Knuth—Bendix过程的发散现象的研究

Ｋｎｕｔｈ－Ｂｅｎｄｉｘ完备过程不终止的起因研究得很少，本文研究引起不终止的重写规则的结构性质，提出了相容交叉规则对的概念，推广了文献６的结论，并提出了为构造系统检验该过程是否不终止的方法。     

支持复合事件的主动规则的可终止性分析

ＥＣＡ规则系统已经成为主动数据库提供主动服务的通用机制．规则集合的可终止性是规则行为分析的一个重要问题．文中给出了ＥＣＡ规则系统的形式化描述，并着重讨论了复合事件机制对可终止性问题的影响．文中结合规则实例给出了分析规则终止性的静态判定算法，这一算法可作为主动规则分析工具的理论基础．     

含环触发图对应的主动规则集可终止性分析

主动规则集的可终止性是主动数据库规则集的三大重要特征之一．主动规则集可否保证终止将直接影响到系统的应用．由于主动规则间存在依赖关系,通过对依赖关系的分析,给出了规则的触发传递闭包、依赖传递闭包等概念．以此为基础,提出了用规则触发-依赖图（T—DG）方法来分析主动规则集的终止性．特别讨论了判定含环的触发图（TG）对应的主动规则集是否保证终止的方法,给出了相应的判定算法、算法证明及分析．     

计算主动数据库中不可归约规则集的有效算法

主动数据库中规则集的可终止性判定是一个重要问题,已经成为一个研究热点．有些研究工作提出了在编译阶段运用触发图和活化图的方法解决这个问题,其中的一个关键技术就是计算主动规则集的不可归约规则集．现有的计算方法由于具有一定保守性,使得计算出的不可归约规则集仍可进一步地归约,这无疑将影响到规则集的可终止性判定的准确性和运行阶段规则分析的效率．经过深入分析活化规则可无限执行的特点,提出了活化路径等概念．基于这些概念,提出了一个计算主动规则集的不可归约规则集的有效算法,使现有方法求得的不可归约规则集得到进一步的归约．     

基于逻辑程序的安全协议验证

安全协议本质上是分布式并发程序，可以自然地描述为多个子进程的并发合成系统．将安全协议对应的并发合成系统抽象为逻辑程序进行消解，能够对安全协议无穷多个会话的交叠运行进行验证．该文提出了安全协议逻辑程序中逻辑规则的一个分类方法，基于该分类方法提出了安全协议逻辑程序不动点的迭代计算方法．逻辑规则的分类优化了安全协议逻辑程序不动点的迭代计算和安全性质验证过程中的计算．由于安全协议逻辑程序不动点迭代计算过程不一定终止，文中提出了每进行k≥1步安全协议逻辑程序不动点迭代计算验证一次安全性质的验证策略．     

ECA规则的模型和行为特定理论

本文给出了ＥＣＡ规则系统的一般性模型，通过扩展系统状态和改变的定义，形式化地描述了规则处理的语义，并着重研究规则系统的行为特征（可终止性和行为一致性）．文中给出的形式化定义和判定方法可作为规则静态分析工具的理论基础.     

基于触发路径的主动规则集终止性分析

为满足用户对网络服务的个性化、定制化和主动化需求,主动规则成为解决这些问题的关键技术.研究了在网络环境下基于规则的复杂应用中,大量规则集同时触发所带来的规则终止性问题,提出的分析方法确保主动规则能够有效运行,以提供更加灵活的主动服务.讨论了以静态分析方法为主的主动规则终止性分析相关工作,随后给出问题描述和相关形式化定义.分析了基于关联图的终止性分析方法的保守性,引入触发路径和有限触发环概念,提出了基于触发路径的两种终止情形分析方法,提高了规则集终止性分析的准确性,采用两阶段分析算法保证了分析效率.与相关分析方法的实验比较说明,文中方法能够更准确高效地检测主动规则集的终止性,并适应基于主动规则的其它应用.     

