使用Petri网T—不变量求解子句的逻辑推论

本文研究了子句逻辑规则的Ｐｅｔｒｉ网模型的表示及使用Ｐｅｔｒｉ网分析方法进行逻辑推论，基于四值逻辑和冲突变迁的概念，表示了非Ｈｏｒｎ子句Ｐｅｔｒｉ网模型的构造，并使用Ｔ－不变量方法解决子句推论问题。     

Petri网用于Horn子句的逻辑推论

这篇论文探索了命题逻辑的Horn子句的Petri网模型,求解逻辑推论Petri网模型的T—不变量是求解逻辑推论的核心步骤,本文提供了计算T—不变量的算法,这些算法基于归约的思想,另外,在算法中利用单字母规则、纯字母规则和割裂规则可提高算法的速度和简化算法的复杂性。     

逻辑推理中的Petri网应用

本文讨论利用Ｐｅｔｒｉ网实现逻辑问题的推理，首先介绍了逻辑问题的Ｐｅｔｒｉ网模型描述方法，并举例说明了利用矩阵演算实现推理的算法。Ｐｅｔｒｉ网的研究与利用对开发逻辑程序并行性，提高推理效率很有意义。     

利用不动点求解子句逻辑推演的Petri网模型

文章研究了子句逻辑推演的Petri网模型表示和不动点求解方法.基于四值逻辑和冲突变迁的概念,可用Horn子句的Petri网模型方法来构造非Horn子句的Petri网模型.逻辑推演的基本方法之一就是寻找逻辑赋值的不动点.该文显示了一种基于Petri网模型的子句逻辑不动点求解算法,比现有算法更为有效.     

基于Petri网的统一知识表示模型

本文讨论知识表示的Ｐｅｔｒｉ网模型。将多种知识分类表示，对于开发具有较宽领域知识的系统具有重要意义。本文从统一的观点出发，在给出了Ｐｅｔｒｉ网的代数规范说明后，将三种主要的知识表示方法分别与Ｐｅｔｒｉ网模型之间建立映射系统，这三种知识表示方法为：逻辑表示法，语义网络和产生式系统。     

时序逻辑电路的Petri网分析方法

本文应用带抑止弧的增广Ｐｅｔｒｉ网，建立了基本门电路和常用触发器的Ｐｅｔｒｉ网模型，讨论了运用该模型描述同步和异步时序逻辑电路，给出了增广Ｐｅｔｒｉ网的矩阵描述和状态转移方程，在此基础上提出了同步和异步时序逻辑电路统一分析的Ｐｅｔｒｉ网方法。     

模糊Petri网及知识表示

在建造专家系统中虽然有很多种知识表示方法，但都有不尽人意的地方，本文试图用一种新的方法－Ｐｅｔｒｉ网模型来表示知识。本文给出了Ｆｕｚｚｚｙ Ｐｅｔｒｉ网和广义Ｆｕｚｚｙ Ｐｅｔｒｉ网两种模型，并给出了相应的推理算法，一旦专家知识用Ｐｅｔｒｉ网表示后，根据Ｐｅｔｒｉ网固有的特性，我们就能处理专家系统中并行推理、无回溯推理，反向推理等问题。     

用Petri网表示产生式知识

本文用Ｐ／Ｔ网，Ｐｒ／Ｔ网及其扩展对基于Ｈｏｒｎ子句的产生式知识进行了模拟，给出了将产生式知识换为Ｐｅｔｒｉ网的算法，并用Ｐｅｔｒｉ网对推理进行了探讨，试解了若干实例。     

概率逻辑可能世界的Petri网模型

本文研究概率逻辑中推导可能世界的Ｐｅｒｔｉ模型，该模型为可能世界的产生提供有效算法，这个算法被证明是正确的，它可以产生所有的一致的可能世界，文章中还分析了算法的复杂性，通过同其它方法的比较可知：此Ｐｅｔｒｉ网模型是概率逻辑可能世界推导的简单、实用和图形化的工具。     

逻辑函数的if-then子句表示法

本文提出了逻辑函数的另一种表示方法,与传统的用布尔表达式中表示逻辑的方法不同,这里采用了if-then子句集的形式。本文还讨论了如何将一个布尔表达式转换成等价的if-then子句形式。逻辑函数的这种表示方法加快了逻辑模拟的速度,并且解决了采用诸如OCCAM等并发进程语言来进行逻辑模拟过程中的死锁问题。     

Logical inference of Horn clauses in Petri net models

Petri net models for the Horn clause form of propositional logic and of first-order predicate logic are studied. A net model for logical inconsistency check is proposed. Algorithms for computing T-invariants of Petri net models of logical inference systems are investigated. The algorithms are based on the idea of resolution and exploit the presence of one-literal, pure-literal, and splitting clauses to lead to faster computation. Algorithms for computing T-invariants of high-level Petri net (HLPN) models of predicate logic are presented     

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.     

