The dynamics of default reasoning

In this paper we study default reasoning from a dynamic, agent-oriented, semantics-based point of view. In a formal framework used to specify and to reason about rational agents, we introduce actions that model the (attempted) jumping to conclusions that is a fundamental part of reasoning by default. Application of such an action consists of three parts. First it is checked whether the formula that the agent tries to jump to is a default, thereafter it is checked whether the default formula can consistently be incorporated by the agent, and if this is the case the formula is included in the agent's beliefs. As for all actions in our framework, we define the ability and opportunity of agents to apply these actions, and the states of affairs following application. To formalise formulae being defaults, we introduce the modality of common possibility. This modality is related to, but not reducible to, the notions of common knowledge and ‘everybody knows’-knowledge. To model the qualitative difference that exists between hard, factual knowledge and beliefs derived by default, we employ different modalities to represent these concepts, thus combining knowledge, beliefs, and defaults in one framework. Based on the concepts used to model the default reasoning of agents, we look into the dynamics of the supernormal fragment of default logic. We show in particular that by sequences of jumps to conclusions agents can end up with extensions in the sense of default logic of their belief.     

Nonmonotonic reasoning as prioritized argumentation

This paper proposes a formalism for nonmonotonic reasoning based on prioritized argumentation. We argue that nonmonotonic reasoning in general can be viewed as selecting monotonic inferences by a simple notion of priority among inference rules. More importantly, these types of constrained inferences can be specified in a knowledge representation language where a theory consists of a collection of rules of first order formulas and a priority among these rules. We recast default reasoning as a form of prioritized argumentation and illustrate how the parameterized formulation of priority may be used to allow various extensions and modifications to default reasoning. We also show that it is possible, but more difficult, to express prioritized argumentation by default logic: Even some particular forms of prioritized argumentation cannot be represented modularly by defaults under the same language     

A Default Logic Based Framework for Context-Dependent Reasoning with Lexical Knowledge

Lexical knowledge is increasingly important in information systems—for example in indexing documents using keywords, or disambiguating words in a query to an information retrieval system, or a natural language interface. However, it is a difficult kind of knowledge to represent and reason with. Existing approaches to formalizing lexical knowledge have used languages with limited expressibility, such as those based on inheritance hierarchies, and in particular, they have not adequately addressed the context-dependent nature of lexical knowledge. Here we present a framework, based on default logic, called the dex framework, for capturing context-dependent reasoning with lexical knowledge. Default logic is a first-order logic offering a more expressive formalisation than inheritance hierarchies: (1) First-order formulae capturing lexical knowledge about words can be inferred; (2) Preferences over formulae can be based on specificity, reasoning about exceptions, or explicit priorities; (3) Information about contexts can be reasoned with as first-order formulae formulae; and (4) Information about contexts can be derived as default inferences. In the dex framework, a word for which lexical knowledge is sought is called a query word. The context for a query word is derived from further words, such as words in the same sentence as the query word. These further words are used with a form of decision tree called a context classification tree to identify which contexts hold for the query word. We show how we can use these contexts in default logic to identify lexical knowledge about the query word such as synonyms, antonyms, specializations, meronyms, and more sophisticated first-order semantic knowledge. We also show how we can use a standard machine learning algorithm to generate context classification trees.     

Default reasoning and belief revision: A syntax-independent approach

As an important variant of Reiter‘s default logic.Poole(1988) developed a nonmonotonic reasoning framework in the classical first-order language,Brewka and Nebel extended Poole‘s approach in order to enable a representation of priorities between defaults.In this paper a general framework for default reasoning is presented,which can be viewed as a generalization of the three approaches above.It is proved that the syntax-independent default reasoning in this framework is identical to the general belief revision operation introduced by Zhang et al.(1997).This esult provides a solution to the problem whether there is a correspondence between belief revision and default logic for the infinite case .As a by-product,an answer to the the question,raised by Mankinson and Gaerdenfors(1991),is also given about whether there is a counterpart contraciton in nonmonotonic logic.     

