基于目标演绎距离的一阶逻辑子句集预处理方法

一阶逻辑定理证明是人工智能的核心基础,研究一阶逻辑自动定理证明器的相关理论和高效的算法实现具有重要的学术意义。当前一阶逻辑自动定理证明器首先通过子句集预处理约简子句集规模,然后通过演绎方法对定理进行判定。现有的应用于证明器中的子句集预处理方法普遍只从与目标子句项符号相关性角度出发,不能很好地从文字的互补对关系中体现子句间的演绎。为了在子句集预处理时从演绎的角度刻画子句间的关系,定义了目标演绎距离的概念并给出了计算方法,提出了一种基于目标演绎距离的一阶逻辑子句集预处理方法。首先对原始子句集进行包含冗余子句约简并应用纯文字删除规则,然后根据目标子句计算剩余子句集中的文字目标演绎距离、子句目标演绎距离,并最终通过设定子句演绎距离阈值来实现对子句集的进一步预处理。将该预处理方法应用于顶尖证明器Vampire,以2017年国际一阶逻辑自动定理证明器标准一阶逻辑问题组竞赛例为测试对象,在标准的300 s内,加入提出的子句集预处理方法的Vampire4.1相比原始的Vampire4.1多证明4个定理,能证明10个Vampire4.1未证明的定理,占其未证明定理总数的13.5%;在证明的定理中,提出的子句集预处理方法能对77.2%的子句集进行约简,最大子句集约简规模达到51.7%。实验结果表明,提出的一阶逻辑子句集预处理方法是一种有效的方法,能有效地约简一阶逻辑子句集的规模,提高一阶逻辑自动定理证明器的证明能力。     

命题逻辑提升到一阶逻辑上的子句消去方法

在基于命题逻辑的可满足性问题（SAT）求解器和基于一阶逻辑的定理证明器上，子句集简化一直是必不可少的步骤，而其中子句消去方法在这些子句集简化方法中是非常重要的组成部分。将命题逻辑中的子句消去方法归结隐藏恒真消去方法（RHTE）和归结隐藏包含消去方法（RHSE）提升到一阶逻辑上，并且利用蕴含模归结原则（IMR）证明了这种提升方式在一阶逻辑上具有可靠性（Soundness），即依据这两种子句消去方法删除一阶逻辑公式集中的子句，并不会改变公式集的可满足性或者不可满足性。此外，将这两个方法与一阶逻辑子句消去方法锁子句消去方法（BCE）和归结包含消去方法（RSE）进行组合推广，发展得到一阶逻辑上新型子句消去方法（BC+RHS）E、（RS+RHT）E和（RHS+RHT）E，并且证明了这3种子句消去方法在一阶逻辑上的可靠性。最后，分析比较了这些子句消去方法的有效性，并且证明了这3种新型子句消去方法比组成它们的原始子句消去方法均具有更高的有效性。     

基于演绎长度的学习子句删除策略

学习子句删除策略是CDCL-SAT求解器中的一个重要内容,可以避免内存爆炸和加速单元传播。评估学习子句有用性的标准不同导致所删除的学习子句是不同的,极大地影响求解效率。基于CDCL算法的求解过程可被形式化为增加管理学习子句策略的归结演绎过程,基于此,提出一种基于演绎长度的学习子句评估方法,并与现有的基于文字块距离的评估方法结合,根据排序子句的基准不同,形成两种不同的结合算法。采用国际SAT竞赛的基准实例,与目前主流的求解器进行了实验对比分析。结果表明,所提的结合算法能更好地评估学习子句的有用性,较基于文字块距离策略的求解个数提高了4.1%,说明所提策略具有一定的优势。     

逻辑函数的if-then子句表示法

本文提出了逻辑函数的另一种表示方法,与传统的用布尔表达式中表示逻辑的方法不同,这里采用了if-then子句集的形式。本文还讨论了如何将一个布尔表达式转换成等价的if-then子句形式。逻辑函数的这种表示方法加快了逻辑模拟的速度,并且解决了采用诸如OCCAM等并发进程语言来进行逻辑模拟过程中的死锁问题。     

