模态逻辑公理的粗糙真语义分析

粗糙真是Pawlak粗糙逻辑的5个逻辑值之一,介于真与假之间．通过对论域U^n上所有近似空间相互关系的讨论,构造了一类代数结构——格,这类格形成了特殊的克里普克语义模型．其目的就是要在这种模型中,对模态逻辑形式推理系统的公理进行语义分析．这种分析不限于真与假的二值讨论,而主要对粗糙真进行重点研究．最终的结果表明模态逻辑形式系统的公理在这类特殊语义模型中基本部粗糙真有效．从而也得到了利用某些公理进行粗糙真形式推理的可靠性．     

Rough逻辑公式的语义分析及基于语义分析推理的研究

在粗糙集理论的近似空间M=(U,R)中展开讨论,其目的是要把Pawlak粗糙逻辑中的公式进行推广,将其所涉及的论域从与U有关扩展到n个U的笛卡尔积Un之上,并对这些推广的n元公式进行研究.讨论以Pawlak粗糙逻辑中的5种逻辑值为基础,并在n元公式上对此进行推广定义.针对这些关于n元公式的粗糙逻辑值,从语义出发,研究n元公式之间的逻辑推理关系.其结果是经典逻辑中的一些逻辑推理的结论对于某些粗糙逻辑值仍然成立,但自然也增添新的性质.     

判定粗糙XML函数依赖的一种算法

为了刻画和处理不确定XML数据,利用粒计算方法研究粗糙XML树信息系统中粗糙XML函数依赖的判定问题。基于粗糙集给出粗糙XML树信息系统的上近似、下近似的定义,借助粗糙相似关系进一步给出粗糙XML函数依赖;分析如何利用位模式表示粗糙XML树信息系统中的信息值;提出粗糙XML树信息系统中路径间的依赖关系的判定算法,并对算法的时间复杂性进行了分析。实例分析表明,信息值采用位模式时,数据格式更接近机器的内部表示,该方法可以快速判定粗糙XML函数依赖,算法的运算效率与速度也得到了提高。     

粗糙逻辑中公式的Borel型概率粗糙真度

以一种特殊的粗糙逻辑为研究对象,视全体赋值之集为通常乘积拓扑空间,通过利用赋值集上的Borel概率测度,提出了能融合粗糙逻辑与计量逻辑为一体的公式的Borel型概率粗糙真度理论,给出了公式概率粗糙真度的公理化定义,建立起了相应的概率真度表示定理.公式的概率粗糙真度理论可被看作粗糙逻辑中已有工作的计量化,也可看作计量逻辑学中真度理论的粗糙化.基于这一核心概念,进一步给出了粗糙逻辑中已有概念的程度化表示形式,如公式的粗糙度、精确度、公式之间的粗糙相似度等,并建立起了基于粗糙相似度的3种近似推理模式.该结果实现了粗糙逻辑与计量逻辑的和谐统一,为进一步基于粗糙真值的程度化推理搭建了一个可能的框架.     

逻辑之间的语义忠实语义满翻译

翻译在计算机科学中的一个重要应用是实现一个逻辑与另一个逻辑在表达能力上的比较,以及利用目标逻辑的推理机实现源逻辑的推理.现有逻辑之间的翻译理论和性质没有深入研究逻辑的语义翻译,以及翻译是否保持不可满足性等问题.该文研究了一类同时保持公式的可满足性和不可满足性的翻译——语义忠实语义满翻译,给出了语义忠实语义满翻译的定义,比较了语义忠实语义满翻译与已有文献中翻译定义的区别和联系,讨论了逻辑的可靠性、完备性、可判定性、紧致性、公式的逻辑等价性,以及模型的初等等价性在语义忠实语义满翻译下被保持的问题.运用语义忠实语义满翻译的定义给出了逻辑之间的同义性定义,并证明了同义关系是逻辑之间的一个等价关系.     

