国家知识基础设施中的数学知识表示

数学知识表示是知识表示中的一个重要方面,是数学知识检索、自动定理机器证明、智能教学系统等的基础.根据在设计NKI(national knowledge infrastructure)的数学知识表示语言中遇到的问题,并在讨论了数学对象的本体论假设的基础上提出了两种数学知识的表示方法:一种是以一个逻辑语言上的公式为属性值域的描述逻辑;另一种是以描述逻辑描述的本体为逻辑语言的一部分的一阶逻辑.在前者的表示中,如果对公式不作任何限制,那么得到的知识库中的推理不是可算法化的;在后者的表示中,以描述逻辑描述的本体中的推理是可算法化的,而以本体为逻辑语言的一部分的一阶逻辑所表示的数学知识中的推理一般是不可算法化的.因此,在表示数学知识时,需要区分概念性的知识(本体中的知识)和非概念性的知识(用本体作为语言表示的知识).框架或者描述逻辑可以表示和有效地推理概念性知识,但如果将非概念性知识加入到框架或知识库中,就可能使得原来可以有效推理的框架所表示的知识库不存在有效的推理算法,甚至不存在推理算法.为此,建议在表示数学知识时,用框架或描述逻辑来表示概念性知识;然后,用这样表示的知识库作为逻辑语言的一部分,以表示非概念性知识.     

Expressivity of coalgebraic modal logic: The limits and beyond

Modal logic has a good claim to being the logic of choice for describing the reactive behaviour of systems modelled as coalgebras. Logics with modal operators obtained from so-called predicate liftings have been shown to be invariant under behavioural equivalence. Expressivity results stating that, conversely, logically indistinguishable states are behaviourally equivalent depend on the existence of separating sets of predicate liftings for the signature functor at hand. Here, we provide a classification result for predicate liftings which leads to an easy criterion for the existence of such separating sets, and we give simple examples of functors that fail to admit expressive normal or monotone modal logics, respectively, or in fact an expressive (unary) modal logic at all. We then move on to polyadic modal logic, where modal operators may take more than one argument formula. We show that every accessible functor admits an expressive polyadic modal logic. Moreover, expressive polyadic modal logics are, unlike unary modal logics, compositional.     

一类扩展的动态描述逻辑

作为描述逻辑的扩展,动态描述逻辑为语义Web服务的建模和推理提供了一种有效途径.在将语义Web服务建模为动作之后,动态描述逻辑从动作执行结果的角度提供了丰富的推理机制,但对于动作的执行过程却不能加以处理.借鉴Pratt关于命题动态逻辑的相关研究,一方面,对动态描述逻辑中动作的语义重新进行定义,将每个动作解释为由关于可能世界的序列组成的集合;另一方面,在动态描述逻辑中引入动作过程断言,用来对动作的执行过程加以刻画.在此基础上提出一类扩展的动态描述逻辑EDDL(X),其中的X表示从ALC(attributive language with complements)到SHOIN(D)等具有不同描述能力的描述逻辑.以X为描述逻辑ALCQO(attributive language with complements,qualified number restrictions and nominals)的情况为例,给出了EDDL(ALCQO)的表判定算法,并证明了算法的可终止性、可靠性和完备性.EDDL(X)可以从动作执行过程和动作执行结果两个方面对动作进行全面的刻画和推理,为语义Web服务的建模和推理提供了进一步的逻辑支持.     

动态描述逻辑的Tableau判定算法

动态描述逻辑在描述逻辑的基础上引入了动态维,用于描述和推理动态领域的知识,但目前缺少有效的判定算法作为支撑.文中以描述逻辑ALCO的动态扩展为例,构建出动态描述逻辑D-ALCO.以D-ALCO的构建过程为基础,将ALCO的Tableau算法、命题动态逻辑的Tableau算法以及对可能模型途径的处理有机地结合起来,给出了D-ALCO的Tableau判定算法,证明了算法的可终止性、可靠性和完备性.应用该算法,可以在采用开世界假设的情况下对D-ALCO中公式的可满足性进行判定.对于D-ALCQO、D-ALCQIO等具有更强描述能力的动态描述逻辑,可以对该算法扩展后得到相应的Tableau判定算法.     

