结合方向关系和拓扑关系的约束满足推理

结合定性空间推理中的区域连接演算（RCC）和基于区域的主方向关系模型,应用拓扑和方向关系上的复合表,将方向关系和拓扑关系的推理看作约束满足问题（CSP）,给出了结合RCC8和主方向关系的约束满足问题推理算法,该算法可结合拓扑关系和方向关系进行推理。     

RCC8的一致分割及其算法

区域连接演算（Region Connection Calculus,RCC）是一种用于空间定性表示和推理的形式化模型,如RCC5,RCC8等,其一致性检查被证明是一个NP问题。幸运的是,在其可处理子集上,路径一致性和一致性等价,即便这样也有[O(n3)]的时间复杂度和[O(n2)]的空间复杂度。为了提高一致性检查的效率,提出了一致分割的概念,给出了其定义和成立的充分必要条件,用来将RCC8的约束图在保持一致性的前提下分割成若干个子图,分而求解各个子图的一致性;并随后给出了几种一致分割的充分条件,和相应的高效分割算法。在随机生成的大型、稀疏约束图上的实验表明了一致分割的有效性。     

基于区域延伸的定性空间表示

在区域连接演算(region connection calculus,RCC)理论基础上给出了区域延伸的形式定义.通过区域延伸,定义了关联空间的概念,进而提出了空间表示的一个模型,在这个模型中给出了空间中物体的空间拓扑关系、距离关系、方向关系以及位置等信息的定性表示.智能体对空间关系的确定是通过区域延伸实现的,模型为智能体在约束空间环境中的行动推理提供了一个新的表示方法.     

基于区域伸缩的空间关系表示

区域连接演算(RCC)是定性空间推理的重要基础理论之一.但由于缺乏必要的度量,RCC只是粗略地描述空间拓扑关系而难以对其更准确地描述,也难以利用RCC描述除拓扑关系之外的其它空间关系,如距离、方向等.本文在RCC理论的基础上,提出了区域伸缩演算(RESC).RESC增加了一个全等CG的原始空间关系,引入了两个新颖的对区域的演算函数,即区域延伸和区域收缩,从而给出了一种以区域为单位的形式化的度量方法.利用RESC,不仅可以扩展RCC-8拓扑关系,而且能以灵活多样的粒度来描述区域间的距离关系、方向关系、位置关系以及运动关系.RESC增强了RCC的空间关系表示能力,拓展了RCC理论的适用范围.     

定性空间推理中区域连接演算的多维扩展

区域连接演算(RCC)是定性空问推(QSR)的基础理论之一．但RCC理论只支持区域，不能处理包括点、线和区域在内的空问多维对象，这阻碍了RCC应用的发展．扩展了区域概念，将点和线对象视为特殊的区域．提出了能直接用RCC理论描述空间多维对象拓扑关系的MRCC理论．在保留RCC公理的前提下，MRCC增加了2条新公理，并由此推导出了36种MRCC基本关系．进而讨论了基于概念邻域图和复合表的推理．MRCC拓展了RCC理论的适用范围，促进了RCC向实际应用的发展．     

RCC5与主方位关系结合的定性空间推理

解决实际问题需要将多方面空间信息结合进行推理,仅考虑单方面空间信息是不够的.多方面空间信息结合推理已成为定性空间推理的一个研究热点.现有拓扑与方位结合推理工作主要集中在与基于最小外包矩形或单片方位模型的结合.方位信息描述是近似的,不适于精确推理;因此分别采用主方位模型和RCC5描述方位、拓扑信息.根据定义给出基本RCC5和主方位关系间的相互依赖及异质复合表;讨论了其上约束满足问题,得到一个路径相容算法,并分析了推理复性问题.     

基于区域伸缩的空间关系研究与实现

区域连接演算(RCC)是空间推理的重要基础理论之一,它只能粗略地描述空间拓扑关系,难以描述除拓扑关系之外的其他空间关系,如距离和方向。在RCC理论的基础上,引入2个对区域的演算函数,即区域延伸和区域收缩,给出一种以区域为单位的形式化的度量方法。在RESC理论的基础上,利用栅格区域法应用简单和易于实现的特性,准确地得出区域间的空间关系。     

基于FJ的多版本类动态更新演算

针对面向对象软件在动态更新中遇到类型安全问题,定义了一个多版本类的动态更新演算(MCUFJ演算(multi-version class dynamic updamble calculus based on FJ calculus))来描述类动态更新.MCUFJ演算以FJ(featherweight Java)演算为核心,通过增加update操作表示类的动态更新,运用多版本技术使动态更新可以在保持新旧对象共存的情况下完成,讨论了类的数据域和方法进行增加、删除、修改以及类型变化对程序类型安全性的影响,并且指出MCUFJ上类型安全的动态更新需要满足的约束.定义了类的可动态更新限制,并且证明了在该条件下多版本类的动态更新在类型上的安全性.该演算可以用于指导Java语言和面向对象程序语言的类动态更新.     

