On the discovery of mathematical concepts

The Graph Theorist (GT) is a system intended to perform mathematical research in graph theory. This paper focuses upon GT's ability to discover new mathematical concepts by varying the definitions in its input knowledge base. Each new definition is a correct and complete generator for a class of graphs. the new concepts arise from the specialization of an existing concept, the generalization of an existing concept, and the merger of two or more existing concepts. Discovery is driven both by examples (specific graphs) and by definitional form (algorithms). GT explores new concepts either to develop an area of knowledge or to link a newly-acquired concept into a pre-existing knowledge base. From an initial knowledge base containing only the definition of “graph,” GT discovers such concepts as acyclic graphs, connected graphs and bipartite graphs. Given an input concept, such as “star,” GT discovers “trees” while searching for the appropriate links to integrate star into its knowledge base. the discovery processes construct a semantic net linking frames for all of GT's concepts together.     

知识图谱研究综述

知识图谱是以图的形式表现客观世界中的概念和实体及其之间关系的知识库,是语义搜索、智能问答、决策支持等智能服务的基础技术之一.目前,知识图谱的内涵还不够清晰;且因建档不全,已有知识图谱的使用率和重用率不高.为此,本文给出知识图谱的定义,辨析其与本体等相关概念的关系.本体是知识图谱的模式层和逻辑基础,知识图谱是本体的实例化;本体研究成果可以作为知识图谱研究的基础,促进知识图谱的更快发展和更广应用.本文罗列分析了国内外已有的主要通用知识图谱和行业知识图谱及其构建、存储及检索方法,以提高其使用率和重用率.最后指出知识图谱未来的研究方向.     

Knowledge representation for mathematical discovery: Three experiments in graph theory

This paper describes the nature of mathematical discovery (including concept definition and exploration, example generation, and theorem conjecture and proof), and considers how such an intelligent process can be simulated by a machine. Although the material is drawn primarily from graph theory, the results are immediately relevant to research in mathematical discovery and learning.The thought experiment, a protocol paradigm for the empirical study of mathematical discovery, highlights behavioral objectives for machine simulation. This thought experiment provides an insightful account of the discovery process, motivates a framework for describing mathematical knowledge in terms of object classes, and is a rich source of advice on the design of a system to perform discovery in graph theory. The evaluation criteria for a discovery system, it is argued, must include both a set of behavior to display (behavioral objectives) and a target set of facts to be discovered (factual knowledge).Cues from the thought experiment are used to formulate two hierarchies of representational languages for graphy theory. The first hierarchy is based on the superficial terminology and knowledge of the thought experiment. Generated by formal grammars with set-theoretic semantics, this eminently reasonable approach ultimately fails to meet the factual knowledge criteria. The second hierarchy uses declarative expressions, each of which has a semantic interpretation as a stylized, recursive algorithm that defines a class by generating it correctly and completely. A simple version of one such representation is validated by a successful, implemented system called Graph Theorist (GT) for mathematical research in graph theory. GT generates correct examples, defines and explores new graph theory properties, and conjectures and proves theorems.Several themes run through this paper. The first is the dual goals, behavioral objectives and factural knowledge to be discovered, and the multiplicity of their demands on a discovery system. The second theme is the central role of object classes to knowledge representation. The third is the increased power and flexibility of a constructive (generator) definition over the more traditional predicate (tester) definition. The final theme is the importance of examples and recursion in mathematical knowledge. The results provide important guidance for further research in the simulation of mathematical discovery.     

Design of engineering databases: A case for more varied semantic modelling concepts

Interest in database support for engineering applications is rapidly growing. In this paper we concentrate on conceptual database design and address the question of what a semantic model should look like, that meets the needs of engineering applications and is sufficiently formal to support validation, optimization, analysis, as well as transformation to an implementation schema. We present several case studies of engineering databases in order to determine major modelling requirements, and compare these to modelling concepts from the data base and knowledge representation fields. We demonstrate that the main issue is not adding further concepts, but to integrate the existing ones in a selective and precise fashion. We suggest to do so by tailoring the semantic model, starting from a set of base concepts and extending these. An initial model and an extensibility mechanism allowing an explicit and declarative definition of higher-order abstractions are presented. This is demonstrated by specifying some simple concepts such as generalization and a more complex time concept for image sequence evaluation.     

