带函数析取逻辑程序的无基集及其应用

基于回答集（也称稳定模型）语义的带函数析取逻辑程序是一种重要的知识表示和推理方法。由于判定一个析取逻辑程序是否有回答集是困难的（Σ2完全的）,目前还没有有效的方法来计算带函数析取逻辑程序的回答集,主要原因之一是检查一个集合是否是回答集是coNP完全的。提出了带函数析取逻辑程序无基集（unfounded sets）的概念,发现了空无基集（unfounded-free sets）与稳定模型之间的一一对应关系,在此基础上,证明了一个逻辑程序的模型是该程序的稳定模型当且仅当它们对应的一个命题公式是不可满足的,从而在理论上为计算带函数析取逻辑程序的回答集提供了一种有效的途径。     

正规逻辑程序回答集存在性研究

判断逻辑程序的回答集是否存在是回答集程序设计的一个重要问题,也是NP完全问题。当前利用否定圈边数的奇偶性来判断回答集存在性的方法还具有一定的局限性,即:对于非分层逻辑程序,现有方法并不能准确判断其回答集存在性。针对该问题,提出了一种新的基于否定圈的判断方法,给出了该判断方法的算法框架,证明了算法的正确性,并以实例分析说明了方法的有效性。     

基于逻辑程序的访问控制描述与推理

提出访问控制的逻辑描述方法,满足最小模型语义的条件(不含负逻辑),并分析访问控制逻辑程序中不动点的迭代计算方法。通过迭代计算,得到访问控制逻辑程序的最小Herbrand模型——Mp。使用基于逻辑程序的方法对访问控制策略进行了较为精确的推理。     

评价目标前提的逻辑框架

多前提决策问题是决策领域中重要的研究内容,其决策质量可反映决策理论研究的成果。在多前提决策中,目标会有多种实现方式,每种实现方式都有相应的实现难度。在多前提决策研究中,定义了目标的条件集,提出了将条件集分解到最简单形式的算法,并证明了算法的输出为目标的极小最简不完备条件集。然后,提出了条件集可信度的概念及其计算方式,利用可信度评估目标的所有极小最简不完备条件集的实现难度,并以此确定实现该目标的最优条件集。最后,给出了评价目标前提的逻辑框架O的形式定义,证明了框架O的可计算性和推理能力,并用逻辑程序Prolog实现了框架O的原型,通过对框架O的原理性实验和具体的工程应用验证了框架O的有效性。     

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．     

扩展的动态逻辑程序及其在产品个性化推荐中的应用

动态逻辑程序能很好的处理知识库更新问题, 但它不能描述和处理具有偏好的知识更新问题. 因此, 本文在动态逻辑程序的基础上, 提出了一种新的扩展的动态逻辑程序, 它通过对规则头部使用有序析取的方法使其能够描述和处理具有偏好的知识更新问题, 进一步增强了知识的表达和推理能力, 并且定义了其最优回答集语义. 同时将这种新的扩展的动态逻辑程序应用于产品推荐系统中, 使用户获得的推荐信息具有个性化特点, 达到个性化推荐的目的. 最后以一个产品个性化推荐实例讨论扩展的动态逻辑程序在产品个性化推荐中的应用.     

一类一阶逻辑公式中的公理化真度理论及其应用

设Φ是全体不含函数符号的一阶闭逻辑公式之集.本文基于有限模型和均匀概率的思想对非单调逻辑中的典型案例做了分析,通过概率计算给出了应当赋予文字的完全闭包及其合取的真度值.以此为基础,在Φ中建立了公理化的真度理论.证明了Φ中每个公式的真度都是可计算的,并且证明了Φ中逻辑公式的真度之集H与命题逻辑中的计算结果相一致,特别是其中所有闭文字的真度都等于1/2.在真度理论的基础上引入了Φ中公式之间相似度和伪距离的计算方法,并提出了逻辑理论的相容度理论.作为应用,给出了估计Horn子句型数据库相容度的一种方法.     

