Techniques for Bayesian analysis in expert systems

A causal network is frequently used as a representation for qualitative medical knowledge, in which conditional probability tables on appropriate sets of variables form the quantitative part of the accumulated experience. For probabilities temporarily assumed known, we describe efficient algorithms for propagating the effects of multiple items of evidence around multiply-connected networks and hence providing precise probabilistic revision of beliefs concerning the current patient. As a database accumulates we also require the quantitative aspects of the model to be updated, as well as to learn about the qualitative structure, and we suggest some formal statistical tools for these problems.     

Markov analysis of qualitative dynamics1

Common sense sometimes predicts events to be likely or unlikely rather than merely possible. We extend methods of qualitative reasoning to predict the relative likelihoods of possible qualitative behaviors by viewing the dynamics of a system as a Markov chain over its transition graph. This involves adding qualitative or quantitative estimates of transition probabilities to each of the transitions and applying the standard theory of Markov chains to distinguish persistent states from transient states and to calculate recurrence times, settling times, and probabilities for ending up in each state. Much of the analysis depends solely on qualitative estimates of transition probabilities, which follow directly from theoretical considerations and which lead to qualitative predictions about entire classes of systems. Quantitative estimates for specific systems are derived empirically and lead to qualitative and quantitative conclusions, most of which are insensitive to small perturbations in the estimated transition probabilities. The algorithms are straightforward and efficient.     

THE SCOPE OF DIMENSIONAL ANALYSIS IN QUALITATIVE REASONING

Dimensional analysis, traditionally used in physics and engineering to identify quantitative relationships, has recently been applied to qualitative reasoning of physical systems. We illustrate some problems of this approach. In the light of this, we reexamine the fundamentals of dimensional analysis in order to more precisely characterize its scope and limitations as a tool in qualitative reasoning. We also explore its relationship to state equation representations of physical systems. In particular, we describe its value in providing a set of constraints to reduce the ambiguity that bedevils qualitative reasoning schemes. We argue that dimensional analysis should not be seen as a substitute for knowledge about the physics but rather a supplement to other sources of knowledge.     

基于AADL的混合关键系统随机错误与突发错误安全性分析

许多复杂的嵌入式系统都是混合关键系统(mixed-criticality system,简称MCS).MCS通常需要在指定的关键性(criticality)等级状态下运行,但是它们可能会受到一些危害的影响,这些危害可能会导致随机错误和突发错误,进一步导致执行线程中止,甚至导致系统故障.目前的研究仅集中于对MCS的可调度性分析,未能进一步分析系统安全性,未能考虑线程之间的依赖关系.本文以随机错误和突发错误为研究对象,提出一种集成故障传播分析的基于架构的MCS安全分析方法.使用架构分析和设计语言(Architecture Analysis and Design Language,简称AADL)刻画构件依赖关系.为了弥补AADL的不足,创建新的AADL属性(AADL突发错误属性),并提出新的线程状态机(突发错误行为线程状态机)语义来描述带有突发错误的线程执行过程.为了将概率模型检查应用于安全分析,提出模型转换规则和组装方法,从AADL模型推导出PRISM模型.建立了两个公式,分别获得定量安全属性以验证故障发生的概率,以及定性安全属性以生成相应的正例来求出故障传播路径来进行故障传播分析.最后,以动力艇自动驾驶仪(power boat autopilot,简称PBA)系统为例,验证了该方法的有效性.     

A Rule-Based Object-Oriented OWL Reasoner

In this paper, we describe O-DEVICE, a memory-based knowledge-based system for reasoning and querying OWL ontologies by implementing RDF/OWL entailments in the form of production rules in order to apply the formal semantics of the language. Our approach is based on a transformation procedure of OWL ontologies into an object-oriented schema and the application of inference production rules over the generated objects in order to implement the various semantics of OWL. In order to enhance the performance of the system, we introduce a dynamic approach of generating production rules for ABOX reasoning and an incremental approach of loading ontologies. O-DEVICE is built over the CLIPS production rule system, using the object-oriented language COOL to model and handle ontology concepts and RDF resources. One of the contributions of our work is that we enable a well-known and efficient production rule system to handle OWL ontologies. We argue that although native OWL rule reasoners may process ontology information faster, they lack some of the key features that rule systems offer, such as the efficient manipulation of the information through complex rule programs. We present a comparison of our system with other OWL reasoners, showing that O-DEVICE can constitute a practical rule environment for ontology manipulation.     

