A probabilistic fuzzy approach to modeling nonlinear systems

Recently, the study of incorporating probability theory and fuzzy logic has received much interest. To endow the traditional fuzzy rule-based systems (FRBs) with probabilistic features to handle randomness, this paper presents a probabilistic fuzzy neural network (ProFNN) by introducing the probability of input linguistic terms and providing linguistic meaning into the connectionist architecture. ProFNN integrates the probabilistic information of fuzzy rules into the antecedent parts and quantifies the impacts of the rules on the consequent parts using mutual subsethood, which work in conjunction with volume defuzzification in a gradient descent learning frame work. Despite the increase in the number of parameters, ProFNN provides a promising solution to deal with randomness and fuzziness in a single frame. To evaluate the performance and applicability of the proposed approach, ProFNN is carried out on various benchmarking problems and compared with other existing models with a performance better than most of them.     

ALLPAD: approximate learning of logic programs with annotated disjunctions

Logic Programs with Annotated Disjunctions (LPADs) provide a simple and elegant framework for representing probabilistic knowledge in logic programming. In this paper we consider the problem of learning ground LPADs starting from a set of interpretations annotated with their probability. We present the system ALLPAD for solving this problem. ALLPAD modifies the previous system LLPAD in order to tackle real world learning problems more effectively. This is achieved by looking for an approximate solution rather than a perfect one. A number of experiments have been performed on real and artificial data for evaluating ALLPAD, showing the feasibility of the approach. Editors: Stephen Muggleton, Ramon Otero, Simon Colton.     

Parameter Estimation in Stochastic Logic Programs

Stochastic logic programs (SLPs) are logic programs with parameterised clauses which define a log-linear distribution over refutations of goals. The log-linear distribution provides, by marginalisation, a distribution over variable bindings, allowing SLPs to compactly represent quite complex distributions.We analyse the fundamental statistical properties of SLPs addressing issues concerning infinite derivations, 'unnormalised SLPs and impure SLPs. After detailing existing approaches to parameter estimation for log-linear models and their application to SLPs, we present a new algorithm called failure-adjusted maximisation (FAM). FAM is an instance of the EM algorithm that applies specifically to normalised SLPs and provides a closed-form for computing parameter updates within an iterative maximisation approach. We empirically show that FAM works on some small examples and discuss methods for applying it to bigger problems.     

一种自顶向下和自底向上相结合的ILP算法

归纳逻辑程序设计(ILP)是机器学习的一个重要分支,给定一个样例集和相关背景知识,ILP研究如何构建与其相一致的逻辑程序,这些逻辑程序由有限一阶子句组成。文章描述了一种综合当前一些ILP方法多方面优势的算法ICCR,ICCR溶合了以FOIL为代表的自顶向下搜索策略和以GOLEM为代表的自底向上搜索策略,并能根据需要发明新谓词、学习递归逻辑程序,对比实验表明,对相同的样例及背景知识,ICCR比FOIL和GOLEM能学到精度更高的目标逻辑程序。     

概率逻辑模型与学习研究进展

近年来，概率逻辑学习研究取得了很大进展，已经提出各种不同的形式化方法和学习方法，包括概率关系模（PRMs）、贝叶斯逻辑程序（BLPs）、逻辑贝叶斯网络（LBNs）和随机逻辑程序（SLPs）等。文章重点介绍了贝叶斯网络与一阶逻辑的结合，并以PRMs、BLPs和LBNs为例，描述了基于贝叶斯网络的概率逻辑模型（PLMs）的知识表示方法，给出了此类PLMs一般使用的参数估计方法和结构学习方法，并给出了建议的研究方向。     

Modeling and verifying probabilistic Multi-Agent Systems using knowledge and social commitments

Multi-Agent Systems (MASs) have long been modeled through knowledge and social commitments independently. In this paper, we present a new method that merges the two concepts to model and verify MASs in the presence of uncertainty. To express knowledge and social commitments simultaneously in uncertain settings, we define a new multi-modal logic called Probabilistic Computation Tree Logic of Knowledge and Commitments (PCTL^kc in short) which combines two existing probabilistic logics namely, probabilistic logic of knowledge PCTLK and probabilistic logic of commitments PCTLC. To model stochastic MASs, we present a new version of interpreted systems that captures the probabilistic behavior and accounts for the communication between interacting components. Then, we introduce a new probabilistic model checking procedure to check the compliance of target systems against some desirable properties written in PCTL^kc and report the obtained verification results. Our proposed model checking technique is reduction-based and consists in transforming the problem of model checking PCTL^kc into the problem of model checking a well established logic, namely PCTL. So doing provides us with the privilege of re-using the PRISM model checker to implement the proposed model checking approach. Finally, we demonstrate the effectiveness of our approach by presenting a real case study. This framework can be considered as a step forward towards closing the gap of capturing interactions between knowledge and social commitments in stochastic agent-based systems.     

