多Agent信念逻辑及其在概率意义下的推广

首先建立了一种多Agent信念逻辑MBL(multi-agentbelieflogic),在经典信念逻辑基础上增加了普遍信念算子和公共信念算子,给出MBL的Kripke语义与广义Aumann语义,讨论了两者的等价性,证明了MBL对于上述两种语义的可靠性和完备性.其次,建立了一种多Agent概率信念逻辑MPBL(multi-agentprobabilisticbelieflogic),通过在广义Aumann语义基础上引入概率空间,给出了MPBL的概率Aumann语义,证明了它的可靠性,并给出MPBL的一些推论.     

概率逻辑程序

1 引言最近几十年来,不确定性的管理在知识描述和推理中扮演着越来越重要的角色。为了处理不确定知识,人们提出了各种不同的形式化和方法论,其中大部分是直接或间接地基于概率论的。     

Uniform semantic treatment of default and autoepistemic logics

We revisit the issue of epistemological and semantic foundations for autoepistemic and default logics, two leading formalisms in nonmonotonic reasoning. We develop a general semantic approach to autoepistemic and default logics that is based on the notion of a belief pair and that exploits the lattice structure of the collection of all belief pairs. For each logic, we introduce a monotone operator on the lattice of belief pairs. We then show that a whole family of semantics can be defined in a systematic and principled way in terms of fixpoints of this operator (or as fixpoints of certain closely related operators). Our approach elucidates fundamental constructive principles in which agents form their belief sets, and leads to approximation semantics for autoepistemic and default logics. It also allows us to establish a precise one-to-one correspondence between the family of semantics for default logic and the family of semantics for autoepistemic logic. The correspondence exploits the modal interpretation of a default proposed by Konolige. Our results establish conclusively that default logic can be viewed as a fragment of autoepistemic logic, a result that has been long anticipated. At the same time, they explain the source of the difficulty to formally relate the semantics of default extensions by Reiter and autoepistemic expansions by Moore. These two semantics occupy different locations in the corresponding families of semantics for default and autoepistemic logics.     

Agent逻辑和真假子集语义

理性Agent规约的形式框架通常基于信念、愿望和意图逻辑.为了克服现有的信念、愿望和意图逻辑中存在的问题,为非正规模态算子提供一种合适的语义表示.讨论了理性Agent性态的抽象规约中对语义表示的要求以及现有的信念、愿望和意图逻辑中存在的问题.介绍了作者开发的真假子集语义及其在Agent形式化中的应用.他们的框架使意图的有问题的性质无效.并且证明通过对模型的代数结构施加一定的约束,能获得许多希望的性质.最后对真假子集语义进行了分析.这一切表明真假子集语义为非正规模态算子提供了一种合适的语义表示,是对经典的正规模态算子可能世界语义的一个重要发展,是理性Agent性态的逻辑规约的有力工具,可应用于建立新的合适的Agent逻辑系统.     

A Syntactic Framework with Probabilistic Beliefs and Conditionals for the Analysis of Strategic Form Games

In this paper, I develop a syntactic framework for the analysis ofstrategic form games that is based on a straightforward combination ofstandard systems of doxastic, probabilistic and conditionalpropositional logic. In particular, for the probabilistic part I makeuse of the axiomatization provided in Fagin and Halpern (1994). The use ofconditionals allows to represent a strategic form game by a logicalformula in a very natural way. Also expected utility maximization can benaturally captured. I use this framework to prove a version of a resulton Nash equilibrium conjectures first presented in Aumann and Brandenburger (1995).     

人工智能中概率逻辑的研究

概率论是在不完备的、不确定的数据中进行推理的,它是度量不确定性的重要手段。在人工智能中,研究者结合概率和逻辑各自的优点,进行概率逻辑的研究。本文介绍了传统概率逻辑的三大派别,阐述了二值逻辑概率和三值逻辑概率的发展;最后介绍了泛逻辑,通过对概率逻辑和泛逻辑学的研究,将概率逻辑纳入泛逻辑学的框架内。     