使用Petri网T—不变量求解子句的逻辑推论

本文研究了子句逻辑规则的Ｐｅｔｒｉ网模型的表示及使用Ｐｅｔｒｉ网分析方法进行逻辑推论，基于四值逻辑和冲突变迁的概念，表示了非Ｈｏｒｎ子句Ｐｅｔｒｉ网模型的构造，并使用Ｔ－不变量方法解决子句推论问题。     

模糊Horn子句规则及其发现算法

模糊Horn子句规则可以用自然语言来表达人类知识。但是,发现模糊Horn子句规则及其蕴含度是比较困难的。该文从逻辑的观点出发,定义模糊Horn子句规则、支持度、蕴含度及其相关概念,分析模糊Horn子句规则发现的步骤,并给出发现算法的形式化描述。该算法结合了模糊Horn子句逻辑概念和Apriori发现算法,从给定的数量型数据库中发现模糊Horn子句规则。     

软件构件表示与检索形式化的研究与进展

1 引言软件复用被认为是提高软件生产效率和软件质量较为现实的途径。尽管软件复用的思想已经提出了30多年,但软件复用的现状离人们最初的设想仍然相距甚远。阻碍大规模软件复用的技术与非技术因素很多,主要的技术因素有构件分类、构件表示、构件检索、构件更改及构件库的管理与维护等。其中,软件构件表示与检索是软件复用获得成功的重要前提。     

使用Petri网T－不变量求解子句的逻辑推论

本文研究了子句逻辑规则的Ｐｅｔｒｉ网模型的表示及使用Ｐｅｔｒｉ网分析方法进行逻辑推论．基于四值逻辑和冲突变迁的概念，表示了非Ｈｏｒｎ子句Ｐｅｔｒｉ网模型的构造，并使用Ｔ－不变量方法解决于句推论问题．另外，本文还显示了向前推论和向后推论在子句Ｐｅｔｒｉ网模型中的应用．     

基于刻面描述的构件检索

随着软件复用实践的深入和软件构件库规模的扩大,对软件构件的表示与检索的研究正受到越来越多的重视.针对基于刻面描述的软件构件,结合模式分析中的树匹配思想,根据构件刻面描述的特点,提出了一种基于树包含(tree inclusion)的构件检索方法,并进行了理论上的分析与实验上的检验.实验结果证明了它的可行性与有效性.     

一阶子句搜索方法

子句集的可满足性判定是自动证明领域的热点之一.提出了子句搜索方法判定命题子句集Φ的可满足性,该方法查找Φ中子句的一个公共不可扩展子句C,当且仅当找到C时Φ可满足,此时C中各文字的补构成一个模型.结合部分实例化方法将子句搜索方法提升至一阶.一阶子句搜索方法可以判定子句集的M可满足性,具备终止性、正确性和完备性,是一种判定子句集可满足性的有效方法.     

The lattice structure and refinement operators for the hypothesis space bounded by a bottom clause

Searching the hypothesis space bounded below by a bottom clause is the basis of several state-of-the-art ILP systems (e.g. Progol, Aleph). These systems use refinement operators together with search heuristics to explore a bounded hypothesis space. It is known that the search space of these systems is limited to a sub-graph of the general subsumption lattice. However, the structure and properties of this sub-graph have not been properly characterised. In this paper firstly, we characterise the hypothesis space considered by the ILP systems which use a bottom clause to constrain the search. In particular, we discuss refinement in Progol as a representative of these ILP systems. Secondly, we study the lattice structure of this bounded hypothesis space. Thirdly, we give a new analysis of refinement operators, least generalisation and greatest specialisation in the subsumption order relative to a bottom clause. The results of this study are important for better understanding of the constrained refinement space of ILP systems such as Progol and Aleph, which proved to be successful for solving real-world problems (despite being incomplete with respect to the general subsumption order). Moreover, characterising this refinement sub-lattice can lead to more efficient ILP algorithms and operators for searching this particular sub-lattice. For example, it is shown that, unlike for the general subsumption order, efficient least generalisation operators can be designed for the subsumption order relative to a bottom clause.     

