修正的逻辑程序知识库更新方法

基于逻辑程序的知识库更新方法研究的焦点在于处理知识库的冲突问题,但代价是更新时规则库增大很快,该文提出了“修正的逻辑程序知识库更新方法”,此种方法基于一种规范知识库更新的形式化方法—修正程序,此种更新方法不仅可以最大程度地减少更新时规则库的增大,也避免了重复工作和知识库信息的丢失,还可以同时满足“替换更新”和“丰富更新”。     

认知描述逻辑ALCKR＋：描述逻辑的一个非单调扩展

描述逻辑是语义Web的逻辑基础,是形式化表达领域知识的工具.但是描述逻辑只能表达单调推理,不能处理不完全知识.认知描述逻辑因其非单调特性和良好的时间复杂度等特点在处理不完全知识方面有较好的优势.本文在认知描述逻辑ALCK的基础上提出了新的认知描述逻辑语言ALCKR ,保留了描述逻辑原有的优点,加入传递角色属性,增强了表达能力,并通过认知查询拥有了非单调推理的能力.设计了ALCKR 的语法、语义以及表算法.     

Temporal Languages for Epistemic Programs

This paper adds temporal logic to public announcement logic (PAL) and dynamic epistemic logic (DEL). By adding a previous-time operator to PAL, we express in the language statements concerning the muddy children puzzle and sum and product. We also express a true statement that an agent’s beliefs about another agent’s knowledge flipped twice, and use a sound proof system to prove this statement. Adding a next-time operator to PAL, we provide formulas that express that belief revision does not take place in PAL. We also discuss relationships between announcements and the new knowledge agents thus acquire; such relationships are related to learning and to Fitch’s paradox. We also show how inverse programs and hybrid logic each can be used to help determine whether or not an arbitrary structure represents the play of a game. We then add a past-time operator to DEL, and discuss the importance of adding yet another component to the language in order to prove completeness.     

Temporalizing Epistemic Default Logic

We present an epistemic default logic, based on the metaphore of a meta-level architecture. Upward reflection is formalized by a nonmonotonic entailment relation, based on the objective facts that are either known or unknown at the object level. Then, the meta (monotonic) reasoning process generates a number of default-beliefs of object-level formulas. We extend this framework by proposing a mechanism to reflect these defaults down. Such a reflection is seen as essentially having a temporal flavour: defaults derived at the meta-level are projected as facts in a next object level state. In this way, we obtain temporal models for default reasoning in meta-level formalisms which can be conceived as labeled branching trees. Thus, descending the tree corresponds to shifts in time that model downward reflection, whereas the branching of the tree corresponds to ways of combining possible defaults. All together, this yields an operational or procedural semantics of reasoning by default, which admits one to reason about it by means of branching-time temporal logic. Finally, we define sceptical and credulous entailment relations based on these temporal models and we characterize Reiter extensions in our semantics.     

Epistemic Logic for Rule-Based Agents

The logical omniscience problem, whereby standard models of epistemic logic treat an agent as believing all consequences of its beliefs and knowing whatever follows from what else it knows, has received plenty of attention in the literature. But many attempted solutions focus on a fairly narrow specification of the problem: avoiding the closure of belief or knowledge, rather than showing how the proposed logic is of philosophical interest or of use in computer science or artificial intelligence. Sentential epistemic logics, as opposed to traditional possible worlds approaches, do not suffer from the problems of logical omniscience but are often thought to lack interesting epistemic properties. In this paper, I focus on the case of rule-based agents, which play a key role in contemporary AI research but have been neglected in the logical literature. I develop a framework for modelling monotonic, nonmonotonic and introspective rule-based reasoners which have limited cognitive resources and prove that the resulting models have a number of interesting properties. An axiomatization of the resulting logic is given, together with completeness, decidability and complexity results.     

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.     

逻辑程序的事实维护

事实是逻辑程序的重要组成部分,事实维护影响着整个逻辑程序的一致性和完整性,并能够促进和完善规则维护。论文在分析了人工进行维护操作的弊端后,对事实维护中可能出现的情况进行分类分析,提出了事实维护系统的框架,重点描述了预警检测子系统所扮演的核心作用。     

