Probabilistic Default Reasoning with Conditional Constraints

We present an approach to reasoning from statistical and subjective knowledge, which is based on a combination of probabilistic reasoning from conditional constraints with approaches to default reasoning from conditional knowledge bases. More precisely, we introduce the notions of z-, lexicographic, and conditional entailment for conditional constraints, which are probabilistic generalizations of Pearl's entailment in system Z, Lehmann's lexicographic entailment, and Geffner's conditional entailment, respectively. We show that the new formalisms have nice properties. In particular, they show a similar behavior as reference-class reasoning in a number of uncontroversial examples. The new formalisms, however, also avoid many drawbacks of reference-class reasoning. More precisely, they can handle complex scenarios and even purely probabilistic subjective knowledge as input. Moreover, conclusions are drawn in a global way from all the available knowledge as a whole. We then show that the new formalisms also have nice general nonmonotonic properties. In detail, the new notions of z-, lexicographic, and conditional entailment have similar properties as their classical counterparts. In particular, they all satisfy the rationality postulates proposed by Kraus, Lehmann, and Magidor, and they have some general irrelevance and direct inference properties. Moreover, the new notions of z- and lexicographic entailment satisfy the property of rational monotonicity. Furthermore, the new notions of z-, lexicographic, and conditional entailment are proper generalizations of both their classical counterparts and the classical notion of logical entailment for conditional constraints. Finally, we provide algorithms for reasoning under the new formalisms, and we analyze its computational complexity.     

Deductive,inductive and analogical reasoning in legal decision support systems

In this paper we provide an overview of a number of fundamental reasoning formalisms in artificial intelligence which can and have been used in modelling legal reasoning. We describe deduction, induction and analogical reasoning formalisms, and show how they can be used separately to model legal reasoning. We argue that these formalisms can be used together to model legal reasoning more accurately, and describe a number of attempts to integrate the approaches.     

经验逻辑：一种非单调逻辑的统一形式

人的常识推理是一种充满经验性知识的累积过程,而经验推理具有非单调性。本文提出一种关于典型与例外的经验逻辑,特别研究它的非单调性,它提供了一个现存的主要非单调逻辑的统一基础,这是通过一种类似的规则把它们翻译成经验逻辑获得的。因此,经验逻辑给出了一类更一般而且直观的非单调推理形式。     

Reasoning about Minimal Knowledge in Nonmonotonic Modal Logics

We study the problem of embedding Halpern and Moses's modal logic of minimal knowledge states into two families of modal formalism for nonmonotonic reasoning, McDermott and Doyle's nonmonotonic modal logics and ground nonmonotonic modal logics. First, we prove that Halpern and Moses's logic can be embedded into all ground logics; moreover, the translation employed allows for establishing a lower bound (3p) for the problem of skeptical reasoning in all ground logics. Then, we show a translation of Halpern and Moses's logic into a significant subset of McDermott and Doyle's formalisms. Such a translation both indicates the ability of Halpern and Moses's logic of expressing minimal knowledge states in a more compact way than McDermott and Doyle's logics, and allows for a comparison of the epistemological properties of such nonmonotonic modal formalisms.     

Reasoning under uncertainty for plant disease diagnosis

The present work describes an operational knowledge-based system able to reason with uncertain knowledge, by using methodologies and formalisms that provide for representation of facts and rules with various degrees of certainty and precision. The user interface is windows based, and its design allows high flexibility both in describing the facts in the knowledge base and in adapting the reasoning mechanism. It can therefore be used to evaluate user-generated hypotheses on plant disorders and diagnostic scenarios, as well as provide an environment for education and training in phytopathology.     

A causal approach to nonmonotonic reasoning

We introduce logical formalisms of production and causal inference relations based on input/output logics of Makinson and Van der Torre [J. Philos. Logic 29 (2000) 383–408]. These inference relations will be assigned, however, both standard semantics (giving interpretation to their rules), and natural nonmonotonic semantics based on the principle of explanation closure. The resulting nonmonotonic formalisms will be shown to provide a logical representation of abductive reasoning, and a complete characterization of causal nonmonotonic reasoning from McCain and Turner [Proc. AAAI-97, Providence, RI, 1997, pp. 460–465]. The results of the study suggest production and causal inference as general nonmonotonic formalisms providing an alternative representation for a significant part of nonmonotonic reasoning.     

