用于一致性检查的知识库Petri网模型

知识库是一致性是决定专家系统效率及求解正确性的关键因素。本文以Ｐｅｔｒｉ网为工具对知识库进行模拟分析，把知识库一致性的检查化简为线性代数问题，把这一方法应用于分布式知识库系统，首次得到了检查其一致性的形式方法。本文最后给出了一致性检查的充分必要条件，为建立（分布式）知识库的自动维护系统打下了基础。     

Enhanced high-level Petri nets with multiple colors for knowledgeverification/validation of rule-based expert systems

Exploring the properties of rule-based expert systems through Petri net models has received a lot of attention. Traditional Petri nets provide a straightforward but inadequate method for knowledge verification/validation of rule-based expert systems. We propose an enhanced high-level Petri net model in which variables and negative information can be represented and processed properly. Rule inference is modeled exactly and some important aspects in rule-based systems (RBSs), such as conservation of facts, refraction, and closed-world assumption, are considered in this model. With the coloring scheme proposed in this paper, the tasks involved in checking the logic structure and output correctness of an RES are formally investigated. We focus on the detection of redundancy, conflicts, cycles, unnecessary conditions, dead ends, and unreachable goals in an RES. These knowledge verification/validation (KVV) tasks are formulated as the reachability problem and improper knowledge can be detected by solving a set of equations with respect to multiple colors. The complexity of our method is discussed and a comparison of our model with other Petri net models is presented.     

一种知识库校验工具PKBV的设计与实现

以Petri网建模基于规则的知识库，并据此开发出知识库校验工具PKBV，该工具通过对Petri网可达性及不变量的分析计算，来检查知识库中常见的完整性与一致性错误，针对具有多领域知识库的复杂系统，PKBV具有抽取多领域知识库之间的关联规则并进行校验的功能，满足了复杂知识系统的校验需求。     

An approach towards the verification of expert systems using numerical petri nets

A major difficulty that occurs in the construction of large production rule-based expert systems is maintaining the correctness, consistency, and completeness of the knowledge base. A method of transforming the production rules into a numerical petri nets (NPNs) model is proposed. These NPNs are high level nets that are necessary to effectively model production rules. the net model is then analysed by using a computer-aided tool to perform reachability analysis. an algorithm is given to generate the reachability set of the nets. This allows the verification of the correctness, consistency, and completeness of the knowledge base. Examples showing the use of this approach are given.     

Fuzzy rule base systems verification using high-level Petri nets

In this paper, we propose a Petri nets formalism for the verification of rule-based systems. Typical structural errors in a rule-based system are redundancy, inconsistency, incompleteness, and circularity. Since our verification is based on Petri nets and their incidence matrix, we need to transform rules into a Petri nets first, then derive an incidence matrix from the net. In order to let fuzzy rule-based systems detect above the structural errors, we are presenting a Petri-nets-based mechanism. This mechanism consists of three phases: rule normalization, rules transformation, and rule verification. Rules will be first normalized into Horn clauses, then transform the normalized rules into a high-level Petri net, and finally we verify these normalized rules. In addition, we are presenting our approach to simulate the truth conditions which still hold after a transition firing and negation in Petri nets for rule base modeling. In this paper, we refer to fuzzy rules as the rules with certainty factors, the degree of truth is computed in an algebraic form based on state equation which can be implemented in matrix computation in Petri nets. Therefore, the fuzzy reasoning problems can be transformed as the liner equation problems that can be solved in parallel. We have implemented a Petri nets tool to realize the mechanism presented fuzzy rules in this paper.     

Detection of Ada static deadlocks using Petri net invariants

A method is presented for detecting deadlocks in Ada tasking programs using structural; and dynamic analysis of Petri nets. Algorithmic translation of the Ada programs into Petri nets which preserve control-flow and message-flow properties is described. Properties of these Petri nets are discussed, and algorithms are given to analyze the nets to obtain information about static deadlocks that can occur in the original programs. Petri net invariants are used by the algorithms to reduce the time and space complexities associated with dynamic Petri net analysis (i.e. reachability graph generation)     

基于知识Petri网和归结规则的推理方法

本文提出了一种基于知识Petri网和归结规则的推理方法.通过知识Petri网描述命题逻辑知识库,将归结规则映射到知识Petri网上,根据库所和变迁的连接关系,定义了知识Petri网中的归结结构.利用归结结构,给出了基于知识Petri网的归结推理算法和扩展知识库的推理算法,并利用Wumpus实例验证了推理算法.该推理方法是可靠且完备的,能够利用知识Petri网的网络结构降低计算复杂性.     

