes special sentences of natural language, using which information on behavior of time series is provided. We also outline the principles of mining this information. The last part is devoted to application of the theory of intermediate quantifiers to mining summarized information on time series also in sentences of natural language.     

On pp-elimination and stability in a continuous setting

We generalize pp-elimination for modules, or more generally, abelian structures, to a continuous logic setting where the abelian structure is equipped with a homomorphism to a compact Hausdorff group. We conclude that the continuous logic theory of such a structure is stable.