事件本体中的动作推理研究

事件是随时间变化而变化的具体事实,事件是由动作、时间及其它要素组成,动作是事件定义中的主要构成部分.在面向事件的知识库系统中,关于动作的推理研究一直是重要的研究课题之一.现有的动作推理形式化系统旨在描述和推理现实世界中状态的变化,忽略了时间要素对推理过程的影响.针对这种不足,本文在描述逻辑的基础上扩充了一个Action-TBox和一个Action-ABox,并将事件本体中的动作要素和时间要素相结合,形式化定义了动作的一个三元组表示方式以及多种时间构造算子,用以刻画组合动作的发生过程,在此基础上研究了事件本体中关于动作的几种推理服务.     

Expressiveness and tractability in knowledge representation and reasoning1

A fundamental computational limit on automated reasoning and its effect on knowledge representation is examined. Basically, the problem is that it can be more difficult to reason correctly with one representational language than with another and, moreover, that this difficulty increases dramatically as the expressive power of the language increases. This leads to a tradeoff between the expressiveness of a representational language and its computational tractability. Here we show that this tradeoff can be seen to underlie the differences among a number of existing representational formalisms, in addition to motivating many of the current research issues in knowledge representation.     

Encompassing full nonmonotonicity within belief modification activity

 In this paper, starting from an analysis of the general activity of belief modification, the concept of full nonmonotonicity is introduced and discussed. Such concept is based on the identification of two different types of nonmonotonicity and includes all the cases of belief modification that may occur in reasoning activity. This distinction cannot be encompassed by the most known nonmonotonic logic formalisms nor by the classical view of conditioning and belief revision axiomatically set up by Gardenfors [9]. A conceptual model able to correctly capture fully nonmonotonic reasoning is discussed: such model includes an explicit representation for the concepts of uncertainty about the applicability of a piece of knowledge and of reasoning attitude. Finally, the issue of formalizing fully nonmonotonic reasoning is discussed and preliminary formalization proposals are introduced.     

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.     

国家知识基础设施中的数学知识表示

数学知识表示是知识表示中的一个重要方面,是数学知识检索、自动定理机器证明、智能教学系统等的基础.根据在设计NKI(national knowledge infrastructure)的数学知识表示语言中遇到的问题,并在讨论了数学对象的本体论假设的基础上提出了两种数学知识的表示方法:一种是以一个逻辑语言上的公式为属性值域的描述逻辑;另一种是以描述逻辑描述的本体为逻辑语言的一部分的一阶逻辑.在前者的表示中,如果对公式不作任何限制,那么得到的知识库中的推理不是可算法化的;在后者的表示中,以描述逻辑描述的本体中的推理是可算法化的,而以本体为逻辑语言的一部分的一阶逻辑所表示的数学知识中的推理一般是不可算法化的.因此,在表示数学知识时,需要区分概念性的知识(本体中的知识)和非概念性的知识(用本体作为语言表示的知识).框架或者描述逻辑可以表示和有效地推理概念性知识,但如果将非概念性知识加入到框架或知识库中,就可能使得原来可以有效推理的框架所表示的知识库不存在有效的推理算法,甚至不存在推理算法.为此,建议在表示数学知识时,用框架或描述逻辑来表示概念性知识;然后,用这样表示的知识库作为逻辑语言的一部分,以表示非概念性知识.     

Legal modeling and automated reasoning with ON-LINE

In this paper we present a modeling approach to legal knowledge systems and its computational realization in the ON-LINE architecture. ON-LINE has modules for modeling legal sources, for storing and retrieving legal information and for reasoning with legal knowledge. The approach takes two perspectives: domain and task. In the domain perspective, a core ontology divides legal knowledge into five major categories: normative, world, responsibility, reactive and creative. For the normative knowledge, which is most typical of legal domains, we developed a new representation and inference formalisms which are an alternative to deontic logic. For the world knowledge, we argue for using a terminological knowledge representation language. The structure of the ontology is not a taxonomy, but a network of dependencies between the categories. These dependencies reflect the global structure of arguments in legal reasoning. In the task perspective, we followed a top-down approach using the CommonKADS modeling library. Design, planning and assessment were identified as typical tasks in the legal domain. For assessment, a model was specified and implemented.     