一种不确定性条件下的自适应知识学习方法

通过研究决策表和决策规则的不确定性，分析了由不分明关系划分的粒度引起的规则不确定性的两个方面，即不一致性和随机性，建立基于信息熵和粗糙集表示的不确定性信息度量的方法．利用该方法计算决策表局部最小确定性，并以此为阈值来控制规则集生成的数量，避免不必要的冗余规则的生成．同时结合Skowron的缺省规则获取算法，实现了没有领域先验知识条件下的不确定知识的自适应学习过程．试验结果表明．阈值的选取是合理的，在保持较高的决策正确率的同时，有效地控制了规则集的生成．     

XML中的主动规则的模型及其可终止性分析

在对XML数据模型主动机制研究的基础上,结合规则实例提出了一种新的分析规则终止性的静态判定算法。此算法基于触发环的概念,首先对触发环中每一个被修改的节点产生一个递归等式,然后通过展开递归等式并检验其可满足性,就可以分析规则集的可终止性,这样不仅可以得到更高的精确度及更小的复杂度,而且可以得到有效的判定主动规则可终止性的条件。     

基于活化路径和条件公式的主动规则集可终止性判定方法

支持主动规则机制已经成为现代数据库系统的一个重要特征.主动规则集的可终止性判定是主动数据库中一个核心问题之一,利用触发图和活化图的方法来判定可终止性都存在不同的保守性.为此,提出了为有效活化路径建立条件公式的思想,在此基础上给出了一个新的判定主动规则集可终止性的方法.分析的结果表明,提出的方法较现有方法可以发现更多的可终止性情形,最后给出了相应的算法及其可终止性、正确性证明.     

Proof rules for recursive procedures

Four proof rules for recursive procedures in a Pascal-like language are presented. The main rule deals with total correctness and is based on results of Gries and Martin. The rule is easier to apply than Martin's. It is introduced as an extension of a specification format for Pascal-procedures, with its associated correctness and invocation rules. It uses well-founded recursion and is proved under the postulate that a procedure is semantically equal to its body.This rule for total correctness is compared with Hoare's rule for partial correctness of recursive procedures, in which no well-founded relation is needed. Both rules serve to prove correctness, i.e. sufficiency of certain preconditions. There are also two rules for proving necessity of preconditions. These rules can be used to give formal proofs of nontermination and refinement. They seem to be completely new.     

Regaining cut admissibility in deduction modulo using abstract completion

Deduction modulo is a way to combine computation and deduction in proofs, by applying the inference rules of a deductive system (e.g. natural deduction or sequent calculus) modulo some congruence that we assume here to be presented by a set of rewrite rules. Using deduction modulo is equivalent to proving in a theory corresponding to the rewrite rules, and leads to proofs that are often shorter and more readable. However, cuts may be not admissible anymore.We define a new system, the unfolding sequent calculus, and prove its equivalence with the sequent calculus modulo, especially w.r.t. cut-free proofs. It permits to show that it is even undecidable to know if cuts can be eliminated in the sequent calculus modulo a given rewrite system.Then, to recover the cut admissibility, we propose a procedure to complete the rewrite system such that the sequent calculus modulo the resulting system admits cuts. This is done by generalizing the Knuth–Bendix completion in a non-trivial way, using the framework of abstract canonical systems.These results enlighten the entanglement between computation and deduction, and the power of abstract completion procedures. They also provide an effective way to obtain systems admitting cuts, therefore extending the applicability of deduction modulo in automated theorem proving.     

Towards Restructuring and Normalization of Types in Databases

The equivalence-preserving transformation and normalization of types in object-oriented databases are discussed.Specifically,A normal form of types based on set-theoretic equivalence is proposed,rewrite rules which transform types into normal forms are presented,and the uniqueness of normal form and the completeness of rewrite rules are proved.The emphasis of this work is on normal forms and corresponding rewrite rules.It provides a new formal approach for the study of restructuring of database schema and other manipulations in object-oriented databases.     