An end-to-end tabular information-oriented causality event evolutionary knowledge graph for manufacturing documents

Industrial tabular information extraction and its semantic fusion with text (ITIESF) is of great significance in converting and fusing industrial unstructured data into structured knowledge to guide cognitive intelligence analysis in the manufacturing industry. A novel end-to-end ITIESF approach is proposed to integrate tabular information and construct a tabular information-oriented causality event evolutionary knowledge graph (TCEEKG). Specifically, an end-to-end joint learning strategy is presented to mine the semantic information in tables. The definition and modeling method of the intrinsic relationships between tables with their rows and columns in engineering documents are provided to model the tabular information. Due to this, an end-to-end joint entity relationship extraction method for textual and tabular information from engineering documents is proposed to construct text-based knowledge graphs (KG) and tabular information-based causality event evolutionary graphs (CEEG). Then, a novel NSGCN (neighborhoods sample graph convolution network)-based entity alignment is proposed to fuse the cross-knowledge graphs into a unified knowledge base. Furthermore, a translation-based graph structure-driven Q&A (question and answer) approach is designed to respond to cause analysis and problem tracing. Our models can be easily integrated into a prototype system to provide a joint information processing and cognitive analysis. Finally, the approach is evaluated by employing the aerospace machining documents to illustrate that the TCEEKG can considerably help workers strengthen their skills in the cause-and-effect analysis of machining quality issues from a global perspective.     

中文语义相关度计算模型研究

现有的中文语义相关度计算模型对相关度的定义并不明确和统一,且计算方法多以相似度计算为基础,导致应用语义相关度存在局限。提出了一个新的语义相关的定义,认为两个词所表达的概念之间,如果存在用类似“知网”的知识描述体系所描述的语义关系,那么这两个概念之间就是语义相关的。通过挖掘这些直接或间接的关系,提出了一种新的语义相关度的计算模型,适用于所有类似知网的知识体系中语义相关度的计算。最后将该计算模型应用于词义排歧,验证了该计算模型的有效性。     

一种准确而高效的领域知识图谱构建方法

作为语义网的数据支撑,知识图谱在知识问答、语义搜索等领域起着至关重要的作用,一直以来也是研究领域和工程领域的一个热点问题,但是构建一个质量较高、规模较大的知识图谱往往需要花费巨大的人力和时间成本.如何平衡准确率和效率,快速地构建出一个高质量的领域知识图谱,是知识工程领域的一个重要挑战.本文对领域知识图谱构建方法做了系统研究,提出了一种准确高效的领域知识图谱构建方法——“四步法”,我们将此方法应用到中国基础教育九门学科知识图谱的构建中,在较短时间构建出了准确率较高的学科知识图谱,证明了该方法构建领域知识图谱的有效性.以地理学科知识图谱为例,使用“四步法”共得到67万个实例,1421万条三元组,其中标注数据的学科知识覆盖率和知识准确率均在99%以上.     

Compiling conceptual graphs

The paper addresses problems in conceptual graph implementation: subsumption and classification in a taxonomy. Conceptual graphs are typically stored using a directed acyclic graph data structure based on the partial order over conceptual graphs. We give an improved algorithm for classifying conceptual graphs into this hierarchy. It prunes the search space in the database using the information gathered while searching. We show how conceptual graphs in this hierarchy can be compiled into instructions which represent specialized cases of the canonical formation rules. This compiles subsumption of conceptual graphs and compresses knowledge in a knowledge base. Conceptual graphs are compiled as differences between adjacent graphs in the hierarchy. The differences represent the rules used in deriving the graph from the adjacent graphs. We illustrate how the method compresses knowledge bases in some experiments. Compilation is effected in three ways: removal of redundant data, use of simple instructions which ignore redundant checks when performing matching, and by sharing common processing between graphs     

领域知识图谱研究综述

知识图谱由Google公司提出, 作为增强其搜索功能的知识库, 在近几年得到了迅速发展. 随着知识图谱价值不断地被发掘, 各类领域知识图谱也迅速建设起来. 本文通过领域知识图谱和通用知识图谱的对比来清晰化领域知识图谱的定义, 介绍了领域知识图谱的架构, 并以医学知识图谱为例讲解了领域知识图谱的构建技术. 最后, 本文介绍了当前热门的领域知识图谱的发展状况和应用, 对当前领域知识图谱状况进行了较为全面的总结.     

