Distance-based software measurement: necessary and sufficient properties for software measures

Axiomatic approaches to software measurement present sets of necessary, but not sufficient measure axioms. The insufficiency of the measure axioms implies that they are useful to invalidate existing software measures, but not to validate them. In this paper, a set of measure axioms is presented whose sufficiency is guaranteed by measurement theory. The axioms referred to are the metric axioms, used in mathematics to define measures of distance. We present a constructive procedure that defines software measures satisfying these axioms. As an illustration of distance-based software measurement, a measure is defined for the aggregation coupling of object classes.     

Meta-linguistic axioms as a foundation for computing with words

Meta-linguistic axioms are proposed in analogy to the axioms of classical theory as a foundation for Computing With Words. Consequences of these meta-linguistic expressions are explored in the light of Interval-valued Type-2 Fuzzy Sets. The mapping of meta-linguistic axioms to Fuzzy Disjunctive and Conjunctive Canonical forms generate two set theoretic axioms for each meta-linguistic axiom that is composed of two elements such as commutativity and four set theoretic axioms for each meta-linguistic axiom that is composed of three elements such as associativity as opposed to one axiom that is generated in the classical theory. The set theoretic axioms double or quadruple because the basic equivalences of the classical theory break down in fuzzy theory. In this setting, we become aware that first, these new axioms hold as a matter of degree, and secondly there is an upper and lower limit with which they hold as a matter of degree.     

Single axioms for groups and Abelian groups with various operations

This paper summarizes the results of an investigation into single axioms for groups, both ordinary and Abelian, with each of following six sets of operations: {product, inverse}, {division}, {double division, identity}, {double division, inverse}, {division, identity}, and {division, inverse}. In all but two of the twelve corresponding theories, we present either the first single axioms known to us or single axioms shorter than those previously known to us. The automated theorem-proving program OTTER was used extensively to construct sets of candidate axioms and to search for and find proofs that given candidate axioms are in fact single axioms.This work was supported by the Applied Mathematical Sciences subprogram of the Office of Energy Research, U.S. Department of Energy, under Contract W-31-109-Eng-38.     

基于ORM的OWL 2本体可视化表达

无相关技术背景的领域专家较难直接阅读和理解OWL 2本体。为此,提出一种使用对象角色建模(ORM)可视化表达OWL 2本体的方法,并介绍一系列相应规则。通过语义等价的模型变换和扩展构造原语,使用ORM可视化表达OWL 2的构造原语、类表达式、类公理、对象特性公理、数据特性公理和键公理。实验结果表明,内置数据类型、类等价公理和对象特性的传递性公理需要对ORM进行扩展才能表达,其余OWL 2类和公理均可语义无损地转换为ORM模型。     

概念格的公理化

概念格是数据分析和知识表示的一种有效工具。研究概念格的公理化问题。得到了两组关于概念格的公理组,且每组含有六个独立的公理。公理化的研究有助于概念格理论的进一步完善。     

使用OWL DL形式化表达对象角色建模模型

对象角色建模(ORM)方法已应用于本体工程,因此需要将ORM模型转换为OWL DL公理,以便将ORM本体发布到语义Web上,同时还可使用支持DL的推理机来检查ORM本体的语义一致性和冗余问题。通过模型语义分析、模型等价转换、引入新的运算符和特性等方法,提出将ORM模型形式化表达为OWL DL公理的规则。除了外部唯一约束等四种约束外,其他形态的ORM模型都可以形式化表达为OWL DL公理。     

Automated discovery of new axiomatizations of the left group and right group calculi

This paper shows how the automated theorem-proving program OTTER was used to discover new axiomatizations, including single axioms, for the left group and righ group calculi. J. A. Kalman's original axiomatizations of the two calculi each contain five axioms. Three of Kalman's axioms (L1, L4, and L5) for the left group calculus were shown to be dependent on the remaining two axioms. Four of Kalman's axioms (R1, R3, R4, and R5) for the right group calculus were shown to be dependent on the remaining axiom. Alternative simpler axiomatizations were discovered for both calculi, including a single axiom for the left group calculus and five additional single axioms for the right group calculus. The program OTTER was vital in discovering candidate axiomatizations as well as in finding proofs of new axiomatizations. All of the relevant OTTER proofs are included.This work was supported by the Applied Mathematical Sciences subprogram of the Office of Energy Research, U.S. Department of Energy, under Contract W-31-109-Eng-38.     

A framework for testing first-order logic axioms in program verification

Program verification systems based on automated theorem provers rely on user-provided axioms in order to verify domain-specific properties of code. However, formulating axioms correctly (that is, formalizing properties of an intended mathematical interpretation) is non-trivial in practice, and avoiding or even detecting unsoundness can sometimes be difficult to achieve. Moreover, speculating soundness of axioms based on the output of the provers themselves is not easy since they do not typically give counterexamples. We adopt the idea of model-based testing to aid axiom authors in discovering errors in axiomatizations. To test the validity of axioms, users define a computational model of the axiomatized logic by giving interpretations to the function symbols and constants in a simple declarative programming language. We have developed an axiom testing framework that helps automate model definition and test generation using off-the-shelf tools for meta-programming, property-based random testing, and constraint solving. We have experimented with our tool to test the axioms used in Auto-Cert, a program verification system that has been applied to verify aerospace flight code using a first-order axiomatization of navigational concepts, and were able to find counterexamples for a number of axioms.     