Strategies in Combined Learning via Logic Programs

We discuss the adoption of a three-valued setting for inductive concept learning. Distinguishing between what is true, what is false and what is unknown can be useful in situations where decisions have to be taken on the basis of scarce, ambiguous, or downright contradictory information. In a three-valued setting, we learn a definition for both the target concept and its opposite, considering positive and negative examples as instances of two disjoint classes. To this purpose, we adopt Extended Logic Programs (ELP) under a Well-Founded Semantics with explicit negation (WFSX) as the representation formalism for learning, and show how ELPs can be used to specify combinations of strategies in a declarative way also coping with contradiction and exceptions.Explicit negation is used to represent the opposite concept, while default negation is used to ensure consistency and to handle exceptions to general rules. Exceptions are represented by examples covered by the definition for a concept that belong to the training set for the opposite concept.Standard Inductive Logic Programming techniques are employed to learn the concept and its opposite. Depending on the adopted technique, we can learn the most general or the least general definition. Thus, four epistemological varieties occur, resulting from the combination of most general and least general solutions for the positive and negative concept. We discuss the factors that should be taken into account when choosing and strategically combining the generality levels for positive and negative concepts.In the paper, we also handle the issue of strategic combination of possibly contradictory learnt definitions of a predicate and its explicit negation.All in all, we show that extended logic programs under well-founded semantics with explicit negation add expressivity to learning tasks, and allow the tackling of a number of representation and strategic issues in a principled way.Our techniques have been implemented and examples run on a state-of-the-art logic programming system with tabling which implements WFSX.     

Logic Programs with Ordered Disjunction

Logic programs with ordered disjunction (LPODs) contain a new connective which allows representing alternative, ranked options for problem solutions in the heads of rules: A × B intuitively means that if possible A , but if A is not possible, then at least B . The semantics of logic programs with ordered disjunction is based on a preference relation on answer sets. We show how LPODs can be implemented using answer set solvers for normal programs. The implementation is based on a generator, which produces candidate answer sets and a tester which checks whether a given candidate is maximally preferred and produces a better candidate if it is not. We also discuss the complexity of reasoning tasks based on LPODs and possible applications.     

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.     

时序逻辑程序的模型检测

时序逻辑程序的形式化验证对提高程序的正确性具有重要意义。以投影时序逻辑的可执行子集、框架投影时序逻辑语言Framed Tempura为研究对象,使用命题投影时序逻辑描述Framed Tempura程序的性质,将程序p和性质Ф统一表示在投影时序逻辑中,模型检测需要判定p→Ф是否有效,可转化为判定p∧Ф是否不可满足,这可以通过构造p∧Ф的正则图加以解决。最后,给出了Framed Tempura程序的模型检测实例。     

Probabilistic Dynamic Epistemic Logic

In this paper I combine the dynamic epistemic logic ofGerbrandy (1999) with the probabilistic logic of Fagin and Halpern (1994). The resultis a new probabilistic dynamic epistemic logic, a logic for reasoning aboutprobability, information, and information change that takes higher orderinformation into account. Probabilistic epistemic models are defined, and away to build them for applications is given. Semantics and a proof systemis presented and a number of examples are discussed, including the MontyHall Dilemma.     

Consistency Property of Finite FC-Normal Logic Programs

Marek＇s forward-chaining construction is one of the important techniques for investigating the non-monotonic reasoning. By introduction of consistency property over a logic program, they proposed a class of logic programs, FC-normal programs, each of which has at least one stable model. However, it is not clear how to choose one appropriate consistency property for deciding whether or not a logic program is FC-normal. In this paper, we firstly discover that, for any finite logic programⅡ, there exists the least consistency property LCon（Ⅱ） overⅡ, which just depends onⅡitself, such that, Ⅱ is FC-normal if and only ifⅡ is FC-normal with respect to （w.r.t.） LCon（Ⅱ）. Actually, in order to determine the FC-normality of a logic program, it is sufficient to check the monotonic closed sets in LCon（Ⅱ） for all non-monotonic rules, that is LFC（Ⅱ）. Secondly, we present an algorithm for computing LFC（Ⅱ）. Finally, we reveal that the brave reasoning task and cautious reasoning task for FC-normal logic programs are of the same difficulty as that of normal logic programs.     

On Local StratifiabUity of Logic Programs and Databases

In this paper,we deal with the problem of verifying local stratifiability of logic programs anddatabases presented by Przymusinski.Necessary and sufficient conditions for the local stratifiability oflogic programs are presented and algorithms for performing the verification are developed.Finally,weprove that a database DB containing clauses with disjunctive consequents can be easily converted into alogic program P such that DB is locally stratified iff P is locally stratified.     

Approximating the Semantics of Logic Programs by Recurrent Neural Networks

In [1] we have shown how to construct a 3-layered recurrent neural network that computes the fixed point of the meaning function T_P of a given propositional logic program P, which corresponds to the computation of the semantics of P. In this article we consider the first order case. We define a notion of approximation for interpretations and prove that there exists a 3-layered feed forward neural network that approximates the calculation of T_P for a given first order acyclic logic program P with an injective level mapping arbitrarily well. Extending the feed forward network by recurrent connections we obtain a recurrent neural network whose iteration approximates the fixed point of T_P. This result is proven by taking advantage of the fact that for acyclic logic programs the function T_P is a contraction mapping on a complete metric space defined by the interpretations of the program. Mapping this space to the metric space R with Euclidean distance, a real valued function f_P can be defined which corresponds to T_P and is continuous as well as a contraction. Consequently it can be approximated by an appropriately chosen class of feed forward neural networks.