GENEX: a tool for testing in ILP

Inductive Logic Programming (ILP) is a field of research in which logic programs are synthesized (learned) from examples. There is a need for a variety of large datasets to evaluate ILP learners. The paper describes an example generator program GEN EX that provides the user with a language in which to describe large sets of structured examples. GEN EX is available on the WWW. Copyright © 2001 John Wiley & Sons, Ltd.     

Generalized ordering-search for learning directed probabilistic logical models

Recently, there has been an increasing interest in directed probabilistic logical models and a variety of formalisms for describing such models has been proposed. Although many authors provide high-level arguments to show that in principle models in their formalism can be learned from data, most of the proposed learning algorithms have not yet been studied in detail. We introduce an algorithm, generalized ordering-search, to learn both structure and conditional probability distributions (CPDs) of directed probabilistic logical models. The algorithm is based on the ordering-search algorithm for Bayesian networks. We use relational probability trees as a representation for the CPDs. We present experiments on a genetics domain, blocks world domains and the Cora dataset. Editors: Stephen Muggleton, Ramon Otero, Simon Colton.     

A new approach to hybrid probabilistic logic programs

This paper presents a novel revision of the framework of Hybrid Probabilistic Logic Programming, along with a complete semantics characterization, to enable the encoding of and reasoning about real-world applications. The language of Hybrid Probabilistic Logic Programs framework is extended to allow the use of non-monotonic negation, and two alternative semantical characterizations are defined: stable probabilistic model semantics and probabilistic well-founded semantics. These semantics generalize the stable model semantics and well-founded semantics of traditional normal logic programs, and they reduce to the semantics of Hybrid Probabilistic Logic programs for programs without negation. It is the first time that two different semantics for Hybrid Probabilistic Programs with non-monotonic negation as well as their relationships are described. This proposal provides the foundational grounds for developing computational methods for implementing the proposed semantics. Furthermore, it makes it clearer how to characterize non-monotonic negation in probabilistic logic programming frameworks for commonsense reasoning. An erratum to this article can be found at     

Compressing probabilistic Prolog programs

ProbLog is a recently introduced probabilistic extension of Prolog (De Raedt, et al. in Proceedings of the 20th international joint conference on artificial intelligence, pp. 2468–2473, 2007). A ProbLog program defines a distribution over logic programs by specifying for each clause the probability that it belongs to a randomly sampled program, and these probabilities are mutually independent. The semantics of ProbLog is then defined by the success probability of a query in a randomly sampled program. This paper introduces the theory compression task for ProbLog, which consists of selecting that subset of clauses of a given ProbLog program that maximizes the likelihood w.r.t. a set of positive and negative examples. Experiments in the context of discovering links in real biological networks demonstrate the practical applicability of the approach. Editors: Stephen Muggleton, Ramon Otero, Simon Colton.     

The Variable Precision Rough Set Inductive Logic Programming Model and Strings

The Variable Precision Rough Set Inductive Logic Programming model (VPRSILP model) extends the Variable Precision Rough Set (VPRS) model to Inductive Logic Programming (ILP). The generic Rough Set Inductive Logic Programming (gRS-ILP) model provides a framework for ILP when the setting is imprecise and any induced logic program will not be able to distinguish between certain positive and negative examples. The gRS-ILP model is extended in this paper to the VPRSILP model by including features of the VPRS model. The VPRSILP model is applied to strings and an illustrative experiment on transmembrane domains in amino acid sequences is presented.     

人工智能科学中的概率逻辑

人工智能科学，从其诞生之日起便与逻辑学密不可分。本文首先对逻辑学的分类、相互关系以及泛逻辑的概念等进行了讨论，并对人工智能中逻辑学的应用及发展进行了必要的分析。然后讲述了逻辑学与概率论两大理论基础之上的不确定性推理方法——概率逻辑，重点研究了二值概率逻辑与三值概率逻辑。最后阐述了概率逻辑在人工智能科学中的应用以及对它的思考。     

基于归纳逻辑程序设计的学习方法及其实现的研究

归纳逻辑程序设计是机器学习领域中的一个新方法，它研究的是从实例和背景知识进行逻辑程序（新知识）的构造．本文介绍了归纳逻辑程序设计的基本理论和方法，并介绍了这种学习方法在专家系统中的应用情况．     

Borel型概率计量逻辑

视全体赋值之集为通常乘积拓扑空间,利用该空间上的Borel概率测度在二值命题逻辑中引入了公式的概率真度概念.该方法既克服了计量逻辑学要求赋值集上的概率测度必须为均匀概率测度的无穷可数乘积的局限,又弥补了概率逻辑学只讲局部而缺乏整体性的不足;证明了计量逻辑学中公式的真度、随机真度以及概率逻辑学中公式的概率等概念都可作为本文提出的概率真度的特例而纳入到统一的框架中,从而实现了计量逻辑学与概率逻辑学的融合与统一;证明了逻辑闭理论与赋值空间中的拓扑闭集是一一对应的以及概率真度函数与赋值空间上的Borel概率测度是一样多的等若干结论;本文的第4节给出了公式的概率真度的公理化定义,证明了公式集上满足Kolmogorov公理的任一[0,1]值函数均可由赋值空间上的某Borel概率测度按本文的方法所表出,从而建立了二值命题逻辑框架下的概率计量逻辑的理论体系.     