Rewriting with Equivalence Relations in ACL2

Traditionally, a conditional rewrite rule directs replacement of one term by another term that is provably equal to it, perhaps under some hypotheses. This paper generalizes the notion of rewrite rule to permit the connecting relation to be merely an equivalence relation. We then extend the algorithm for applying rewrite rules. Applications of these generalized rewrite rules are only admissible in certain equivalential contexts, so the algorithm tracks which equivalence relations are to be preserved and admissible generalized rewrite rules are selected according to this context. We introduce the notions of congruence rule and refinement rule. We also introduce the idea of generated equivalences, corresponding to a new equivalence relation generated by a set of pre-existing ones. Generated equivalences are used to give the rewriter broad access to admissible generalized rewrite rules. We discuss the implementation of these notions in the ACL2 theorem prover. However, the discussion does not assume familiarity with ACL2, and these ideas can be applied to other reasoning systems as well.     

Uncurrying for Termination and Complexity

First-order applicative rewrite systems provide a natural framework for modeling higher-order aspects. In this article we present a transformation from untyped applicative term rewrite systems to functional term rewrite systems that preserves and reflects termination. Our transformation is less restrictive than other approaches. In particular, head variables in right-hand sides of rewrite rules can be handled. To further increase the applicability of our transformation, we study the method for innermost rewriting and derivational complexity, and present a version for dependency pairs.     

用sendmail仿真一个图灵机

简单地介绍了sendmail的重写规则,提出了在sendmail的配置文件中,利用重写规则编写仿真图灵机操作的方法,最后给出了两个图灵机程序(规则集)的实现.     

Increasing interpretations

The article at hand introduces a refinement of interpretation-based termination criteria for term rewrite systems in the dependency pair setting. Traditional methods share the property that—in order to be successful—all rewrite rules must (weakly) decrease with respect to some measure. One novelty of our approach is that we allow some rules to increase the interpreted value. These rules are found by simultaneously searching for adequate polynomial interpretations while considering the information of the dependency graph. We prove that our method extends the termination proving power of linear interpretations. Furthermore, this generalization perfectly fits the dependency pair framework which is implemented in virtually every termination prover dealing with term rewrite systems. We present two dependency pair processors for increasing interpretations. The novelty of the second one is that it can be used to eliminate single edges from the dependency graph.     

How to decide the lark

We present a decision algorithm for Smullyan's lark combinator. The method of choice consists in designing a canonical rewrite system which is confluent and terminating, or equivalently, Church–Rosser and strongly normalizing. This is related to the completion of an equational theory, but since traditional completion is divergent, we consider a set of rule schemes rather than a set of rules. This yields a polynomial decision procedure for the Lark combinator and many other fragments of combinatory logic.     

Dynamically Typed Computations for Order-sorted Equational Presentations

Equational presentations with ordered sorts encompass partially defined functions and subtyping information in an algebraic framework. In this work we address the problem of computing in order-sorted algebras, with few restrictions on the allowed presentations. We adopt the G-algebra framework, where equational, membership and existence formulas can be expressed, and this provides a complete deduction calculus which incorporates the interaction between all these formulas.To practically deal with this calculus, we introduce an operational semantics for G-algebra using rewrite systems over so-called decorated terms, that has assertions concerning the sort membership of any subterm in its head node. Decorated rewrite rules perform equational replacement, decoration rewrite rules enrich the decorations and record sort information. Therefore we use the semantic sort principle, i.e. equal terms belong to equal sorts, rather than the syntactic sort principle that does not use the equational part of a presentation.In order to have a complete and decidable unification on decorated terms, we restrict to sort-inheritance theories. Then a completion procedure on decorated terms is designed to compute all interactions between equational and membership formulas. When the completion terminates, the resulting set of rewrite rules provides a way to decide equational theorems of the form (t = t′) and typing theorems of the form (t : A).The sort inheritance property is undecidable in general but we propose a test to check it for a given presentation. The test provides information on how to extend the presentation in a model conservative way, in order to obtain sort inheritance.     

Clausal Presentation of Theories in Deduction Modulo

Resolution modulo is an extension of first-order resolution in which rewrite rules are used to rewrite clauses during the search. In the first version of this method, clauses are rewritten to arbitrary propositions. These propositions are needed to be dynamically transformed into clauses. This unpleasant feature can be eliminated when the rewrite system is clausal, i.e., when it rewrites clauses to clauses. We show in this paper how to transform any rewrite system into a clausal one, preserving the existence of cut free proofs of any sequent.