逻辑系统L_n*中一类特殊公式的Σ_Γ-真度

在模糊命题系统L_n~*中,利用公式A的原子公式集S_A与有限理论Γ的原子公式集S_Γ之间的关系,讨论了公式A的Σ_Γ-真度,给出了当S_ΓS_A和S_A∩S_Γ=Φ时τ_Γ(A)的简单表示形式。利用这些结论,给出了当S_ΓS_A时Σ_Γ-真度的一些性质的简单证明。     

■ukasiewicz命题逻辑系统中有限命题集的约简理论

在n值■ukasiewicz命题逻辑中提出了命题集Γ的约简理论,引入由命题集Γ所诱导的形式背景的概念,从Γ及其子集的关系出发给出了n值命题逻辑中有限命题集Γ约简的判定定理以及求Γ约简的方法。说明了无穷值■ukasiewicz命题逻辑中命题集Γ的约简可转化为n值情形。     

(L)ukasiewicz命题逻辑系统中有限命题集的约简理论

在n值(L)ukasiewicz命题逻辑中提出了命题集T的约简理论,引入由命题集F所诱导的形式背景的概念,从T及其子集的关系出发给出了n值命题逻辑中有限命题集T约简的判定定理以及求T约简的方法.说明了无穷值(L)ukesiewicz命题逻辑中命题集T的约简可转化为n值情形.     

n值命题逻辑系统Ln^＊中有限命题集的相容性与约简

设Г为有限命题集,首先讨论了Г在不同的n值命题逻辑系统Ln^＊中的相容性问题,提出了Г的约简理论,从命题集Г所诱导的多值形式背景出发,运用概念格的方法从Г及其子集的关系出发给出了Г约简的判定定理。     

n值命题逻辑系统Ln*中有限命题集的相容性与约简

设Г为有限命题集,首先讨论了Г在不同的n值命题逻辑系统L_n^*中的相容性问题,提出了Г的约简理论,从命题集Г所诱导的多值形式背景出发,运用概念格的方法从Г及其子集的关系出发给出了Г约简的判定定理。     

基于有限布尔命题集上的条件事件代数及应用

本文以Ｇｏｏｄｍａｎ条件事件代数理论为基础，在有限布尔命题集上建立了一个自由布尔多项式代数，Ｂ并在Ｂ上利用布尔关系给出条件事件的一种新的表示法。     

有限集AR_n→有限集BR的高阶神经网络实现

随着人工神经网络(ANN)理论和技术的不断发展,人们加深了对高阶神经网络映射能力的研究。本文对高阶神经网络实现有限集A(?)R~n→有限集B(?)R的函数逼近问题进行了理论上的研究,得出了高阶神经网络可以实现任何有限集到有限集函数逼近的结论。     

相干命题逻辑自然推理系统NR的自动证明*

给出了相干命题逻辑自然推理系统NR的自动证明算法。首先将待证命题公式A的子公式组成一个初始集合P,对其中的元素采用系统NR的推理规则得到新的命题公式加入P,当得到秩为0的A时命题得证;然后对A的证明树进行整理即得到演绎序列。对系统NR的大部分定理证明取得了良好的效果,算法生成的演绎序列清晰可读,接近手工推理。     

模糊推理的证据理论方法

1.基本证据理论 设θ是变量X的所有可能值的穷举集合,并且θ中的元素是相互排斥的,即在任一时刻X只能且必须取θ中的某一元素为值。满足这种条件的集合θ称为变量X的辨别框。θ的每一个子集A都与一个关于X取值情况的命题相对应,这个命题一般可描述为“X的值在A中”。     

格值有限状态自动机的半群

提出了格值有限状态自动机的定义,给出了格值有限状态自动机的两种同余关系,研究了格值有限状态自动机的半群的若干性质,最后给出了两种有限半群E(A)和E(A)的关系。     

逻辑系统Gn中理论的真度概念及其应用

首次在命题逻辑系统中引入理论的真度概念,使得真度的概念由公式的真度推广为公式集的真度,从而简化了发散度的概念;在逻辑系统G_n中讨论了理论Γ1、Γ2和Γ1∪Γ2的真度、相容度和发散度之间的关系。     

Universal abstract consistency class and universal refutation

Refutation methods based on the resolution principle are generally applied to a (finite)set of sentences,which must have a series of pre-transformations(prenex normalization,Skolemization and conjunction normalization)before starting the refutation.In this paper,the authors first generalize the concept of abstract consistency class to the most general form-universal abstract consistency class,and prove its universal univfying principle.Then,based on the R-refutation,a universal refutation method is proposed and its soundness and completeness are proved by means of the universal unifying principle.This method can be applied directly to any finite set of wffs sithout preprocessing the wffs at all so that the refutation procedure is more natural.     

On the consistency of rule bases based on lattice‐valued first‐order logic LF(X)

The consistency of a rule base is an essential issue for rule‐based intelligent information processing. Due to the uncertainty inevitably included in the rule base, it is necessary to verify the consistency of the rule base while investigating, designing, and applying a rule‐based intelligent system. In the framework of the lattice‐valued first‐order logic system LF(X), which attempts to handle fuzziness and incomparability, this article focuses on how to verify and increase the consistency degree of the rule base in the intelligent information processing system. First, the representations of eight kinds of rule bases in LF(X) as the generalized clause set forms based on these rule bases' nonredundant generalized Skolem standard forms are presented. Then an α‐automated reasoning algorithm in LF(X), also used as an automated simplification algorithm, is proposed. Furthermore, the α‐consistency and the α‐simplification theories of the rule base in LF(X) are formulated, and especially the coherence between these two theories is proved. Therefore, the verification of the α‐consistency of the rule base, often an infinity problem that is difficult to solve, can be transformed into a finite and achievable α‐simplification problem. Finally, an α‐simplification stepwise search algorithm for verifying the consistency of the rule base as well as a kind of filtering algorithm for increasing the consistency level of the rule base are proposed. © 2006 Wiley Periodicals, Inc. Int J Int Syst 21: 399–424, 2006.     