A fuzzy Petri net-based expert system and its application to damageassessment of bridges

In this paper, a fuzzy Petri net approach to modeling fuzzy rule-based reasoning is proposed to bring together the possibilistic entailment and the fuzzy reasoning to handle uncertain and imprecise information. The three key components in our fuzzy rule-based reasoning-fuzzy propositions, truth-qualified fuzzy rules, and truth-qualified fuzzy facts-can be formulated as fuzzy places, uncertain transitions, and uncertain fuzzy tokens, respectively. Four types of uncertain transitions-inference, aggregation, duplication, and aggregation-duplication transitions-are introduced to fulfil the mechanism of fuzzy rule-based reasoning. A framework of integrated expert systems based on our fuzzy Petri net, called fuzzy Petri net-based expert system (FPNES), is implemented in Java. Major features of FPNES include knowledge representation through the use of hierarchical fuzzy Petri nets, a reasoning mechanism based on fuzzy Petri nets, and transformation of modularized fuzzy rule bases into hierarchical fuzzy Petri nets. An application to the damage assessment of the Da-Shi bridge in Taiwan is used as an illustrative example of FPNES.     

基于Petri 网知识库维护方法的实现

知识库的维护是知识系统的关键部分，直接关系到系统能否正常运行，本文介绍了基于Petri网知识库维护方法的实现。     

Verifying time Petri nets by linear programming

The paper proposes an approach to solving some verification problems of time petri nets using linear programming.The approach is based on the observation that for loop-closed time Ptri nets,it is only necessary to investigate a finite prefix of an untimed run of the underlying Petri net.Using the technique the paper gives solutions to reachabiltiy and bounded delay timing analysis problems.For both problems algorithms are given,that are decision procedures for loop-closed time Petri nets.and semi-decision procedures for general time Petri nets.     

Normal Petri nets

A class of Petri nets, called normal Petri nets, is introduced, and it is shown that, for each initial marking, the reachability set of a normal marked Petri net is an effectively computable semilinear set. More generally, we show that the reachability set of a marked Petri net is an effectively computable semilinear set unless the total number of tokens in a minimal circuit is decreased to 0. We also show that a Petri net is normal if and only if it is weakly persistent for each initial marking without token-free circuits.     

Complexity of some problems in Petri nets

We consider the complexity of several standard problems for various classes of Petri nets. In particular, the reachability problem, the liveness problem and the k-boundedness problems are analyzed. Some polynomial time and polynomial space complete problems for Petri nets are given. We then show that the problem of deciding whether a Petri net is persistent is reducible to reachability, partially answering a question of Keller. Reachability and boundedness are proved to be undecidable for the Time Petri net introduced by Merlin. Also presented is the concept of controllability, i.e., the capability of a set of transitions to disable a given transition. We show that the controllability problem requires exponential space, even for 1-bounded nets.     

多主体计划的Petri网方法及其研究

利用Petri网对主体Petri的各种行为进行描述和分析，通过Petri网系统的可达性分析考虑主体计划生成问题是求解单个主体计划问题的一种有效方法。系统中的每一个主体可以通过其Petir网系统进行描述，进而得到多主体系统相应的有界层次Petri网系统。利用层次Petri网系统的可达标识图得到多主体系统关于目标状态的可达动作序列的集合，对可行可达动作序列及其中动作间关系确定得到多主体系统的计划。     

Petri网的符号ZBDD可达树分析技术

Petri网是一种适合于并发系统建模、分析和控制的图形工具.可达树是Petri网分析的典型技术之一,它通过标识向量集合表征系统的状态空间,组合复杂性严重制约了该分析技术可处理系统问题的规模.零压缩决策图(Zero-Suppressed Binary Decision Diagrams,ZBDD)是一种新型的数据结构,是表示和处理稀疏向量集合的一种有效技术.文章基于Petri网町达标识向量的稀疏特征,给出了Petri网分析的符号ZBDD技术,该技术通过对标识向量(状态)的布尔向量表示、可达标识向最(状态)的符号ZBDD生成,实现Petri网可达状态空间的高效符号操作和紧凑符号表示.实验表明,基于ZBDD的符号可达性分析算法能够有效处理较大规模Petri网问题.     