一种利用适合性测试支持方法重定向的演算

一些面向上下文的编程语言使用结构化的块结构(block-structured construct)将方法调用重定向到层中方法.但该结构无法支持层的动态添加与激活,这增加了程序可执行文件的大小.为了解决该问题,提出一种新方法:使用适合性测试支持方法的重定向,并定义一个运行时的适合性测试演算(runtime fitness testing calculus on top offeatherweight Java calculus)形式化描述该方法.该演算以FJ 演算(featherweight Java calculus)为核心,通过融入新的语言结构——层,基于上下文的方法查找与对象转化描述基于适合性测试的方法重定向,分析它对程序类型安全的影响,制定相应约束,并证明在满足该约束的条件下能够保持程序的类型安全,从而证明所提方法的有效性.以该演算为指导,描述如何通过扩展Java 的编译器与虚拟机,实现将层、基于上下文的方法查找与对象转化融入到Java 语言,并通过实验测试实现,证明所提方法的可行性.该演算及其实现可用于指导如何扩展类似Java(Java-like)的语言以支持程序基于上下文动态调整其行为,并同时保证程序的类型安全.     

两种改进的模拟退火算法求解大值域约束满足问题

随机约束满足问题的相变现象及求解算法是NP-完全问题的研究热点。RB模型（Revised B）是一个非平凡的随机约束满足问题,它具有精确的可满足性相变现象和极易产生难解实例这两个重要特征。针对RB模型这一类具有大值域的随机约束满足问题,提出了两种基于模拟退火的改进算法即RSA（Revised Simulated Annealing Algorithm）和GSA（Genetic-simulated Annealing Algorithm）。将这两种算法用于求解RB模型的随机实例,数值实验结果表明：在进入相变区域时,RSA和GSA算法依然可以有效地找到随机实例的解,并且在求解效率上明显优于随机游走算法。在接近相变阈值点时,由这两种算法得到的最优解仅使得极少数的约束无法满足。     

Reasoning about cardinal directions between extended objects

Direction relations between extended spatial objects are important commonsense knowledge. Recently, Goyal and Egenhofer proposed a relation model, known as the cardinal direction calculus (CDC), for representing direction relations between connected plane regions. The CDC is perhaps the most expressive qualitative calculus for directional information, and has attracted increasing interest from areas such as artificial intelligence, geographical information science, and image retrieval. Given a network of CDC constraints, the consistency problem is deciding if the network is realizable by connected regions in the real plane. This paper provides a cubic algorithm for checking the consistency of complete networks of basic CDC constraints, and proves that reasoning with the CDC is in general an NP-complete problem. For a consistent complete network of basic CDC constraints, our algorithm returns a ‘canonical’ solution in cubic time. This cubic algorithm is also adapted to check the consistency of complete networks of basic cardinal constraints between possibly disconnected regions.     

Reasoning about cardinal directions between extended objects: The NP-hardness result

The cardinal direction calculus (CDC) proposed by Goyal and Egenhofer is a very expressive qualitative calculus for directional information of extended objects. Early work has shown that consistency checking of complete networks of basic CDC constraints is tractable, while reasoning with the CDC in general is NP-hard. This paper shows, however, that if some constraints are unspecified, then consistency checking of incomplete networks of basic CDC constraints is already intractable. This draws a sharp boundary between the tractable and intractable subclasses of the CDC. The result is achieved by a reduction from the well-known 3-SAT problem.     

GNet: A generalized network model and its applications in qualitative spatial reasoning

A data model, named generalized network (GNet), is proposed to perform various network-tracing tasks, especially tracing conceptual proposition networks in qualitative spatial reasoning (QSR). The GNet model can be defined as a 6-tuple: (V, A, q, ⊕, ∼, L). By specifying each element in the 6-tuple, a GNet can function as a conventional network, or an activity on edge (AOE) network, etc. The algorithm for searching for the generalized optimum path weight (GOPW) between two vertices in a GNet is developed by extending the Bellman-Ford algorithm (EBFA). Based on the GNet model, this paper focuses on representing spatial knowledge, which consists of a set of binary relations. We present two applications of GNets, namely the RCC8 network and the hybrid RCC8 network involving cardinal direction relations. Both can be traced to infer new spatial knowledge using EBFA. The applications demonstrate that the GNet model provides a promising approach to dealing with proposition-based geospatial knowledge based on weak composition. We also point out that EBFA can check whether a network is algebraically closed, or path-consistent when the corresponding composition table is extensional.     