扩展时段时序逻辑的模型、一致性和推理

给出了扩展时段时序逻辑的时间Petri网（TPN）模型构造方法，在构造模型的同时对时序关系进行一致性检验，在模型的基础上提出了一种时序关系推理算法，这种推理算法基于TPN模型的性质及基本不等式规则，可由一组已知的扩展时段时序关系推出一些未知的扩展时段时序关系，这种推广理算法的优势在于利用了TNP模型的分析技术，减小了推理的时间复杂度比单纯利用不等式规则的推理更直观，也更简单，是一种有效的方法，最后，对扩展时段时序逻辑的TPN模型进行了扩充，增强了其模型和分析的能力。     

A Petri net model for reasoning in the presence of inconsistency

Petri nets provide a promising framework for executing queries to logic programs. Petri net models for query processing in logic programming were initially developed by T. Murata and D. Zhang (IEEE Trans. Software Eng., vol.14, no.4, p.481-97, 1988). It is shown how this framework can be extended to be applicable to reasoning in the presence of inconsistency. This yields a Petri net model of programs that be inconsistent in classical logic. This is interesting because large expert systems may often contain inconsistent information. The Petri net method proposed suggests a robust way of preventing inconsistency from infecting a system and rendering it useless     

基于Petri网和逻辑电路的网络安全验证

利用Petri网的库所和变迁来描述网络的状态和行为,用逻辑代数的0和1形象表示库所的状态,将复杂的PN模型转换成简单的逻辑表达式,提出了Petri网与逻辑电路相结合的新型网络数据流验证方式。这种方法具有的形式化步骤与数学模型相支持,是一种新型快捷的网络安全验证方法。     

Synthesis of 3D models by Petri net

This paper presents a synthesis method for 3D models using Petri net. Feature structure units from the example model are extracted, along with their constraints, through structure analysis, to create a new model using an inference method based on Petri net. Our method has two main advantages: first, 3D model pieces are delineated as the feature structure units and Petri net is used to record their shape features and their constraints in order to outline the model, including extending and deforming operations; second, a construction space generating algorithm is presented to convert the curve drawn by the user into local shape controlling parameters, and the free form deformation (FFD) algorithm is used in the inference process to deform the feature structure units. Experimental results showed that the proposed method can create large-scale complex scenes or models and allow users to effectively control the model result.     

基于Petri网的一种时序分析方法

Ｐｅｔｒｉ网由于有强大的建模能力和成熟的理论支持,被广泛应用于各种系统的建模．本文通过把Ｐｅｔｒｉ网转换成转移系统,利用转移系统和Ｋｒｉｐｋｅ结构给出时序逻辑语义的解释,从而建立了一种在Ｐｅｔｒｉ网上进行时序分析的方法．这种方法是根据不动点理论,用模型检查验证公式正确性．通过对Ａｄａ程序会合性质进行模型检查,验证了这种方法的有效性．     

Learning compact Markov logic networks with decision trees

Statistical-relational learning combines logical syntax with probabilistic methods. Markov Logic Networks (MLNs) are a prominent model class that generalizes both first-order logic and undirected graphical models (Markov networks). The qualitative component of an MLN is a set of clauses and the quantitative component is a set of clause weights. Generative MLNs model the joint distribution of relationships and attributes. A state-of-the-art structure learning method is the moralization approach: learn a set of directed Horn clauses, then convert them to conjunctions to obtain MLN clauses. The directed clauses are learned using Bayes net methods. The moralization approach takes advantage of the high-quality inference algorithms for MLNs and their ability to handle cyclic dependencies. A?weakness of moralization is that it leads to an unnecessarily large number of clauses. In this paper we show that using decision trees to represent conditional probabilities in the Bayes net is an effective remedy that leads to much more compact MLN structures. In experiments on benchmark datasets, the decision trees reduce the number of clauses in the moralized MLN by a factor of 5?C25, depending on the dataset. The accuracy of predictions is competitive with the models obtained by standard moralization, and in many cases superior.