基于维基百科的领域概念语义知识库的自动构建方法*

针对为检索服务的语义知识库存在的内容不全面和不准确的问题,提出一种基于维基百科的软件工程领域概念语义知识库的构建方法;首先,以SWEBOK V3概念为标准,从维基百科提取概念的解释文本,并抽取其关键词表示概念的语义;其次,通过概念在维基百科中的层次关系、概念与其它概念解释文本关键词之间的链接关系、不同概念解释文本关键词之间的链接关系构建概念语义知识库;接着, LDA主题模型分别和TF-IDF算法、TextRank算法相结合的两种方法抽取关键词;最后,对构建好的概念语义知识库用随机游走算法计算概念间的语义相似度;将实验结果与人工标注结果对比发现,本方法构建的语义知识库语义相似度准确率能够达到84%以上;充分验证了所提方法的有效性。     

区分3种否定的模糊命题逻辑系统及其应用

在模糊知识表示与推理中,否定信息扮演了一个重要角色.从概念层面上区分了模糊知识中存在的3 种否定关系,即矛盾否定关系、对立否定关系和中介否定关系.为了建立能够完全描述这些不同否定关系的逻辑基础,提出一种区分矛盾否定、对立否定和中介否定的模糊命题逻辑形式系统FLCOM.讨论了FLCOM 特有的性质与意义,给出了FLCOM 的一种语义解释,并证明了可靠性定理.为了表明FLCOM 处理实际问题的适用性,进一步研究了FLCOM在一个模糊决策实例中的应用.具体地,基于FLCOM讨论了决策规则中的模糊命题及其不同否定的区分与形式表示,给出一种确定模糊命题及其不同否定的真值及其真值范围阈值的方法,并采用模糊产生式规则讨论了实例中的模糊推理与决策.从而表明,运用FLCOM 处理具有模糊性并且存在不同否定的实际问题是有效的.     

基于连通分量的分类变量聚类算法

针对分类变量相似度定义存在的不足, 提出一种新的相似度定义. 利用新的相似度定义, 将数据集抽象为无向图, 将聚类过程转化为求无向图连通分量的过程, 进而提出一种基于连通分量的分类变量聚类算法. 为了定量地分析该算法的聚类效果, 针对类别归属已知的数据集, 提出一种新的聚类结果评价指标. 实验结果表明, 所提出的算法具有较高的聚类精度和聚类效率.     

《知网》语义关系图的自动构建

在真实语言环境中,词语间的联系普遍存在、错综复杂。为了更好融合和使用各种语义资源库中的语义关系,构建可计算的汉语词汇语义资源,该文提出了通过构建语义关系图整合各种语义资源的方法,并在《知网》上实现。《知网》作为一个知识库系统,对各个词语义项是以分条记录的形式存储的,各种词汇语义关系隐含在词典文件和义原描述文件中。为提取《知网》中语义间的关系,本文首先将《知网》中的概念以概念树的形式重新表示,并从概念树中提取适当的语义关系,构建语义关系图。经过处理,得到88种589 984条语义关系,图上各种节点具有广泛的联系,为基于语义关系图的进一步分析和计算打下了基础。     

一种支持动态自主学习的知识表示结构——语义神经网络

分别分析了传统的语义网络和人工神经网络方法在知识表示方面的特点和不足,提出了将两者结合起来构建具有语义单元和神经单元双重机能的语义神经单元的设想。以此为基础,构造出具有全连通结构的语义神经网络,给出了网络的权值学习方法及概念单元的语义联想机制,从而形成自主学习与语义联想相统一的集成化知识表示结构。它既能对概念语义及其关联关系进行直观、准确的表示,同时又对概念语义的联想、学习和更新等过程提供统一的支持平台。     