双析取逻辑程序设计基础（Ⅰ）

析取逻辑程序设计是传统逻辑程序设计最重要的扩充之一，本文通过一些实例说明，现存语义无法充分 表示信息的不完全性。为此，本文提出了双析取逻辑程序设计的概念，我们不仅从句法上将正规则析取逻辑程序推广为双析取逻辑程序。而且建立了一种高度直观，灵活的辩论语义框架ＢＤＡＳ。     

改进的描述逻辑框架Rough-SHOIN

针对具有不完备、多粒度特点的不确定知识表示,设计了一个粗糙描述逻辑框架--Rough-SHOIN,利用粗糙相似关系作为概念描述的基础,定义概念的粗糙上近似和下近似,实现不完备概念表达,在概念解释中引入上下文,实现在不同粒度上准确定义概念-对象间关系。在此基础上,给出Rough-SHOIN粗糙概念的语法、语义及知识库,并在不增加计算复杂度的前提下,定义Rough-SHOIN的推理规则。通过实例说明该框架的有效性。     

双析取逻辑程序设计基础（Ⅱ）

双析取逻辑程序设计是析取逻辑程序设计的一种扩充，其辩论语框架ＢＤＡＳ为逻辑程序设计中的常识推理提供了一种较为合理的语义框架。     

一种描述逻辑与DL-safe规则复合逻辑中的规则抽取方法

OWL本体描述语言包含相对丰富的概念定义符,但提供的关系定义符描述能力则较差。将OWL与规则相结合是克服这种表达能力限制的一种常用方法。Motik提出了一种可判定的方法,将SHIQ（D）描述逻辑与规则结合,所结合的规则限定在一种叫做DL-safe规则的范围内。本文提出了一种抽取DL-safe规则的方法,方法利用SHIQ（D）逻辑中的UNION定义符满足一些规则在前件中包含析取逻辑运算符的需求,从而扩展了规则的描述能力。     

FLUX中负析取约束的研究与实现*

FLUX是基于流演算的逻辑程序语言,实现agents在不完全状态下对其动作和感知信息进行逻辑推理。FLUX利用不同的约束来编码不完全状态,但现有的约束并不能覆盖所有流演算状态公式,这势必影响FLUX的应用范围。针对以上问题,在FLUX中引入负析取约束,利用约束处理规则集（CHRs）加以实现,并基于流演算基础语义分析了负析取约束的正确性,从而提高了FLUX对不完全状态的表达能力。     

A rough set approach to reasoning under uncertainty

Abstract

Reasoning with uncertain information is a problem of key importance when dealing with information about the real world. Obtaining the precise numbers required by many uncertainty handling formalisms can be a problem. The theory of rough sets makes it possible to handle uncertainty without the need for precise numbers, and so has some advantages in such situations. This paper presents an introduction to various forms of reasoning under uncertainty that are based on rough sets. In particular, a number of sets of numerical and symbolic truth values which may be used to augment propositional logic are developed, and a semantics for these values is provided based upon the notion of possible worlds. Methods of combining the truth values are developed so that they may be propagated when augmented logic formulae are combined, and their use is demonstrated in theorem proving.     

广义多粒度粗糙集属性约简和matlab计算

定义了基于广义多粒度粗糙集的属性约简,研究了约简的一些基本性质,给出matlab计算的过程,并给出计算实例。定义了信息系统的严格协调、软不协调性、粒度协调、粒度不协调,定义了广义多粒度下约简、粒度约简、（下/上近似）分布协调约简、（下/上近似）质量协调约简,并给出部分结论。广义多粒度粗糙集的约简适用于乐观多粒度粗糙集和悲观多粒度粗糙集。研究结果可完善多粒度粗糙集理论,为理论研究和应用奠定基础。     

Uncertainty measures for rough formulae in rough logic: An axiomatic approach

Rough set theory, initiated by Pawlak, is a mathematical tool in dealing with inexact and incomplete information. Various types of uncertainty measure such as accuracy measure, roughness measure, etc, which aim to quantify the imprecision of a rough set caused by its boundary region, have been extensively studied in the existing literatures. However, a few of these uncertainty measures are explored from the viewpoint of formal rough set theory, which, however, help to develop a kind of graded reasoning model in the framework of rough logic. To solve such a problem, a framework of uncertainty measure for formulae in rough logic is presented in this paper. Unlike the existing literatures, we adopt an axiomatic approach to study the uncertainty measure in rough logic, concretely, we define the notion of rough truth degree by some axioms, such a notion is demonstrated to be adequate for measuring the extent to which any formula is roughly true. Then based on this fundamental notion, the notions of rough accuracy degree, roughness degree for any formula, and rough inclusion degree, rough similarity degree between any two formulae are also proposed. In addition, their properties are investigated in detail. These obtained results will be used to develop an approximate reasoning model in the framework of rough logic from the axiomatic viewpoint.     

