Combinations of Modal Logics

There is increasing use of combinations of modal logics in bothfoundational and applied research areas. This article provides anintroduction to both the principles of such combinations and to thevariety of techniques that have been developed for them. In addition,the article outlines many key research problems yet to be tackledwithin this callenging area of work.     

纤维逻辑

形式逻辑已经从简单命题逻辑发展到比较复杂的模态逻辑系列。但是在主体环境下,已有逻辑的复杂性仍然不能有效刻画主体复杂的心智。有一些人工智能研究者根据主体心智的多重性,在模态逻辑中引入多种模态算子,并借此对主体加以刻画。但是原来的可能世界语义却难以容纳如此复杂的语法,出现了很多不合理的地方。本文首先介绍了新近出现的纤维逻辑（fibring logics）,然后归纳了目前将此理论应用在主体BDI建模的研究现状,最后分析纤维逻辑的不足之处,讨论了其他可能的应用,并对今后的工作做了展望。     

Reasoning about Minimal Knowledge in Nonmonotonic Modal Logics

We study the problem of embedding Halpern and Moses's modal logic of minimal knowledge states into two families of modal formalism for nonmonotonic reasoning, McDermott and Doyle's nonmonotonic modal logics and ground nonmonotonic modal logics. First, we prove that Halpern and Moses's logic can be embedded into all ground logics; moreover, the translation employed allows for establishing a lower bound (3p) for the problem of skeptical reasoning in all ground logics. Then, we show a translation of Halpern and Moses's logic into a significant subset of McDermott and Doyle's formalisms. Such a translation both indicates the ability of Halpern and Moses's logic of expressing minimal knowledge states in a more compact way than McDermott and Doyle's logics, and allows for a comparison of the epistemological properties of such nonmonotonic modal formalisms.     

Alternative Translation Techniques for Propositional and First-Order Modal Logics

We describe and analyze techniques, other than the standard relational/functional methods, for translating validity problems of modal logics into first-order languages. For propositional modal logics we summarize the -as-Pow method, a complete and automatic translation into a weak set theory, and then describe an alternative method, which we call algebraic, that achieves the same full generality of -as-Pow but is simpler and computationally more attractive. We also discuss the relationships between the two methods, showing that -as-Pow generalizes to the first-order case. For first-order modal logics, we describe two extensions, of different degrees of generality, of -as-Pow to logics of rigid designators and constant domains.     

一种应用描述逻辑推理实现本体映射的方法

本体匹配用于找到两个本体中元素间的映射关系,是数据库应用领域的一个重要问题.本文提出了一种基于描述逻辑的本体匹配方法,利用语义解释实现匹配.该方法首先利用多匹配器发现字面语义关系,并据此利用描述逻辑推理器推理元素相互间关系.借助概念包含推理设计了概念间关系的判定算法,可推理出各种对应关系,如等价、泛化、特化、相离、相交.该方法最终利用推理器RacerPro实现了本体匹配,最后通过实验证明了方法的有效性.     

基于泛逻辑学的概率命题逻辑的研究与分析

概率逻辑是不确定推理的一个重要逻辑基础,但其目前还不太完善.泛逻辑学是何华灿教授在探索各种不确定性问题求解中建立起来的一种新的柔性逻辑体系.理论上,概率逻辑仅是泛逻辑学的一个特例.在对目前比较典型的几种概率逻辑模型进行分析的基础上,基于命题泛逻辑学的思想和方法,指出了概率命题逻辑中存在的一些主要问题,探讨了解决这些问题的思路与方法.     

A Subset-Matching Size-Bounded Cache for Testing Satisfiability in Modal Logics

The implementation of efficient decision procedures for modal logics is a major research problem in automated deduction. Caching the result of intermediate consistency checks has experimentally proved to be a very important technique for attaining efficiency. Current state-of-the-art systems implement caching mechanisms based on hash tables. In this paper we present a data type – that we call bit matrix – for caching the (in)consistency of sets of formulas. Bit matrices have three distinguishing features: (i) they can be queried for subsets and supersets, (ii) they can be bounded in size, and (iii) if bounded, they can easily implement different policies to resolve which results have to be kept. We have implemented caching mechanisms based on bit matrices and hash tables in *SAT. In *SAT, the bit matrix cache is bounded, and keeps the latest obtained (in)consistency results. We experiment with the benchmarks proposed for the modal logic K at the TABLEAUX Non Classical Systems Comparison (TANCS) 2000. On the basis of the results, we conclude that *SAT performances are improved by (i) caching the results of intermediate consistency checks, (ii) using bit matrices instead of hash tables, and (iii) storing a small number of results in the bit matrices.     

