Regular disjunction-free default theories

In this paper, the class of regular disjunction-free default theories is introduced and investigated.A transformation from regular default theories to normal default theories is established. The initial theory andthe transformed theory have the same extensions when restricted to old variables. Hence, regular default theoriesenjoy some similar properties (e.g., existence of extensions, semi-monotonicity) as normal default theories. Then,a new algorithm for credulous reasoning of regular theories is developed. This algorithm runs in a time not morethan 0(1.45~n), where n is the number of defaults. In case of regular prerequisite-free or semi-2CNF defaulttheories, the credulous reasoning can be solved in polynomial time. However, credulous reasoning for semi-Horndefault theories is shown to be NP-complete although it is tractable for Horn default theories. Moreover, skepticalreasoning for regular unary default theories is co-NP-complete.     

Maximal consistent extensions of information systems relative to their theories

Knowledge encoded in information systems can be represented by different sets of rules generated by these systems. One can consider sets of deterministic, nondeterministic or probabilistic rules. Such sets of rules can be treated as theories of information systems. Any such a theory generated from a given information system corresponds to a subjective view on knowledge encoded in this information system. Such theories can be used for solving different problems. For example, the maximal consistent extensions of information systems were studied for synthesis of concurrent processes specified by information systems. In this approach, the maximal consistent extension of a given information system consists of all objects perceived by means of attributes which are consistent with the theory including all the so called true and realizable deterministic rules extracted from the original information system. In this paper, we report results on the maximal consistent extensions of information systems relative to some other theories of information systems, e.g., theories consisting of rules such as true and realizable inhibitory rules, true inhibitory rules, and true deterministic rules. We also discuss algorithmic problems related to the maximal consistent extensions. In particular, from the obtained results it follows that solutions based on these new sets of rules, e.g., on inhibitory rules can be of higher quality than in the case of deterministic rules.     

Constraints on extensions of a default theory

In this paper,the representability of a family of theories as the set of extensions of a default theory is studied.Firest,a new necessary condition is given for the representability by means of general default theories.then a sufficient one is presented.The families of theories represneted by default theories are also fully characterized.Finally,the paper gives an example of denumerable families of mutually inconsistent theories that are represented by a default theory but not by normal ones.     

A proof procedure for normal default theories

Recent research by Delgrande [6] and Geffner and Pearl [10] suggests two different semantic interpretations for normal defaults with one single representation as conditional sentences. However, they both need additional formal mechanisms for handling irrelevant information when their approaches are applied to formalising default reasoning. Delgrande in [5, 6] suggests two meta-strategies which he considers to be adequately strong to handle the orderings of defaults, and he claims they are equivalent. Furthermore, each of Delgrande's strategies is defined in terms of all sentences of the object language. In this paper, we shall prove that Delgrande's claim that his meta-strategies are equivalent is incorrect and that one of his meta-strategies can be reformulated within the framework of First Order Predicate Calculus (FOPC) and without having to consider every sentence of the object language. One advantage of such a reformalisation is its computational simplicity: to give an extension of a default theory there is only a need to consider those sentences which occur in the default theory under consideration rather than every sentence in the object language; furthermore, to provide a proof procedure for Delgrande's system as based on the meta-strategy we have formalised, one need only employ a FOPC proof procedure, rather than a conditional one.     

Some Results on Default Logic

In the previous paper,some important properties of extensions of general default theories were given.In order to further explore default logic,a characterization of extensions is presented.And a class of defaults,so-called Auto-compatible Default Theory,is also introduced.All these essentially develop the theories of Reiter and his followers.     