Know means no: Incorporating knowledge into discrete-event controlsystems

Modal logic is introduced into the modeling of discrete-event systems. Analysis within this framework includes formal reasoning about what supervisors know or do not know about a given system. This model can be used to develop control strategies that solve decentralized discrete-event control problems. When a problem cannot be solved using fully decentralized supervisors, reasoning about knowledge may provide guidelines for incorporating communication and pooled information into the model     

基于EFTPN不确定性时间信息的线性推理方法及在列车群分析中的应用

针对列车群行为分析中的不确定性时间信息推理问题，结合线性逻辑和扩展模糊时间Petri网（EFTPN）等理论，提出了一种基于EFTPN的线性推理方法．该方法不但能对不确定性时间信息进行精确的、定量的建模和推理；而且效率高，可在线性时间复杂度内完成推导；另外其适用面广，可用于解决其它领域内时间推理和验证问题．     

DEFAULT LOGICS: A UNIFIED VIEW

Default logic has been introduced for handling reasoning with incomplete knowledge. It has been widely studied, and various definitions have been proposed for it. Most of the variants have been defined by means of fixed points of some operator. We propose here another approach, which is based on a study of the way in which general rules with exceptions, used in a default reasoning process, can contradict one another. We then isolate sets of noncontradicting rules, as large as possible in order to exploit as much information as possible, and construct, for each of these sets of rules, the set of conclusions that can be deduced from it. We show that our framework encompasses most of the existing variants of default logic, allowing those variants to be compared from a knowledge representation point of view. Our approach also enables us to provide an operational definition of extensions in some interesting cases. Proof-theoretical and semantical aspects are investigated.     

不协调知识的缺省推理

提出了一个新的缺省推理理论,称为双缺省理论,使得缺省逻辑在四值语义下能够同时处理不协调的知识而不导致扩张的平凡性.为此,定义了命题公式的正变换和负变换,以便分离一个文字与其否定的语义联系.大多数关于缺省逻辑的定理都可以在双缺省逻辑下重建,证明了双缺省逻辑是缺省逻辑在不协调情形下的一般化.提供了一种方法使得超协调逻辑能够获得类似经典逻辑的推理能力.     

An Interpretation of Default Logic in Minimal Temporal Epistemic Logic

When reasoning about complex domains, where information available is usually only partial, nonmonotonic reasoning can be an important tool. One of the formalisms introduced in this area is Reiter's Default Logic (1980). A characteristic of this formalism is that the applicability of default (inference) rules can only be verified in the future of the reasoning process. We describe an interpretation of default logic in temporal epistemic logic which makes this characteristic explicit. It is shown that this interpretation yields a semantics for default logic based on temporal epistemic models. A comparison between the various semantics for default logic will show the differences and similarities of these approaches and ours.     

Outlier detection for simple default theories

It was noted recently that the framework of default logics can be exploited for detecting outliers. Outliers are observations expressed by sets of literals that feature unexpected properties. These observations are not explicitly provided in input (as it happens with abduction) but, rather, they are hidden in the given knowledge base. Unfortunately, in the two related formalisms for specifying defaults — Reiter's default logic and extended disjunctive logic programs — the most general outlier detection problems turn out to lie at the third level of the polynomial hierarchy. In this note, we analyze the complexity of outlier detection for two very simple classes of default theories, namely NU and DNU, for which the entailment problem is solvable in polynomial time. We show that, for these classes, checking for the existence of an outlier is anyway intractable. This result contributes to further showing the inherent intractability of outlier detection in default reasoning.     

DKLFRS:A Default Knowledge Logical Framework Representation System

The traditional resasoning system based on first order predicate logic can‘t represent and handle default knowledge,This paper presents a logical framework representation approach for default reasoning.Based on Mixed SLDNF-resolution,a nonmonotonic reasoning system has been constructed.     

基于次协调逻辑的空战决策支持系统研究

为了解决传统逻辑推理在引入两个相互矛盾的事实时,推理将停止,继而提供不出有价值的结论的问题,给出了基于次协调逻辑理论的一种推理方法.在此基础上构造了次协调逻辑辅助推理空战决策支持系统,在传统逻辑推理因矛盾停止时,启动次协调推理,使得空战决策支持能够在矛盾中求协调,避免了系统陷入平庸状态.在某型空战模拟器上使用取得了初步成效,从仿真结果看具有次协调逻辑辅助推理的空战决策支持系统对复杂的空战环境具有良好的适应性.     