Borel probabilistic and quantitative logic

The present paper introduces the notion of the probabilistic truth degree of a formula by means of Borel probability measures on the set of all valuations,endowed with the usual product topology,in classical two-valued propositional logic.This approach not only overcomes the limitations of quantitative logic,which require the probability measures on the set of all valuations to be the countably infinite product of uniform probability measures,but also remedies the drawback that probability logic behaves onl...     

PRL: A probabilistic relational language

In this paper, we describe the syntax and semantics for a probabilistic relational language (PRL). PRL is a recasting of recent work in Probabilistic Relational Models (PRMs) into a logic programming framework. We show how to represent varying degrees of complexity in the semantics including attribute uncertainty, structural uncertainty and identity uncertainty. Our approach is similar in spirit to the work in Bayesian Logic Programs (BLPs), and Logical Bayesian Networks (LBNs). However, surprisingly, there are still some important differences in the resulting formalism; for example, we introduce a general notion of aggregates based on the PRM approaches. One of our contributions is that we show how to support richer forms of structural uncertainty in a probabilistic logical language than have been previously described. Our goal in this work is to present a unifying framework that supports all of the types of relational uncertainty yet is based on logic programming formalisms. We also believe that it facilitates understanding the relationship between the frame-based approaches and alternate logic programming approaches, and allows greater transfer of ideas between them. Editors: Hendrik Blockeel, David Jensen and Stefan Kramer An erratum to this article is available at .     

Dimensional variation propagation analysis in straight-build mechanical assemblies using a probabilistic approach

Product quality in mechanical assemblies is determined by controlling the propagation of manufacturing variations as the structure is built. This paper focuses on straight-build assembly and uses a probabilistic approach to analyse the influence of component variation on the eccentricity of the build. Connective models are used to predict assembly variations arising from individual component variations, and a probabilistic approach is used to calculate the probability density function (pdf) for the eccentricity of the build. The probabilistic approach considers three different straight-build scenarios: (i) direct build; (ii) best build; and (iii) worst build, for two-dimensional “axi-symmetric” assemblies. The probabilistic approach is much more efficient than Monte Carlo simulation. The paper also uses numerical examples to investigate the accuracy of the probabilistic approach in comparison to Monte Carlo simulation.     

Performance analysis of probabilistic timed automata using digital clocks

Probabilistic timed automata, a variant of timed automata extended with discrete probability distributions, is a modelling formalism suitable for describing formally both nondeterministic and probabilistic aspects of real-time systems, and is amenable to model checking against probabilistic timed temporal logic properties. However, the previously developed verification algorithms either suffer from high complexity, give only approximate results, or are restricted to a limited class of properties. In the case of classical (non-probabilistic) timed automata it has been shown that for a large class of real-time verification problems correctness can be established using an integral model of time (digital clocks) as opposed to a dense model of time. Based on these results we address the question of under what conditions digital clocks are sufficient for the performance analysis of probabilistic timed automata and show that this reduction is possible for an important class of systems and properties including probabilistic reachability and expected reachability. We demonstrate the utility of this approach by applying the method to the performance analysis of three probabilistic real-time protocols: the dynamic configuration protocol for IPv4 link-local addresses, the IEEE 802.11 wireless local area network protocol and the IEEE 1394 FireWire root contention protocol.

Model checking probabilistic social commitments for intelligent agent communication

Interaction among autonomous agents in Multi-Agent Systems (MASs) is a key aspect for agents to coordinate with one another. Social approaches, as opposed to the mental approaches, have recently received a considerable attention in the area of agent communication. They exploit observable social commitments to develop a verifiable formal semantics through which communication protocols can be specified. Developing and implementing algorithmic model checking for social commitments have been recently addressed. However, model checking social commitments in the presence of uncertainty is yet to be investigated.In this paper, we propose a model checking technique for verifying social commitments in uncertain settings. Social commitments are specified in a modal logical language called Probabilistic Computation Tree Logic of Commitments (PCTLC). The modal logic PCTLC extends PCTL, the probabilistic extension of CTL, with modalities for commitments and their fulfillments. The proposed verification method is a reduction-based model checking technique to the model checking of PCTL. The technique is based upon a set of reduction rules that translate PCTLC formulae to PCTL formulae to take benefit of existing model checkers such as PRISM. Proofs that confirm the soundness of the reduction technique are presented. We also present rules that transform our new version of interpreted systems into models of Markov Decision Processes (MDPs) to be suitable for the PRISM tool. We implemented our approach on top of the PRISM model checker and verified some given properties for the Oblivious Transfer Protocol from the cryptography domain. Our simulation demonstrates the effectiveness of our approach in verifying and model checking social commitments in the presence of uncertainty. We believe that the proposed formal verification technique will advance the literature of social commitments in such a way that not only representing social commitments in uncertain settings is doable, but also verifying them in such settings becomes achievable.