Spatial reasoning with rectangular cardinal relations

Qualitative spatial representation and reasoning plays a important role in various spatial applications. In this paper we introduce a new formalism, we name RCD calculus, for qualitative spatial reasoning with cardinal direction relations between regions of the plane approximated by rectangles. We believe this calculus leads to an attractive balance between efficiency, simplicity and expressive power, which makes it adequate for spatial applications. We define a constraint algebra and we identify a convex tractable subalgebra allowing efficient reasoning with definite and imprecise knowledge about spatial configurations specified by qualitative constraint networks. For such tractable fragment, we propose several polynomial algorithms based on constraint satisfaction to solve the consistency and minimality problems. Some of them rely on a translation of qualitative networks of the RCD calculus to qualitative networks of the Interval or Rectangle Algebra, and back. We show that the consistency problem for convex networks can also be solved inside the RCD calculus, by applying a suitable adaptation of the path-consistency algorithm. However, path consistency can not be applied to obtain the minimal network, contrary to what happens in the convex fragment of the Rectangle Algebra. Finally, we partially analyze the complexity of the consistency problem when adding non-convex relations, showing that it becomes NP-complete in the cases considered. This analysis may contribute to find a maximal tractable subclass of the RCD calculus and of the Rectangle Algebra, which remains an open problem.     

Spatial reasoning in a fuzzy region connection calculus

Although the region connection calculus (RCC) offers an appealing framework for modelling topological relations, its application in real-world scenarios is hampered when spatial phenomena are affected by vagueness. To cope with this, we present a generalization of the RCC based on fuzzy set theory, and discuss how reasoning tasks such as satisfiability and entailment checking can be cast into linear programming problems. We furthermore reveal that reasoning in our fuzzy RCC is NP-complete, thus preserving the computational complexity of reasoning in the RCC, and we identify an important tractable subfragment. Moreover, we show how reasoning tasks in our fuzzy RCC can also be reduced to reasoning tasks in the original RCC. While this link with the RCC could be exploited in practical reasoning algorithms, we mainly focus on the theoretical consequences. In particular, using this link we establish a close relationship with the Egg-Yolk calculus, and we demonstrate that satisfiable knowledge bases can be realized by fuzzy regions in any dimension.     

基于邻域粗糙集下知识划分的信息表降维

Pawlak粗糙集的知识约简包括对决策表的知识约简和对信息表的知识约简。作为Pawlak粗糙集的扩展,邻域粗糙集在针对决策表的属性约简方面应用广泛,而针对信息表的属性约简方面应用鲜少。为了设计一种适用于信息表的属性约简算法,根据Pawlak粗糙集的信息表知识约简标准,首先提出一种邻域粗糙集的信息表知识约简标准,然后根据这种标准,结合贪心思想,进一步提出了一种适用于聚类任务的信息表属性约简算法。与主成分分析(principal component analysis,PCA)算法相比,实验结果表明用该算法对数据集降维后,得到的属性约简集合的属性个数较多,K-means算法根据属性集合进行聚类的精度较高。实验结果证明该算法能有效地应用于信息表的属性约简方面。     

Solving hard qualitative temporal reasoning problems: Evaluating the efficiency of using the ORD-Horn class

While the worst-case computational properties of Allen's calculus for qualitative temporal reasoning have been analyzed quite extensively, the determination of the empirical efficiency of algorithms for solving the consistency problem in this calculus has received only little research attention. In this paper, we will demonstrate that using the ORD-Horn class in Ladkin and Reinefeld's backtracking algorithm leads to performance improvements when deciding consistency of hard instances in Allen's calculus. For this purpose, we prove that Ladkin and Reinefeld's algorithm is complete when using the ORD-Horn class, we identify phase transition regions of the reasoning problem, and compare the improvements of ORD-Horn with other heuristic methods when applied to instances in the phase transition region. Finally, we give evidence that combining search methods orthogonally can dramatically improve the performance of the backtracking algorithm.     

基于分解合并策略的属性约简算法

在基于粗集理论的知识获取研究中,属性约简是最核心的工作之一。结合分治法的思想,从论域划分的角度将一个大的决策表分解成两个子决策表,并利用经典的属性约简算法计算两个子决策表的约简,在此基础上利用合并约简算法将这两个子决策表合并,并求出原问题的解。该方法为解决大数据集的属性约简提供了一个新的途径。实验说明了算法的有效性。