Event calculus and temporal action logics compared

We compare the event calculus and temporal action logics (TAL), two formalisms for reasoning about action and change. We prove that, if the formalisms are restricted to integer time, inertial fluents, and relational fluents, and if TAL action type specifications are restricted to definite reassignment of a single fluent, then the formalisms are not equivalent. We argue that equivalence cannot be restored by using more general TAL action type specifications. We prove however that, if the formalisms are further restricted to single-step actions, then they are logically equivalent.     

The Situation Calculus: A Case for Modal Logic

The situation calculus is one of the most established formalisms for reasoning about action and change. In this paper we will review the basics of Reiter’s version of the situation calculus, show how knowledge and time have been addressed in this framework, and point to some of the weaknesses of the situation calculus with respect to time. We then present a modal version of the situation calculus where these problems can be overcome with relative ease and without sacrificing the advantages of the original.     

The Logical Approach to Temporal Reasoning

Temporal reasoning started to be considered as a subject of study in artificial intelligence in the late 1970's. Since then several ways to represent and use temporal knowledge have been suggested. As a result of that, there are several formalisms capable of coping with temporal notions in some way or other. They range from isolated proposals to complex systems where the temporal aspect is used together with other important features for the task of modelling an intelligent agent. The purposes of this article are to summarize logic-based temporal reasoning research and give a glance on the different research tracks envisaging future lines of research. It is intended to be useful to those who need to be involved in systems having these characteristics and also an occasion to present newcomers some problems in the area that still waits for a solution.     

IKARUS-Onto: a methodology to develop fuzzy ontologies from crisp ones

Fuzzy Ontologies comprise a relatively new knowledge representation paradigm that is being increasingly applied in application scenarios in which the treatment and utilization of vague or imprecise knowledge are important. However, the majority of research in the area has mostly focused on the development of conceptual formalisms for representing (and reasoning with) fuzzy ontologies, while the methodological issues entailed within the development process of such an ontology have been so far neglected. With that in mind, we present in this paper IKARUS-Onto, a comprehensive methodology for developing fuzzy ontologies from existing crisp ones that significantly enhances the effectiveness of the fuzzy ontology development process and the quality, in terms of accuracy, shareability and reusability, of the process’s output.     

gfp-模型的描述逻辑FLε的循环术语集推理

描述逻辑（DL）一族知识表示形式系统,是人工智能领域的一个热门研究方向。循环定义下描述逻辑系统的表达在许多情况下更符合人们的直觉,而且具有更强的表达力,是非循环定义下的描述逻辑系统不可代替的。首先给出描述逻辑系统FLε有最大不动点模型的证明,然后初步探讨基于最大不动点语义下描述逻辑系统FLε循环定义的包含关系推理算法,并给出算法的可靠性和完全性证明。     

Structural and probabilistic knowledge for abductive reasoning

Different ways of representing probabilistic relationships among the attributes of a domain ar examined, and it is shown that the nature of domain relationships used in a representation affects the types of reasoning objectives that can be achieved. Two well-known formalisms for representing the probabilistic among attributes of a domain. These are the dependence tree formalism presented by C.K. Chow and C.N. Liu (1968) and the Bayesian networks methodology presented by J. Pearl (1986). An example is used to illustrate the nature of the relationships and the difference in the types of reasoning performed by these two representations. An abductive type of reasoning objective that requires use of the known qualitative relationships of the domain is demonstrated. A suitable way to represent such qualitative relationships along with the probabilistic knowledge is given, and how an explanation for a set of observed events may be constituted is discussed. An algorithm for learning the qualitative relationships from empirical data using an algorithm based on the minimization of conditional entropy is presented