Lp, a logic for representing and reasoning with statistical knowledge

This paper presents a logical formalism for representing and reasoning with statistical knowledge. One of the key features of the formalism is its ability to deal with qualitative statistical information. It is argued that statistical knowledge, especially that of a qualitative nature, is an important component of our world knowledge and that such knowledge is used in many different reasoning tasks. The work is further motivated by the observation that previous formalisms for representing probabilistic information are inadequate for representing statistical knowledge. The representation mechanism takes the form of a logic that is capable of representing a wide variety of statistical knowledge, and that possesses an intuitive formal semantics based on the simple notions of sets of objects and probabilities defined over those sets. Furthermore, a proof theory is developed and is shown to be sound and complete. The formalism offers a perspicuous and powerful representational tool for statistical knowledge, and a proof theory which provides a formal specification for a wide class of deductive inferences. The specification provided by the proof theory subsumes most probabilistic inference procedures previously developed in AI. The formalism also subsumes ordinary first-order logic, offering a smooth integration of logical and statistical knowledge.     

Quantitative deduction and its fixpoint theory

Logic programming provides a model for rule-based reasoning in expert systems. The advantage of this formal model is that it makes available many results from the semantics and proof theory of first-ordet predicate logic. A disadvantage is that in expert systems one often wants to use, instead of the usual two truth values, an entire continuum of “uncertainties” in between. That is, instead of the usual “qualitative” deduction, a form of “quantitative” deduction is required. We present an approach to generalizing the Tarskian semantics of Horn clause rules to justify a form of quantitative deduction. Each clause receives a numerical attenuation factor. Herbrand interpretations, which are subsets of the Herbrand base, are generalized to subsets which are fuzzy in the sense of Zadeh. We show that as result the fixpoint method in the semantics of Horn clause rules can be developed in much the same way for the quantitative case. As for proof theory, the interesting phenomenon is that a proof should be viewed as a two-person game. The value of the game turns out to be the truth value of the atomic formula to be proved, evaluated in the minimal fixpoint of the rule set. The analog of the PROLOG interpreter for quantitative deduction becomes a search of the game tree ( = proof tree) using the alpha-beta heuristic well known in game theory.     

Hybrid knowledge bases

Deductive databases that interact with, and are accessed by, reasoning agents in the real world (such as logic controllers in automated manufacturing, weapons guidance systems, aircraft landing systems, land-vehicle maneuvering systems, and air-traffic control systems) must have the ability to deal with multiple modes of reasoning. Specifically, the types of reasoning we are concerned with include, among others, reasoning about time, reasoning about quantitative relationships that may be expressed in the form of differential equations or optimization problems, and reasoning about numeric modes of uncertainty about the domain which the database seeks to describe. Such databases may need to handle diverse forms of data structures, and frequently they may require use of the assumption-based nonmonotonic representation of knowledge. A hybrid knowledge base is a theoretical framework capturing all the above modes of reasoning. The theory tightly unifies the constraint logic programming scheme of Jaffar and Lassez (1987), the generalized annotated logic programming theory of Kifer and Subrahmanian (1989), and the stable model semantics of Gelfond and Lifschitz (1988). New techniques are introduced which extend both the work on annotated logic programming and the stable model semantics     

The Local Geometry of Multiattribute Tradeoff Preferences

Existing representations for multiattribute ceteris paribus preference statements have provided useful treatments and clear semantics for qualitative comparisons, but have not provided similarly clear representations or semantics for comparisons involving quantitative tradeoffs. We use directional derivatives and other concepts from elementary differential geometry to interpret conditional multiattribute ceteris paribus preference comparisons that state bounds on quantitative tradeoff ratios. This semantics extends the familiar economic notion of marginal rate of substitution to multiple continuous or discrete attributes. The same geometric concepts also provide means for interpreting statements about the relative importance of different attributes.     

基于可达概率区间的不确定决策树

针对不确定数据的概率分布难以获取的客观实际,讨论了缺失概率分布的值不确定离散对象的决策树。定义了(条件)概率区间,并证明了(条件)概率区间是可达概率区间;基于可达概率区间,定义了(条件)熵区间,并给出了求解(条件)熵区间的上/下界的方法;采用条件熵区间作为属性选择度量,提出了一种新的不确定决策树,将以0-1划分对象的决策树扩展到以概率区间分配对象的决策树,这样不仅可以处理缺失概率分布的值不确定离散对象,也可以处理确定离散对象。通过在基于UCI数据集的不确定数据集上的实验,证实了不确定决策树是有效的。     

Temporal Semantics for Concurrent M M

Concurrent is a programming language based on the notion of concurrent, communicating objects, where each object directly executes a specification given in temporal logic, and communicates with other objects using asynchronous broadcast message-passing. Thus, Concurrent represents a combination of the direct execution of temporal specifications, together with a novel model of concurrent computation. In contrast to the notions of predicates as processes and stream parallelism seen in concurrent logic languages, Concurrent represents a more coarse-grained approach, where an object consists of a set of logical rules and communication is achieved by the evaluation of certain types of predicate. Representing concurrent systems as groups of such objects provides a powerful tool for modelling complex reactive systems. In order to reason about the behaviour of Concurrent systems, we requir a suitable semantics. Being based upon executable temporal logic, objects in isolation have an intuitive semantics. However, the addition of both operational constraints upon the object's execution and global constraints provided by the asynchronous model of concurrency and communication, complicates the overall semantics of networks of objects. It is this, more complex, semantics that we address here, where temporal semantics for varieties of Concurrent are provided.     