Describing properties of concurrent systems (Logic for Traces): (invited talk)

Mazurkiewicz traces are one of the simplest non-interleaving model of executions. For some systems the trace model may be exponentially smaller than the transition system model. This is one of the motivations for studying formalisms describing directly the properties of traces. Traces have also very nice theoretical properties. For example, there are characterizations of first-order definable and monadic second order definable (i.e. regular) languages and these characterizations are very similar to the ones in the case of words.Our goal is to find formalism that have the same expressive power as first or monadic-second order logic but that are manageable at the same time (i.e. with satisfiability and model checking problems in PSPACE). In other words, we want to understand what can be LTL and the mu-calculus variants for traces.A temporal logic over trace is called local if the meaning of a formula is a set of positions in the trace. A logic is called global if the meaning of a formula is a set of configurations (finite downwards closed subsets of positions). We will survey the results on both kind of logics. Among global logics it is relatively easy to find an expressively complete formalism but these logics have high complexity. Somewhat surprisingly there exist local expressively complete logics. Unfortunately, the presently known formalisms require some operators that are not completely satisfactory.     

强弱例外下的交互时态逻辑

非单调推理是众多人工智能应用系统都可能面对的问题,多Agent系统也不例外。在前期关于Agent BDI逻辑、多Agent合作逻辑、多Agent合作问题求解过程建模等研究工作的基础上,借鉴Baral等人开发非单调线性时态逻辑N-LTL的技术,利用强弱例外对多Agent合作逻辑的开创性工作交互时态逻辑(ATL)进行拓展,建立非单调交互时态逻辑NATL,给出其语法和语义。是对ATL进行非单调拓展的首次有益尝试。可以考虑以之为理论工具对多Agent思维状态及其动态修正机制进行妥善刻画。     

A decidable first-order logic for knowledge representation

Decidable first-order logics with reasonable model-theoretic semantics have several benefits for knowledge representation. These logics have the expressive power of standard first order logic along with an inference algorithm that will always terminate, both important considerations for knowledge representation. Knowledge representation systems that include a faithful implementation of one of these logics can also use its model-theoretic semantics to provide meanings for the data they store. One such logic, a variant of a simple type of first-order relevance logic, is developed and its properties described. This logic, although extremely weak, does capture a non-trivial and well-motivated set of inferences that can be entrusted to a knowledge representation system.This is a revised and much extended version of a paper of the same name that appears in the Proceedings of the Ninth International Joint Conference on Artificial Intelligence, Los Angeles, California, 1985.     

On temporal logic constraint solving for analyzing numerical data time series

Temporal logics and model-checking have proved successful in expressing biological properties of complex biochemical systems, and automatically verify their satisfaction, in both qualitative and quantitative models. In this article, we go beyond model-checking and present a constraint solving algorithm for quantifier-free first-order temporal logic formulae, with constraints over the reals. This algorithm computes the domain of the real valued variables occurring in a formula that makes it true in a model. We illustrate this approach for the automatic generation of a temporal logic specification from biological data time series. We provide a set of biologically relevant patterns of formulae, and apply them to numerical data time series of models of the cell cycle control and MAPK signal transduction. We show in these examples that this approach infers automatically semi-qualitative, semi-quantitative information about concentration thresholds, amplitude of oscillations, stability properties, checkpoints and influences between species.     

First-Order Temporal Verification in Practice

First-order temporal logic, the extension of first-order logic with operators dealing with time, is a powerful and expressive formalism with many potential applications. This expressive logic can be viewed as a framework in which to investigate problems specified in other logics. The monodic fragment of first-order temporal logic is a useful fragment that possesses good computational properties such as completeness and sometimes even decidability. Temporal logics of knowledge are useful for dealing with situations where the knowledge of agents in a system is involved. In this paper we present a translation from temporal logics of knowledge into the monodic fragment of first-order temporal logic. We can then use a theorem prover for monodic first-order temporal logic to prove properties of the translated formulas. This allows problems specified in temporal logics of knowledge to be verified automatically without needing a specialized theorem prover for temporal logics of knowledge. We present the translation, its correctness, and examples of its use. Partially supported by EPSRC project: Analysis and Mechanisation of Decidable First-Order Temporal Logics (GR/R45376/01).     