Wire frame: A reliable approach to build sealed engineering geological models

The technique of 3D geological modeling (3DGM) is an effective tool for representing complex geological objects. In order to improve the accuracy of geological models applied in numerical simulation methods such as finite elements and finite differences, we can use 3DGM as a modeling tool. To do this, however, 3DGM must provide the ability to model geological and artificial objects in a unified way, and its geological model must be seamless for mesh generation. We present the concept of a sealed engineering geological model (SEGM), and describe its topological representation. Three kinds of conditions: geometric continuity, topological consistency and geological consistency, which must be satisfied by SEGM, are discussed in detail. A new method for constructing an SEGM based on a wire frame is proposed. It includes three main components: wire frame construction, interface modification and reconstruction, and block tracing. Building a unitary wire frame, which is composed of many simple arcs and connects all interfaces seamlessly, is the key of this method. An algorithm, involving two intersections computations and partition of simple arcs, is proposed for building a wire frame. Additionally, we also propose a local iterative algorithm for computing fault traces. As an example, we build an SEGM for the dam area of a hydraulic engineering project in the HuNan province of China.     

Realm-based spatial data types: The ROSE algebra

Spatial data types or algebras for database systems should (1) be fully general, that is, closed under set operations, (2) have formally defined semantics, (3) be defined in terms of finite representations available in computers, (4) offer facilities to enforce geometric consistency of related spatial objects, and (5) be independent of a particular DBMS data model, but cooperate with any. We present an algebra that usesrealms as geometric domains underlying spatial data types. A realm, as a general database concept, is a finite, dynamic, user-defined structure underlying one or more system data types. Problems of numerical robustness and topological correctness are solved within and below the realm layer so that spatial algebras defined above a realm have very nice algebraic properties. Realms also interact with a DMBS to enforce geometric consistency on object creation or update. The ROSE algebra is defined on top of realms and offers general types to represent point, line, and region features, together with a comprehensive set of operations. It is described within a polymorphic type system and interacts with a DMBS data model and query language through an abstractobject model interface. An example integration of ROSE into the object-oriented data model O₂ and its query language is presented.     

Putting Consistent Theories Together in Institutions

The problem of putting consistent theories together in institutions is discussed.A general necessary condition for consistency of the resulting theory is carried out,and some sufficient conditions are given for diagrams of theories in which shapes are tree bundles or directed graphs.Moreover,some transformations from complicated cases to simple ones are established.     

Ordered seminormal default theories and their extensions

Abstract

The concept of extension plays an important role in default logic. The notion of an ordered seminormal default theory has been introduced (Etherington 1987) to characterize a class of seminormal default theories which have extensions. However, the original definition has a drawback because of its dependence on specific representations of the default theory. We introduce the ‘canonical representation’ of a default theory and redefine the orderedness of a default theory based on its canonical representation. We show that under the new definition, the orderedness of a default theory Δ = (W,D) is intrinsic to the theory itself, independent of the specific representations of W and D. We present a modification of the algorithm in Etherington (1987) for computing extensions of a default theory. More importantly, we prove the conjecture (Etherington 1987) that a modified version of the algorithm in Etherington (1987) converges for general ordered, finite seminormal default theories, while the original algorithm was proven (Etherington 1987) to converge for ordered, finite network default theories which form a proper subset of the theories considered in this paper.     

Consistency and Completeness in Rough Sets

Consistency and completeness are defined in the context of rough set theory and shown to be related to the lower approximation and upper approximation, respectively. A member of a composed set (union of elementary sets) that is consistent with respect to a concept, surely belongs to the concept. An element that is not a member of a composed set that is complete with respect to a concept, surely does not belong to the concept. A consistent rule and a complete rule are useful in addition to any other rules learnt to describe a concept. When an element satisfies the consistent rule, it surely belongs to the concept, and when it does not satisfy the complete rule, it surely does not belong to the concept. In other cases, the other learnt rules are used. The results in the finite universe are extended to the infinite universe, thus introducing a rough set model for the learning from examples paradigm. The results in this paper have application in knowledge discovery or learning from database environments that are inconsistent, but at the same time demand accurate and definite knowledge. This study of consistency and completeness in rough sets also lays the foundation for related work at the intersection of rough set theory and inductive logic programming.     

Strongly Subgame-Consistent Core in Stochastic Games

This paper investigates stochastic games on finite tree graphs. A given n-player normal-form game is defined at each node of a tree. Transition to a next node of the tree is random and depends on the strategy profile realized in a current game. We construct a cooperative solution of the game by maximizing the total expected payoff of the players. The core is used as the solution concept of the cooperative game. We introduce the definition of a strongly subgame-consistent (strongly time-consistent) core. Finally, we suggest a method for designing a cooperative distribution procedure of an imputation from the core that guarantees its strong subgame consistency.