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.     

Probabilistic knowledge representation using the principle of maximum entropy and Gröbner basis theory

An often used methodology for reasoning with probabilistic conditional knowledge bases is provided by the principle of maximum entropy (so-called MaxEnt principle) that realises an idea of least amount of assumed information and thus of being as unbiased as possible. In this paper we exploit the fact that MaxEnt distributions can be computed by solving nonlinear equation systems that reflect the conditional logical structure of these distributions. We apply the theory of Gröbner bases that is well known from computational algebra to the polynomial system which is associated with a MaxEnt distribution, in order to obtain results for reasoning with maximum entropy. We develop a three-phase compilation scheme extracting from a knowledge base consisting of probabilistic conditionals the information which is crucial for MaxEnt reasoning and transforming it to a Gröbner basis. Based on this transformation, a necessary condition for knowledge bases to be consistent is derived. Furthermore, approaches to answering MaxEnt queries are presented by demonstrating how inferring the MaxEnt probability of a single conditional from a given knowledge base is possible. Finally, we discuss computational methods to establish general MaxEnt inference rules.     

Bee colony optimization for the satisfiability problem in probabilistic logic

This paper presents the first heuristic method for solving the satisfiability problem in the logic with approximate conditional probabilities. This logic is very suitable for representing and reasoning with uncertain knowledge and for modeling default reasoning. The solution space consists of variables, which are arrays of 0 and 1 and the associated probabilities. These probabilities belong to a recursive non-Archimedean Hardy field which contains all rational functions of a fixed positive infinitesimal. Our method is based on the bee colony optimizationmeta-heuristic. The proposed procedure chooses variables from the solution space and determines their probabilities combining some other fast heuristics for solving the obtained linear system of inequalities. Experimental evaluation shows a high percentage of success in proving the satisfiability of randomly generated formulas. We have also showed great advantage in using a heuristic approach compared to standard linear solver.     

State estimation for systems with sojourn-time-dependent Markovmodel switching

A switching process in which the switching probabilities depend on a random sojourn time is a class of semi-Markov processes and is encountered in target tracking, systems subject to failures, And also in the socioeconomic environment. In such a system, knowledge of the sojourn time is needed for the computation of the conditional transition probabilities. It is shown how one can infer the transition probabilities through the evaluation of the conditional distribution of the sojourn time. Subsequently, a recursive state estimation for such systems is obtained using the conditional sojourn time distribution for dynamic systems with imperfect observations and changing structures (models)     

Qualitative reasoning based on fuzzy relative orders of magnitude

This paper proposes a fuzzy set-based approach for handling relative orders of magnitude stated in terms of closeness and negligibility relations. At the semantic level, these relations are represented by means of fuzzy relations controlled by tolerance parameters. A set of sound inference rules, involving the tolerance parameters, is provided, in full accordance with the combination/projection principle underlying the approximate reasoning method of Zadeh. These rules ensure a local propagation of fuzzy closeness and negligibility relations. A numerical semantics is then attached to the symbolic computation process. Required properties of the tolerance parameter are investigated, in order to preserve the validity of the produced conclusions. The effect of the chaining of rules in the inference process can be controlled through the gradual deterioration of closeness and negligibility relations involved in the produced conclusions. Finally, qualitative reasoning based on fuzzy closeness and negligibility relations is used for simplifying equations and solving them in an approximate way, as often done by engineers who reason about a mathematical model. The problem of handling qualitative probabilities in reasoning under uncertainty is also investigated in this perspective.     

Connectionist computations of intuitionistic reasoning

The construction of computational models with provision for effective learning and added reasoning is a fundamental problem in computer science. In this paper, we present a new computational model for integrated reasoning and learning that combines intuitionistic reasoning and neural networks. We use ensembles of neural networks to represent intuitionistic theories, and show that for each intuitionistic theory and intuitionistic modal theory there exists a corresponding neural network ensemble that computes a fixed-point semantics of the theory. This provides a massively parallel model for intuitionistic reasoning. In our model, the neural networks can be trained from examples to adapt to new situations using standard neural learning algorithms, thus providing a unifying foundation for intuitionistic reasoning, knowledge representation, and learning.