人工智能中概率逻辑的研究

概率论是在不完备的、不确定的数据中进行推理的,它是度量不确定性的重要手段。在人工智能中,研究者结合概率和逻辑各自的优点,进行概率逻辑的研究。本文介绍了传统概率逻辑的三大派别,阐述了二值逻辑概率和三值逻辑概率的发展;最后介绍了泛逻辑,通过对概率逻辑和泛逻辑学的研究,将概率逻辑纳入泛逻辑学的框架内。     

Probabilistic coherence spaces as a model of higher-order probabilistic computation

We study a probabilistic version of coherence spaces and show that these objects provide a model of linear logic. We build a model of the pure lambda-calculus in this setting and show how to interpret a probabilistic version of the functional language PCF. We give a probabilistic interpretation of the semantics of probabilistic PCF closed terms of ground type. Last we suggest a generalization of this approach, using Banach spaces.     

Paraconsistent Declarative Semantics for Extended Logic Programs

We introduce a fixpoint semantics for logic programs with two kinds of negation: an explicit negation and a negation-by-failure. The programs may also be prioritized, that is, their clauses may be arranged in a partial order that reflects preferences among the corresponding rules. This yields a robust framework for representing knowledge in logic programs with a considerable expressive power. The declarative semantics for such programs is particularly suitable for reasoning with uncertainty, in the sense that it pinpoints the incomplete and inconsistent parts of the data, and regards the remaining information as classically consistent. As such, this semantics allows to draw conclusions in a non-trivial way, even in cases that the logic programs under consideration are not consistent. Finally, we show that this formalism may be regarded as a simple and flexible process for belief revision.     

缺省理论与相信理论的关系

本文在相信逻辑中引入相信解释与相信模的概念，从语义上把相信逻辑改造成非单调逻辑。一个缺省理论可以直接转换成一个相信逻辑理论，本文中证明了一个缺省理论外延的模集就是对应相信理论的模，从而为缺省理论提供了一种简便的语义。     

概率逻辑、不确定逻辑和模糊逻辑之比较

通过一个实例分析比较了概率逻辑、主观概率逻辑、不确定逻辑和模糊逻辑的思想方法。提出了自己的观点：基于数据统计的概率逻辑是最科学的。不确定逻辑比主观概率逻辑更科学。当具有不确定性的原子命题具有独立性时,不确定逻辑和模糊逻辑的观点是一致的。而对于处理带有不确定性的相关性命题,不确定逻辑比模糊逻辑更科学。但是模糊逻辑在建立推理理论方面见长。     

实时并发系统的PTSL模型检测

随着实时并发系统的软件规模越来越大、复杂性日趋增加,如何保证并发实时系统正确性和可靠性成为日益紧迫的问题。模型检测技术采用自动化的验证算法判断系统是否具有某一性质,它不仅包括对系统模型的遍历以及基于图形的分析方法,而且还需要大量的数值计算。本文把实时并发模型看成对并发博弈模型（CGS）的扩展,在此基础上添加了概率与时间性质,提出了概率时间并发博弈结构（PTCGS）。同时本文还提出了新的逻辑语言-概率时间策略逻辑（PTSL）,它显式地把策略作为一阶逻辑中的对象,从而使我们能够以简单而自然的方式指定PTCGS系统中的非零和属性。PTSL模型检测方法能够让设计者准确知道模型是否满足用户的需求,从而提高系统的可靠性。最后,本文以ZeroConf协议为例来说明PTSL模型检测方法的正确性。     

Symmetric structure in logic programming

It is argued that some symmetric structure in logic programs could be taken into account when implementing semantics in logic programming. This may enhance the declarative ability or expressive power of the semantics. The work presented here may be seen as representative examples along this line. The focus is on the derivation of negative information and some other classic semantic issues. We first define a permutation group associated with a given logic program. Since usually the canonical models used to reflect the common sense or intended meaning are minimal or completed models of the program, we expose the relationships between minimal models and completed models of the original program and its so-called G-reduced form newly-derived via the permutation group defined. By means of this G-reduced form, we introduce a rule to assume negative information termed G-CWA, which is actually a generalization of the GCWA. We also develop the notions of G-definite, G-hierarchical and G-stratified logic programs,     