A predicate-transition net model for parallel interpretation of logic programs

A predicate/transition net model for a subset of Horn clause logic programs is presented. The syntax, transformation procedure, semantics, and deduction process for the net model are discussed. A possible parallel implementation for the net model is described, which is based on the concepts of communicating processes and relations. The proposed net model offers a syntactical variant of Horn clause logic and has two distinctions from other existing schemes for the logic programs: representation formalism and the deduction method. The net model provides an approach towards the solutions of the separation of logic from control and the improvement of the execution efficiency through parallel processing for the logic programs. The abstract nature of the net model also lends itself to different implementation strategies.<>     

可重构制造系统可重构逻辑控制器设计与实现

针对可重构制造系统的逻辑控制问题,提出一种可重构逻辑控制器的解决方案．该逻辑控制器具有递阶分布式的控制体系结构,并根据模块化的设计思想设计成多个分离的功能模块．然后给出基于CORBA组件模型(CCM)的可重构逻辑控制器软件的开发过程．由递阶分布式体系、模块化设计和软件组件开发技术实现的可重构逻辑控制器具有快速动态重构的能力,能满足可重构制造系统逻辑控制的要求．     

A Fuzzy Proof Theory

Based on the first order peicate logic,in this paper,we present a new approach to generalizing the syntax of ordinary Horn clause rules to establish a fuzzy proof theory,First of all,each Horn clause rule is associated with a numerical implication strength f.Therefore we obtain f-Horn clause rules.Secondly,Herbrand interpretations can be generalized to fuzzy subsets of the Herbrand base in the sense of Zadch.As a result the proof theory for Horn clause rules can be developed in much the same way for f-Horm clause rules.     

基于XMLC的EOS页面构件设计与实现

基于构件的软件开发是软件工程的基本目标之一,Primeton EOS中间件系统基于J2EE架构成功的实现了WEB应用开发的构件化,并创造性的以XML总线显著降低了各构件耦合度,使运算构件,逻辑构件,展现构件,数据构件,流程构件无缝的融合。但是对于页面构件,仍然使用传统的JSP页面,无论在构件设计理念还是运行效率方面都不尽人意。该文将探讨如何使用XMLC技术重新设计EOS表示购件,使其充分利用XML总线的设计优势,实现构件理念与运行效率的最优化。     

A Disjunctive Positive Refinement of Model Elimination and its Application to Subsumption Deletion

The Model Elimination (ME) calculus is a refutationally complete,goal-oriented calculus for first-order clause logic. In this article, weintroduce a new variant called disjunctive positive ME (DPME); it improveson Plaisteds positive refinement of ME in that reduction steps areallowed only with positive literals stemming from clauses having at leasttwo positive literals (so-called disjunctive clauses). DPME is motivated byits application to various kinds of subsumption deletion: in order to applysubsumption deletion in ME equally successful as in resolution, it iscrucial to employ a version of ME that minimizes ancestor context (i.e., thenecessary A-literals to find a refutation). DPME meets this demand. Wedescribe several variants of ME with subsumption, the most important onesbeing ME with backward and forward subsumption and theT*-Context Check. We compare their pruning power, also takinginto consideration the well-known regularity restriction. All proofs aresupplied. The practicability of our approach is demonstrated with experiments.     

The anatomy of vampire

We present an implementation technique for a class of bottom-up logic procedures. The technique is based oncode trees. It is intended to speed up most important and costly operations, such as subsumption and resolution. As an example, we consider the forward subsumption problem which is the bottleneck of many systems implementing first-order logic.To efficiently implement subsumption, we specialize subsumption algorithms at run time, using theabstract subsumption machine. The abstract subsumption machine makes subsumption-check using sequences of instructions that are similar to the WAM instructions. It gives an efficient implementation of the clause at a time subsumption problem. To implement subsumption on the set at a time basis, we combine sequences of instructions incode trees.We show that this technique yields a new way of indexing clauses. Some experimental results are given.The code trees technique may be used in various procedures, including binary resolution, hyper-resolution, UR-resolution, the inverse method, paramodulation and rewriting, OLDT-resolution, SLD-AL-resolution, bottom-up evaluation of logic programs, and disjunctive logic programs.Supported by Swedish TFR grant No. 93–409     

Synthesis of a unification algorithm in a logic programming calculus

A formal specification of unification is presented and a unification algorithm is synthesized from it. The synthesis is done by logical deduction within the logic programming calculus developed by Hansson and Tärnlund. First-order logic with identity is used as the specification language and extended Horn clause logic as the target language.