模态逻辑推理的翻译方法

文中研究了模态逻辑推理的翻译法，即把模态逻辑公式按照一定的规则翻译成经典逻辑公式，再用传统的定理器进行推理，文中指出，该方法在理论上保持了正规命题模态逻辑的可判定性，还给出了一些试验结果，说明该方法实际可行的。     

一种新的安全协议形式化验证方法

形式化方法能有效检验安全协议的安全性，BAN类逻辑的发展极大地促进了这一领域的研究，但是现有的BAN类逻辑仍然存在许多问题．在分析现有BAN类逻辑的基础上，提出一种新的安全协议形式化验证方法，实现现有BAN类逻辑的验证功能，并使安全协议验证工作简单可行，便于实现机器自动验证．为安全协议形式化验证提供了一种新的途径．     

Taxonomic reasoning with many-sorted logics

This paper provides an introduction to many-sorted logics and motivates their use for representation and reasoning. Perhaps the most important reason to be interested in many-sorted logic is that computational efficiency can be achieved because the search space can be smaller and the length of a derivation shorter than in unsorted logic. There are many possible many-sorted logics of varying degrees of expressiveness, and the dimensions in which many-sorted logics differ are outlined and logics at various points in this space described. The relationship of many-sorted logic to unsorted logic is discussed and the reason why many-sorted logics derivations may be shorter is demonstrated. The paper concludes with a discussion of some many-sorted logic programming languages and some implementation issues.     

Rasiowa–Sikorski deduction systems in computer science applications

A Rasiowa-Sikorski system is a sequence-type formalization of logics. The system uses invertible decomposition rules which decompose a formula into sequences of simpler formulae whose validity is equivalent to validity of the original formula. There may also be expansion rules which close indecomposable sequences under certain properties of relations appearing in the formulae, like symmetry or transitivity. Proofs are finite decomposition trees with leaves having “fundamental”, valid labels. The author describes a general method of applying the R-S formalism to develop complete deduction systems for various brands of C.S and A.I. logic, including a logic for reasoning about relative similarity, a three-valued software specification logic with McCarthy's connectives and Kleene quantifiers, a logic for nondeterministic specifications, many-sorted FOL with possibly empty carriers of some sorts, and a three-valued logic for reasoning about concurrency.     

基于Primeton EOS Studio平台的运算逻辑构件开发

运算逻辑是用于完成特定的业务计算和程序集成的有特定参数的Java方法。运算逻辑实现就是通过从业务引擎运行时的context中获取EOS XML数据总线上的数据,通过一定的业务处理和算法处理后的数据写入到XML数据中。EOS系统中提供了大量的基础的运算逻辑,但在实际的项目开发中仍然不能满足要求,因此开发项目需求的运算逻辑已成必然。在此以简单的实例开发来阐述运算逻辑的开发过程。     

A Branching Time Temporal Framework for Quantitative Reasoning

Temporal logics such as Computation Tree Logic (CTL) and Linear Temporal Logic (LTL) have become popular for specifying temporal properties over a wide variety of planning and verification problems. In this paper we work towards building a generalized framework for automated reasoning based on temporal logics. We present a powerful extension of CTL with first-order quantification over the set of reachable states for reasoning about extremal properties of weighted labeled transition systems in general. The proposed logic, which we call Weighted Quantified Computation Tree Logic (WQCTL), captures the essential elements common to the domain of planning and verification problems and can thereby be used as an effective specification language in both domains. We show that in spite of the rich, expressive power of the logic, we are able to evaluate WQCTL formulas in time polynomial in the size of the state space times the length of the formula. Wepresent experimental results on the WQCTL verifier.     

强表达描述逻辑本体的后继式公理定位研究

公理定位能够挖掘描述逻辑中可解释的缺陷,并为逻辑蕴含结果寻找隐藏的理由,因此在描述逻辑研究中引起了广泛的关注.平衡描述逻辑表达能力和推理机求解效率问题一直是公理定位研究的重点内容.本文基于一种后继式判定算法,从白盒和黑盒两个角度将其用于公理定位.白盒方法利用修正的后继式规则（即定位规则）来追踪推理的具体过程,并引入定位公式的概念建立子句的布尔公式标签与逻辑蕴含的所有极小公理集之间的对应关系.黑盒方法则直接调用基于未修正的后继式规则的推理机,并进一步利用碰集树方法求得逻辑蕴含的所有理由.最后,基于这样的两种面向强表达描述逻辑本体的公理定位算法设计推理工具,从理论和实验两方面验证其可行性,并与已有的推理工具比较求解性能.