Reasoning with Sets of Defaults in Default Logic

We present a general approach for representing and reasoning with sets of defaults in default logic, focusing on reasoning about preferences among sets of defaults. First, we consider how to control the application of a set of defaults so that either all apply (if possible) or none do (if not). From this, an approach to dealing with preferences among sets of default rules is developed. We begin with an ordered default theory , consisting of a standard default theory, but with possible preferences on sets of rules. This theory is transformed into a second, standard default theory wherein the preferences are respected. The approach differs from other work, in that we obtain standard default theories and do not rely on prioritized versions of default logic. In practical terms this means we can immediately use existing default logic theorem provers for an implementation. Also, we directly generate just those extensions containing the most preferred applied rules; in contrast, most previous approaches generate all extensions, then select the most preferred. In a major application of the approach, we show how semimonotonic default theories can be encoded so that reasoning can be carried out at the object level. With this, we can reason about default extensions from within the framework of a standard default logic. Hence one can encode notions such as skeptical and credulous conclusions, and can reason about such conclusions within a single extension.     

Bilattices and Reasoning in Artificial Intelligence: Concepts and Foundations

The past few decades have seen a resurgence ofreasoning techniques in artificial intelligenceinvolving both classical and non-classical logics. Inhis paper, ``Multi-valued Logics: A Uniform Approach toReasoning in Artificial Intelligence', Ginsberg hasshown that through the use of bilattices,several reasoning techniques can be unified under asingle framework. A bilattice is a structure that canbe viewed as a class of truth values that canaccommodate incomplete and inconsistent informationand in certain cases default information. Inbilattice theory, knowledge is ordered along twodimensions: truth/falsity and certainty/uncertainty. By defining the corresponding bilattices as truthspaces, Ginsberg has shown that the same theoremprover can be used to simulate reasoning in firstorder logic, default logic, prioritized default logicand assumption truth maintenance system. Although thisis a significant contribution, Ginsberg's paper waslengthy and involved. This paper summarizes some ofthe essential concepts and foundations of bilatticetheory. Furthermore, it discusses the connections ofbilattice theory and several other existingmulti-valued logics such as the various three-valuedlogics and Belnap's four-valued logic. It is notedthat the set of four truth values in Belnap's logicform a lattice structure that is isomorphic to thesimplest bilattice. Subsequently, Fitting proposed aconflation operation that can be used to selectsub-sets of truth values from this and otherbilattices. This method of selecting sub-sets oftruth values provides a means for identifyingsub-logic in a bilattice.     

Default logic as a query language

Research in nonmonotonic reasoning has focused largely on the idea of representing knowledge about the world via rules that are generally true but can be defeated. Even if relational databases are nowadays the main tool for storing very large sets of data, the approach of using nonmonotonic AI formalisms as relational database query languages has been investigated to a much smaller extent. In this work, we propose a novel application of Reiter's default logic by introducing a default query language (DQL) for finite relational databases, which is based on default rules. The main result of this paper is that DQL is as expressive as SO_∃∀ the existential-universal fragment of second-order logic. This result is not only of theoretical importance: We exhibit queries-which are useful in practice-that can be expressed with DQL and cannot with other query languages based on nonmonotonic logics such as DATALOG with negation under the stable model semantics. In particular, we show that DQL is well-suited for diagnostic reasoning     

Modal nonmonotonic logics demodalized

The study of the relation between default logic and modal nonmonotonic logics has been mostly concerned with the task of translating default logic to autoepistemic or some other modal nonmonotonic logic. Here, we discuss the reverse problem, that is, the possibility of translating modal nonmonotonic logics into default-type systems formulated in the language without modal operators. To this end, we first consider a reformulation of both formalisms in terms of what we call default consequence relations. These consequence relations turn out to be especially suitable for studying default and modal nonmonotonic reasoning. We show, in particular, that different kinds of such reasoning naturally correspond to different structural rules imposed on default consequence relations. Our main results also demonstrate that all modal nonmonotonic objects considered have exact nonmodal counterparts. As an immediate consequence of these results, we obtain a method of reducing common types of modal nonmonotonic reasoning to nonmodal default reasoning.     

Restricted semantics for default reasoning

In nonmonotonic reasoning there are the problems of inconsistency and incoherence in general, and in default reasoning there may be only one trivial extension or no extension in special. We propose the restricted semantics of four-valued logic for default reasoning to resolve the problems of inconsistency and incoherence and in the meantime retain classical extensions in the presence of consistency and coherency. The restricted semantics can maintain both the expressiveness and reasoning ability of default logic. We provide a transformation approach to compute the restricted extensions by reducing them into classical ones.