ASSUMPTION-BASED REASONING AND CLAUSE MANAGEMENT SYSTEMS

A truth maintenance system is a subsystem that manages the utilization of assumptions in the reasoning process of a problem solver. Doyle's original motivation for creating a truth maintenance system was to augment a reasoning system with a control strategy for activities concerning its nonmonotonic state of beliefs. Hitherto, much effort has been invested in designing and implementing the concept of truth maintenance, and little effort has been dedicated to the formalization that is essential to understanding it. This paper provides a complete formalization of the principle of truth maintenance. Motivated by Reiter and de Kleer's preliminary report on the same subject, this paper extends their study and gives a formal account of the concept of truth maintenance under the general title of assumption-based reasoning. The concept of assumption-based theory is defined, and the notions of explanation and direct consequence are presented as forms of plausible conclusions with respect to this theory. Additionally, the concepts of extension and irrefutable sentences are discussed together with other variations of explanation and direct consequence. A set of algorithms for computing these conclusions for a given theory are presented using the notion of prime implicates. Finally, an extended example on Boolean circuit diagnosis is shown to exemplify these ideas.     

命题逻辑公式模糊软集语义及其在决策分析中的应用

基于论域公式引入软命题逻辑公式概念,给出软命题逻辑公式的模糊软语义解释.将决策模糊信息系统转化为决策模糊软集,软决策规则表示为包含有蕴含联结词的软命题逻辑公式.引入软命题逻辑公式的基本真度、条件真度、绝对真度等指标,从充分性、必要性等方面评价软决策规则的有效性、合理性.提出基于决策软集的典型软决策规则提取算法和基于软决策分析的推荐算法,并通过实例和数值实验证明算法的有效性.     

Belief, information acquisition, and trust in multi-agent systems—A modal logic formulation

In this paper, we consider the influence of trust on the assimilation of acquired information into an agent's belief. By use of modal logic, we semantically and axiomatically characterize the relationship among belief, information acquisition and trust. The belief and information acquisition operators are respectively represented by KD45 and KD normal modalities, whereas trust is denoted by a modal operator with minimal semantics. One characteristic axiom of the basic system is if agent i believes that agent j has told him the truth of p and he trusts the judgement of j on p, then he will also believe p. In addition to the basic system, some variants and further axioms for trust and information acquisition are also presented to show the expressive richness of the logic. The applications of the logic to computer security and database reasoning are also suggested by its connection with some previous works.     

Resolving contradictions: A plausible semantics for inconsistent systems

The purpose of a knowledge systemS is to represent the worldW faithfully. IfS turns out to be inconsistent containing contradictory data, its present state can be viewed as a result of information pollution with some wrong data. However, we may reasonably assume that most of the system content still reflects the world truthfully, and therefore it would be a great loss to allow a small contradiction to depreciate or even destroy a large amount of correct knowledge. So, despite the pollution,S must contain a meaningful subset, and so it is reasonable to assume (as adopted by many researchers) that the semantics of a logic system is determined by that of its maximally consistent subsets,mc-subsets. The information contained inS allows deriving certain conclusions regarding the truth of a formulaF inW. In this sense we say thatS contains a certain amount ofsemantic information and provides anevidence of F. A close relationship is revealed between the evidence, the quantity of semantic information of the system, and the set of models of its mc-subsets. Based on these notions, we introduce thesemantics of weighted mc-subsets as a way of reasoning in inconsistent systems. To show that this semantics indeed enables reconciling contradictions and deriving plausible beliefs about any statement including ambiguous ones, we apply it successfully to a series of justifying examples, such as chain proofs, rules with exceptions, and paradoxes.