分布式环境下的访问控制

为适应分布式环境下的安全需求,提出了一种描述访问控制策略和判定访问请求的方法。采用类似于无函数的扩展逻辑程序的表示方法对安全访问策略进行描述,限定权限传播的深度,利用不同的优先次序定义了多种消解冲突的规则,并给出了类似扩展逻辑程序的回答集语义解释。结合确定性推理和可能性推理,描述了如何判定访问请求的算法。解决了3个问题：分布式授权、私有权限和冲突消解方法。     

关于三值逻辑程序中否定和蕴涵完备化程序的不动点语义

逻辑程序具有丰富的表达能力和非确定性等特点,在定理机器证明、关系数据库系统、程序验证、模块化程序设计和非单调推理等方面都有了广泛的应用。本文是继续文[8]的工作。首先通过两个反例,指出了文[7]中关于否定完备化程序Comp（→,Pr）和蕴涵完备化程序Comp（→,Pr）的两个重要定理都存在一定程度的错误。然后对这两个定理进行了修改,用后继算予Tpt和Fitting算予FPr的不动点语义,分别给出了否定完备化程序（Somp（→,Pr）和蕴涵完备化程序Comp（→,Pr）的Herbrand模型的充分条件和必要条件,这将在逻辑程序的最优不动点和最小不动点的语义研究中有着重要的应用价值。     

析取回答集程序设计结构化测试方法

针对析取回答集程序的结构化测试基础理论匮乏的问题,系统化地提出析取回答集程序结构化测试覆盖的概念。首先,定义针对析取回答集程序的测试用例,确立析取回答集程序的主要测试实体为程序中的逻辑规则;其次,通过对规则的头、规则的体、规则的集合等不同测试目标构建了规则覆盖、定义覆盖、环覆盖等基本概念来模拟结构化测试中的语句覆盖、分支覆盖等概念;最后,提出了析取回答集程序的测试覆盖率计算公式,并举例说明各种覆盖下的覆盖率计算方法,并讨论了析取回答集程序的部分特殊性质和关键指标。     

A characterization of answer sets for logic programs

Checking if a program has an answer set, and if so, compute its answer sets are just some of the important problems in answer set logic programming. Solving these problems using Gelfond and Lifschitz's original definition of answer sets is not an easy task. Alternative characterizations of answer sets for nested logic pro- grams by Erdem and Lifschitz, Lee and Lifschitz, and You et al. are based on the completion semantics and various notions of tightness. However, the notion of tightness is a local notion in the sense that for different answer sets there are, in general, different level mappings capturing their tightness. This makes it hard to be used in the design of algorithms for computing answer sets. This paper proposes a characterization of answer sets based on sets of generating rules. From this char- acterization new algorithms are derived for computing answer sets and for per- forming some other reasoning tasks. As an application of the characterization a sufficient and necessary condition for the equivalence between answer set seman- tics and completion semantics has been proven, and a basic theorem is shown on computing answer sets for nested logic programs based on an extended notion of loop formulas. These results on tightness and loop formulas are more general than that in You and Lin's work.     

On Definability in Dependence Logic

We study the expressive power of open formulas of dependence logic introduced in Väänänen [Dependence logic (Vol. 70 of London Mathematical Society Student Texts), 2007]. In particular, we answer a question raised by Wilfrid Hodges: how to characterize the sets of teams definable by means of identity only in dependence logic, or equivalently in independence friendly logic.     

从经典逻辑知识构建ASP知识库的新方法

回答集程序设计(ASP)是一种主流的非单调知识表示工具。为了能够在利用ASP求解问题过程中使用现有的以经典逻辑表示的知识,给出了一种把以谓词逻辑公式表示的约束型知识和定义型知识转化为ASP程序或知识库的新方法,并以实例说明了其有效性。该方法满足转化后ASP程序的回答集与原公式集的模型具有一一对应关系。在实际应用中,该方法提供了一项从现存的以谓词逻辑为表示语言的知识库,构建以ASP为知识表示语言的非单调知识库的技术。     

提高一阶多值逻辑Tableau推理效率的布尔剪枝方法

含有量词的一阶多值Tableau方法具有统一的扩展规则，并由Zabel等人给出了可靠性和完备性的证明，但由于扩展后的分枝随着真值数目的增加而呈指数的增加，因而影响了机器推理执行的效率，该文提出了布尔剪枝方法，将带符号的公式与集合的上集／下集联系起来，使含量词的一阶多值逻辑公式的扩展规则大大简化，进一步，通过对布尔剪枝方法的分析，建立了一类特殊一阶多值逻辑正则公式的更为简洁的Tableau推理方法，该方法使得含量词的一阶多值逻辑Tableau推理类同于经典逻辑Tableau方法。     