The minimization of axiom sets characterizing generalized approximation operators

In the axiomatic approach of rough set theory, rough approximation operators are characterized by a set of axioms that guarantees the existence of certain types of binary relations reproducing the operators. Thus axiomatic characterization of rough approximation operators is an important aspect in the study of rough set theory. In this paper, the independence of axioms of generalized crisp approximation operators is investigated, and their minimal sets of axioms are presented.     

A Formal Axiomatization for Alphabet Reasoning with Parametrized Processes

In the process-algebraic verification of systems with three or more components put in parallel, alphabet axioms are considered to be useful. These are rules that exploit the information about the alphabets of the processes involved. The alphabet of a process is the set of actions it can perform. In this paper, we extend μCRL (a formal proof system for ACP_τ + data) with such axioms. The alphabet axioms that are added to the proof theory are completely formal and therefore highly suited for computer-checked verification. This is new compared to previous papers where the formulation of alphabet axioms relies for a considerable amount on informal data parameters and implicit (infinite) set theory. Received April 1995 / Accepted in revised form March 1998     

The logic of events

An event space is a set of instantaneous events that vary both in time and specificity. The concept of an event space provides a foundation for a logical – i.e., modular and open – approach to causal reasoning. In this article, we propose intuitively transparent axioms for event spaces. These axioms are constructive in the intuitionistic sense, and hence they can be used directly for causal reasoning in any computational logical framework that accommodates type theory. We also put the axioms in classical form and show that in this form they are adequate for the representation in terms of event trees established by Shafer [40] using stronger axioms. This revised version was published online in June 2006 with corrections to the Cover Date.     

An algebra of mixed computation

Algebraic tools for mixed computation are presented. Some axioms for informational objects, program functions, inputs and outputs are introduced. These axioms are sufficient for the correct mixed computation of some basic program composition forms.     

Logical organization of knowledge with inconsistent and undecidablealgorithms using imaginary and transfinite exponential number forms in anon-Boolean field-I. Basic principles

In order to consider the organization of knowledge using inconsistent algorithms, a mathematical set-theoretic definition of axioms and undecidability is discussed. Ways in which imaginary numbers, exponentials, and transfinite ordinals can be given logical meanings that result in a new way to definite axioms are presented. This presentation is based on a proposed logical definition for axioms that includes an axiom and its negation as parts of an undecidable statement which is forced to the tautological truth value: true. The logical algebraic expression for this is shown to be isomorphic to the algebraic expression defining the imaginary numbers. This supports a progressive and Hegelian view of theory development, which means that thesis and antithesis axioms that exist in quantum mechanics (QM) and the special theory of relativity (STR) can be carried along at present and might be replaced by a synthesis of a deeper theory prompted by subsequently discovered experimental concept     

粗集的公理化

粗集是知识发现领域的基础理论 ,该文在 L in等工作的基础上对粗集的公理化进行了深入的研究 ,去除了以往文献中给出的粗集公理组中的冗余性 ,得到了两个关于粗集的最小公理组 ,它们各自只包含 3个公理 .     

Set-Theoretical Algebraic Approaches to Connectivity in Continuous or Digital Spaces

Connectivity has been defined in the framework of topological spaces, but also in graphs; the two types of definitions do not always coincide. Serra gave a set of formal axioms for connectivity, which consists in a list of properties of the family of all connected subsets of a space; this definition includes as particular case connected sets in a topological space or in a graph. He gave an equivalent characterization of connectivity in terms of the properties of the operator associating to a subset and a point of that space, the connected component of that subset containing that point. In this paper we give another family of axioms, equivalent to those of Serra, where connectivity is characterized in terms of separating pairs of sets. In the case of graphs, where connected sets are generated by pairs of end-vertices of edges, this new set of axioms is equivalent to the separation axioms given by Haralick.     

An axiomatic comparison of learned term-weighting schemes in information retrieval: clarifications and extensions

Machine learning approaches to information retrieval are becoming increasingly widespread. In this paper, we present term-weighting functions reported in the literature that were developed by four separate approaches using genetic programming. Recently, a number of axioms (constraints), from which all good term-weighting schemes should be deduced, have been developed and shown to be theoretically and empirically sound. We introduce a new axiom and empirically validate it by modifying the standard BM25 scheme. Furthermore, we analyse the BM25 scheme and the four learned schemes presented to determine if the schemes are consistent with the axioms. We find that one learned term-weighting approach is consistent with more axioms than any of the other schemes. An empirical evaluation of the schemes on various test collections and query lengths shows that the scheme that is consistent with more of the axioms outperforms the other schemes.     

一种利用RDF(S)建立本体论的方法

首先介绍了如何使用RDF(S)表示本体论 (Ontology)中的对象模型 ,然后分析了如何在RDF(S)中表示本体论中的公理     

基于本体论的民族知识获取与分析

1.引言民族学是一个非常重要的学科,它与语言学、宗教学、地理知识和历史知识等都有密切的联系。许多计算机应用系统都需要大量的民族文化、宗教、历史等知识。例如自然语言理解(词法和语法分析)、民族知识教学系统、民族知识的普及等等都离不开有关民族的基础和专业知识。但在人工智能中,民族知识的获取及知识表示一直得不到足够的重视。Harvard大学有一个ad2000的项目,其中包含了一千多个民族。但ad2000项目主要是为基督教的传播服务的,它虽然在尽可能地收录民族,但它对民族的描述主要是针对宗教,并没有给出