基于实体活跃度及复制生成的时序知识图谱推理

现有时序知识图谱推理主要是基于静态知识图谱的推理方法,通过知识图谱的结构特征挖掘潜在的语义信息和关系特征,忽略了实体时序信息的重要性,因此提出一种基于实体活跃度及复制生成机制的时序知识图谱推理方法（EACG）。首先,通过改进的图卷积神经网络对多关系实体建模,有效挖掘知识图谱的潜在语义信息和结构特征。其次,时序编码器基于实体活跃度学习实体的时序特征。最后,使用复制生成机制进一步学习知识图谱的历史信息,提升对时序数据建模的能力。在时序知识图谱数据集ICEWS14、ICEWS05-15、GDELT上推理的实验结果表明,EACG在MRR评估指标中分别优于次优方法2%、10%和5%。     

基于概念格的多层属性约简方法

属性约简是粗糙集理论中的核心问题之一,概念格是进行知识表示和数据分析的一种有效工具。文中利用概念格作为约简工具,给出基于概念格的多层属性约简算法,提出相融可辨概念、相融等价概念、亏n级等概念,研究内涵亏值对分类能力变化产生的影响,给出概念格中形式背景约简的判定定理。文中算法能完备地求出所有可约简的最大属性集合,从而为概念格中属性约简提供一种有效方法。最后,通过实例分析和实验对比说明该约简算法的可行性与有效性。     

Building spatial temporal relation graph of concepts pair using web repository

Mining semantic relations between concepts underlies many fundamental tasks including natural language processing, web mining, information retrieval, and web search. In order to describe the semantic relation between concepts, in this paper, the problem of automatically generating spatial temporal relation graph (STRG) of semantic relation between concepts is studied. The spatial temporal relation graph of semantic relation between concepts includes relation words, relation sentences, relation factor, relation graph, faceted feature, temporal feature, and spatial feature. The proposed method can automatically generate the spatial temporal relation graph (STRG) of semantic relation between concepts, which is different from the manually generated annotation repository such as WordNet and Wikipedia. Moreover, the proposed method does not need any prior knowledge such as ontology or the hierarchical knowledge base such as WordNet. Empirical experiments on real dataset show that the proposed algorithm is effective and accurate.     

Coordinating Programs in the Network of Tasks Model

The Network of Tasks (NOT) model allows adaptive node programs written in a variety of parallel languages to be connected together in an almost acyclic task graph. The main difference between NOT and other task graphs is that it is designed to make the performance of the graph predictable from knowledge of the performance of the component node programs and the visible structure of the graph. It can therefore be regarded as a coordination language that is transparent about performance. For large-scale computations that are distributed to geographically-distributed compute servers, the NOT model helps programmers to plan, assemble, schedule, and distribute their problems.     

知识赋能的新一代信息系统研究现状、发展与挑战

信息系统的发展目前正处于感知智能迈向认知智能的关键阶段,传统信息系统难以满足发展要求,数字化转型势在必行.数字线索(digitalthread)是面向全生命周期的数据处理框架,通过连接生命周期的各阶段数据,实现物理世界与数字空间的映射与分析.知识图谱(knowledgegraph)是结构化的语义知识库,以符号形式描述物理世界中的概念及其相互关系,通过知识驱动形成体系化的构建与推理流程.两者对知识赋能的信息系统研究具有重要意义.综述了知识赋能的新一代信息系统的研究现状、发展与挑战.首先,从数字线索系统出发,介绍数字线索的概念和发展,分析数字线索的六维数据构成和6个数据处理阶段;然后介绍知识图谱系统,给出普遍认同的知识图谱的定义和发展,概括知识图谱的架构与方法;最后,分析和探索数字线索与知识图谱结合的方向,列举KG4DT (knowledge graph for digital thread)和DT4KG (digital thread for knowledge graph)的受益方向,对未来知识赋能的新一代信息系统提出开放问题.