A generalization of the Lin-Zhao theorem

The theorem on loop formulas due to Fangzhen Lin and Yuting Zhao shows how to turn a logic program into a propositional formula that describes the program’s stable models. In this paper we simplify and generalize the statement of this theorem. The simplification is achieved by modifying the definition of a loop in such a way that a program is turned into the corresponding propositional formula by adding loop formulas directly to the conjunction of its rules, without the intermediate step of forming the program’s completion. The generalization makes the idea of a loop formula applicable to stable models in the sense of a very general definition that covers disjunctive programs, programs with nested expressions, and more.     

语义网的一阶逻辑推理技术支持

研究了一阶逻辑推理工具对语义网的推理支持.语义网的关键推理问题可以化为公式的可满足性判定问题.一阶逻辑的自动定理证明器可以证明不可满足性,而有限模型查找器为可满足的公式在有限域内构造模型.提出在语义网的推理中,同时使用定理证明器和有限模型查找器.实验结果表明,这样可以解决描述逻辑工具的不足,并可以弥补定理证明器对可满足的公式推理的不完备性.     

Enhancing DLV instantiator by backjumping techniques

Disjunctive logic programming (DLP) is a powerful formalism for knowledge representation and reasoning. The high expressiveness of DLP language, together with the recent availability of some efficient DLP system, has favoured the application of DLP in emerging areas like Knowledge Management and Information Integration. These applications have often to deal with huge input data, and have evidenced the need to improve the efficiency of DLP instantiators. Program instantiation is the first phase of a DLP computation; in this phase, variables are replaced by constants to generate a ground program which is then evaluated by propositional algorithms in the second phase of the computation. The instantiation process may be computationally expensive, and in fact its efficiency has been recognized to be a key issue for solving real-world problems by using disjunctive logic programming. Given a program P, a good instantiation for P is a ground program P′ having precisely the same answer sets as P and such that: (1) P′ can be computed efficiently from P, and (2) P′ does not contain “useless” rules, (P′ is as small as possible) and can thus be evaluated efficiently. In this paper, we present a structure-based backjumping algorithm for the instantiation of disjunctive logic programs, that meets the above requirements. In particular, given a rule r to be grounded, our algorithm exploits both the semantical and the structural information about r for computing efficiently the ground instances of r, avoiding the generation of “useless” rules. That is, from each general rule r, we compute only a relevant subset of its ground instances, avoiding the generation of “useless” instances, while fully preserving the semantic of the program. We have implemented this algorithm in DLV—the state-of-the-art implementation of DLP—and we have carried out an experimentation activity on an ample collection of benchmark problems. The experimental results are very positive: the new technique improves sensibly the efficiency of the DLV system on many program classes.     

Continuous stochastic logic characterizes bisimulation of continuous-time Markov processes

In a recent paper Baier et al. [Lecture Notes in Computer Science, Springer-Verlag, 2000, p. 358] analyzed a new way of model-checking formulas of a logic for continuous-time processes—called continuous stochastic logic (henceforth CSL)—against continuous-time Markov chains—henceforth CTMCs. One of the important results of that paper was the proof that if two CTMCs were bisimilar then they would satisfy exactly the same formulas of CSL. This raises the converse question—does satisfaction of the same collection of CSL formulas imply bisimilarity? In other words, given two CTMCs which are known to satisfy exactly the same formulas of CSL does it have to be the case that they are bisimilar? We prove that the answer to the question just raised is “yes”. In fact we prove a significant extension, namely that a subset of CSL suffices even for systems where the state space may be a continuum. Along the way we prove a result to the effect that the set of Zeno paths has measure zero provided that the transition rates are bounded.     

服务组合中基于线性逻辑的消息语义匹配

介绍一种自动服务组合模型服务消息语义化匹配验证的方法。该方法先从服务描述中提取服务消息模型和服务行为模型,后将服务行为模型转换为形式化的有限状态自动机。根据有限状态自动机中的服务接口可以转化为本体概念,服务行为可以转换为线性逻辑表达式描述,使用线性逻辑的演绎方法对服务消息的匹配性和可满足性进行验证。同时,对线性逻辑的演绎定理进行适当扩展以适应服务组合的需要。