一种新的安全协议验证逻辑及其串空间语义

针对典型的安全协议验证逻辑存在的问题,如安全属性验证存在局限性、对混合密码原语的处理能力不强等,提出一种新的验证逻辑,新逻辑能够验证安全协议的认证性、密钥保密性、非否认性、可追究性、公平性及原子性。现有多数验证逻辑缺乏形式化语义,而逻辑语义能够证明逻辑系统的正确性,因此给出新逻辑所含逻辑构件的串空间语义,并应用串空间模型证明了新逻辑主要推理规则的正 确性。     

Strong equivalence of logic programs under the infinite-valued semantics

We consider the notion of strong equivalence [V. Lifschitz, D. Pearce, A. Valverde, Strongly equivalent logic programs, ACM Transactions on Computational Logic 2 (4) (2001) 526-541] of normal propositional logic programs under the infinite-valued semantics [P. Rondogiannis, W.W. Wadge, Minimum model semantics for logic programs with negation-as-failure, ACM Transactions on Computational Logic 6 (2) (2005) 441-467] (which is a purely model-theoretic semantics that is compatible with the well-founded one). We demonstrate that two such programs are strongly equivalent under the infinite-valued semantics if and only if they are logically equivalent in the corresponding infinite-valued logic. In particular, we show that strong equivalence of normal propositional logic programs is decidable, and more specifically coNP-complete. Our results have a direct implication for the well-founded semantics since, as we demonstrate, if two programs are strongly equivalent under the infinite-valued semantics, then they are also strongly equivalent under the well-founded semantics.     

Nondeterministic Probabilistic Petri Net — A New Method to Study Qualitative and Quantitative Behaviors of System

There are many variants of Petri net at present,and some of them can be used to model system with both function and performance specification,such as stochastic Petri net,generalized stochastic Petri net and probabilistic Petri net.In this paper,we utilize extended Petri net to address the issue of modeling and verifying system with probability and nondeterminism besides function aspects.Using probabilistic Petri net as reference,we propose a new mixed model NPPN(Nondeterministic Probabilistic Petri Net) system,which can model and verify systems with qualitative and quantitative behaviours.Then we develop a kind of process algebra for NPPN system to interpret its algebraic semantics,and an actionbased PCTL(Probabilistic Computation Tree Logic) to interpret its logical semantics.Afterwards we present the rules for compositional operation of NPPN system based on NPPN system process algebra,and the model checking algorithm based on the action-based PCTL.In order to put the NPPN system into practice,we develop a friendly and visual tool for modeling,analyzing,simulating,and verifying NPPN system using action-based PCTL.The usefulness and effectiveness of the NPPN system are illustrated by modeling and model checking an elaborate model of travel arrangements workflow.     

概率计算树逻辑的限界模型检测

为了缓解概率计算树逻辑模型检测中的状态空间爆炸问题,提出了概率计算树逻辑的限界模型检测技术.该技术首先定义概率计算树逻辑的限界语义,并证明其正确性;之后,通过实例说明在传统限界模型检测中,以路径长度作为判断检测过程终止的标准已经失效,基于数值计算中牛顿迭代法的终止准则,设计了新的终止判断标准;然后提出基于线性方程组求解的限界模型检测算法;最后,通过3个测试用例说明,概率计算树逻辑限界模型检测方法在反例较短的情况下能够快速完成检测过程,而且比概率计算树逻辑的无界模型检测算法所需求得的状态空间要少.     

一种新的类BAN逻辑模态语义模型--兼论类BAN逻辑的语法缺陷

由于类BAN逻辑缺乏明确而清晰的语义,其语法规则和推理的正确性就受到了质疑。本文定义了安全协议的计算模型,在此基础上定义了符合模态逻辑的类BAN逻辑“可能世界”语义模型,并从语义的角度证明了在该模型下的类BAN逻辑语法存在的缺陷,同时,指出了建立或改进类BAN逻辑的方向。     

认识逻辑(1):关于知识和信念的逻辑框架

知识和信念是人工智能领域研究中经常涉及到的两个重要概念。本文讨论了知识和信念的涵义与关系，定义了认识逻辑系统ＥＩ，讨论了它的语法和语义，证明了认识逻辑ＥＬ不但是可靠的而且是完备的，认为逻辑ＥＬ不但可以用来描述人类的认识过程，还可以用于对常识推理以及分布式系统的形式化描述。