Labelled Modal Logics: Quantifiers

In previous work we gave an approach, based on labelled natural deduction, for formalizing proof systems for a large class of propositional modal logics that includes K, D, T, B, S4, S4.2, KD45, and S5. Here we extend this approach to quantified modal logics, providing formalizations for logics with varying, increasing, decreasing, or constant domains. The result is modular with respect to both properties of the accessibility relation in the Kripke frame and the way domains of individuals change between worlds. Our approach has a modular metatheory too; soundness, completeness and normalization are proved uniformly for every logic in our class. Finally, our work leads to a simple implementation of a modal logic theorem prover in a standard logical framework.     

动态描述逻辑推理的并行计算技术

在设计用于处理大规模本体和数据的推理引擎时,推理引擎的可扩展性是一个需要研究的重要问题.动态描述逻辑要在真实环境中获得成功应用,需要在推理中采用并行计算技术.提出了两种方法将并行计算技术应用于动态描述逻辑推理.方法1是设计分布式动态描述逻辑框架.分布式动态描述逻辑由若干独立的动态描述逻辑所组成,这些动态描述逻辑两两之间通过桥规则联系起来.提出了基于Tableau的分布式推理算法,从而为分布式动态描述逻辑提供了全局推理能力,并且该算法可以将大的推理任务分解为若干子任务,而这些子任务可以被不同的推理主体并行处理.方法2是并行化动态描述逻辑的Tableau算法的不确定分支.不确定分支的并行计算使得推理任务可以在若干独立机器上同时执行.最后,介绍了推理引擎的原型实现并评估了其性能.实验结果表明提出的两种方法取得了明显的推理加速效果.     

基于描述逻辑本体推理的语义级中文校对方法

近年来中文校对技术虽然在字词级和语法级层面取得了较好效果,但是对于语义级层面研究相对薄弱,目前相关研究都有一定局限性. 提出利用本体技术将中文文本中的语义内容提取出来转换为结构化本体,再与正确的领域背景本体库融合,通过描述逻辑推理机来判断提取的语义内容的逻辑一致性,并将检测出的逻辑一致性错误映射为中文语义错误. 此方法在政治敏感错误等领域进行了测试,与其他相关研究相比,具有语义查错的透明性、语义模型的完整性、语义推理的智能型等优势.     

用描述逻辑进行语义Web服务组合

针对面向服务功能的语义Web服务组合问题,特别是经典的人工智能规划方法无法有效地处理Web服务执行过程中动态产生的新个体,以及基于服务匹配的方法则无法充分利用服务I/O参数类型之间大量的语义关联等关键问题,通过动态逻辑和描述逻辑之间的对比研究,采用描述逻辑公理来刻画Web服务的IOPR(inputs,outputs, preconditions and results),扩展了基于动态逻辑的人工智能规划方法,提出了把语义Web服务组合问题转化为描述逻辑推理问题的方法,克服了经典的人工智能规划方法中的困难和基于服务匹配的服务组合方法的缺点.     

基于案例和描述逻辑的海上援救规划方法

实现知识共享和案例检索是开发基于案例的智能决策支持系统面临的首要问题。针对海上援救指挥决策,采用Web本体语言OWL表示危机态势信息和海上援救领域知识,提出一种基于案例推理和描述逻辑推理的援救规划业务流程。以援救搁浅触礁舰船为例,对海损状况及其援救方法等信息进行了描述和推理。实验结果表明,根据具有语义的领域知识使用描述逻辑推理机对危机态势信息进行分类,能事先限定所要搜索的案例库和选择合理的援救方法,并提高案例检索效率和援救规划的实用性。