无界Petri网的可达树的综述

Petri网自提出以来得到了学术界和工业界的广泛关注. Petri网系统的可达性是最基本性质之一.系统的其他相关性质都可以通过可达性进行分析.利用等价的有限可达树来研究无界Petri网可达性,依然是一个开放性问题.该研究可以追溯到40年前,但由于问题本身的复杂性和难度太大,直到最近20年,经过国内外诸多学者的不懈努力,才逐渐取得了一些阶段性的成果和部分突破.本文回顾了近40年来国内外学者为彻底解决该问题作出的贡献.重点对4种开创性的研究成果展开讨论,分别为有限可达树、扩展可达树、改进可达树及新型改进可达树.探讨了今后无界Petri网可达性问题的研究方向.     

Verification of causal models using petri nets

Many different approaches, mainly based on logical formalisms, have been proposed for modeling causal knowledge and the inferential mechanisms based on this type of knowledge. In this article we present an alternative approach to this problem in which the semantics of a causal model is provided by adopting Petri nets. We show how this scheme of modeling is powerful enough to capture all crucial aspects of the corresponding causal model, without resorting to very complex structures; indeed, the model is obtained using a particular type of deterministic Petri net. Moreover, a complete formalization of the aspects concerning the correctness of the represented causal model is provided in terms of reachability in the Petri net. We believe that this aspect is very important in the knowledge acquisition phase when precise correctness criteria should be defined and respected in the construction of the model. We analyze some of these criteria and we discuss an algorithm (based on a backward simulation of the net) capable of discovering incorrectness by exploiting analysis tools available for Petri nets and the explicit parallelism of the model. © 1992 John Wiley & Sons, Inc.     

Transformations of Petri Nets

The aim of this paper is an introduction to the area of Petri net transformations, a rule-based approach for dynamic changes of the net structure of Petri nets. This is especially important for the stepwise construction of Petri nets in the sense of the software development process in software engineering. The concept of Petri net transformations is based on that of graph transformations and high-level replacement systems and it is introduced within a small case study logistics.     

Structuring Acyclic Petri Nets for Reachability Analysis and Control

The incidence matrices—from places to transitions and vice versa—of an acyclic Petri net can obtain a block-triangular structure by reordering their rows and columns. This allows the efficient solution of some reachability problems for acyclic Petri nets. This result is further used in supervisory control of Petri nets; supervisors for Petri nets with uncontrollable transitions are constructed by extending the method of Yamalidou et al. (1996) to Petri nets where transitions can be executed simultaneously. A large class of Petri nets with uncontrollable transitions is given for which the maximally permissive supervisor can be realized by a Petri net. The original specification is algorithmically transformed—by using the results for acyclic Petri nets—into a new specification to take the presence of uncontrollable transitions into account. The supervisor is obtained by simple matrix multiplications and no linear integer programs need to be solved. Furthermore, a class of Petri nets is given for which the supervisor can be realized by extending the enabling rule with OR-logic.     

On reachability graphs of Petri nets

Petri net is a powerful tool for system analysis and design. Several techniques have been developed for the analysis of Petri nets, such as reachability trees, matrix equations and reachability graphs. This article presents a novel approach to constructing a reachability graph, and discusses the application of the reachability graph to Petri nets analysis.     

Some decision problems related to the reachability problem for Petri nets

In this paper, we show that (1) the question to decide whether a given Petri net is consistent, M_o-reversible or live is reduced to the reachability problem in a unified manner, (2) the reachability problem for Petri nets is equivalent to the equality problem and the inclusion problem for the sets of all firing sequences of two Petri nets, (3) the equality problem for the sets of firing sequences of two Petri nets with only two unbounded places under homomorphism is undecidable, (4) the coverability and reachability problems are undecidable for generalized Petri nets in which a distinguished transition has priority over the other transitions, and (5) the reachability problem is undecidable for generalized Petri nets in which some transitions can reset a certain place to zero marking.