Priorities on defaults with prerequisites,and their application in treating specificity in terminological default logic

In a recent paper we have proposed terminological default logic as a formalism that combines means both for structured representation of classes and objects and for default inheritance of properties. The major drawback that terminological default logic inherits from general default logic is that it does not take precedence of more specific defaults over more general ones into account. This behavior has already been criticized in the general context of default logic, but it is all the more problematic in the terminological case where the emphasis lies on the hierarchical organization of concepts.The present paper addresses the problem of modifying terminological default logic such that more specific defaults are preferred. We assume that the specificity ordering is induced by the hierarchical organization of concepts, which means that default information is not taken into account when computing priorities. It turns out that the existing approaches for expressing priorities between defaults do not seem to be appropriate for defaults with prerequisites. Therefore we shall consider an alternative approach for dealing with prioritization in the framework of Reiter's default logic. The formalism is presented in the general setting of default logic where priorities are given by an arbitrary partial ordering on the defaults. We shall exhibit some interesting properties of the new formalism, compare it with existing approaches, and describe an algorithm for computing extensions. In the terminological case, we thus obtain an automated default reasoning procedure that takes specificity into account.This is an extended version of a paper presented at the13th International Joint Conference on Artificial Intelligence, August 1993, Chambery, France.     

Characterization of an auto-compatible default theory

In this paper,an equivalence condition for deciding whether a default theory is an auto-compatible default one is presented.Under the condition,the existence of extension of an auto-compatible default theory is a natural result.By introducing a well-ordering over the set D of default rules,the extensions of an auto-compatible default theory(D,W) can be computed directly.The condition represents clearly the characterization of an auto-compatible default theory,and some properties about auto-compatible default theory,such as semi-monotonicity,become natural corollaries.Based on the characterization,the revision of default beliefs is discussed to ensure the existence of extension of the default theory,and the methos is applied to investigate stable models of a general logic program.     

Valuation of a loan-only credit default swap with negatively correlated default and prepayment intensities

In this paper, we consider pricing of a single-name and a two-reference basket loan-only credit default swap. Under a reduced-form framework, it is assumed that the default and prepayment intensity rates for the reference loan, which are negatively correlated, follow one-factor Cox-Ingersoll-Ross (CIR) and inverse CIR models, respectively. The default and prepayment probability formulas are calculated using a partial differential equation method and closed-form solutions are obtained. A numerical analysis and the parameters are also discussed.     

系统信用事件与信用违约互换估值研究

本文以系统信用事件为载体,研究了双边交易对手风险下信用违约互换(credit default swap,CDS)的估值,研究表明:1)完备的信用事件组将形成一个信用风险系统,并可作为CDS估值的基础;2)在CDS估值中,买方违约的可能性是不可以忽略的.如果忽略,将产生一个错误的定价,并且这个错误的定价将低于真实价值而使信用保护的卖方受到损失;3)CDS交易中的替换成本是不可以忽略的,由于替换成本的存在,CDS合约的价值会发生超常变化,其变化幅度取决于合约当前的市场价格;4)CDS合约价格对参考资产信用价差十分敏感,信用价差的变化,将会显著改变合约的价格.     

Tableau-based characterization and theorem proving for default logic

In this paper, we present a new method for computing extensions and for deriving formulae from a default theory. It is based on the semantic tableaux method and works for default theories with a finite set of defaults that are formulated over a decidable subset of first-order logic. We prove that all extensions (if any) of a default theory can be produced by constructing the semantic tableau ofone formula built from the general laws and the default consequences. This result allows us to describe an algorithm that provides extensions if there are any, and to decide if there are none. Moreover, the method gives a necessary and sufficient criterion for the existence of extensions of default theories with finitely many defaults provided they are formulated on a decidable subset of FOL.This work was completed while the author was at CNRS, Marseille.     

Nonmonotonic theories and their axiomatic varieties

The properties of monotonic inference systems and the properties of their theories are strongly linked. These links, however, are much weaker in nonmonotonic inference systems. In this paper we introduce the notion of anaxiomatic variety for a theory and show how this notion, instead of the notion of a theory, can be used for the syntactic and semantic analysis of nonmonotonic inferences.     

Inferences,suppositions and explanatory extensions in argument interpretation

We describe a probabilistic approach for the interpretation of user arguments that integrates three aspects of an interpretation: inferences, suppositions and explanatory extensions. Inferences fill in information that connects the propositions in a user’s argument, suppositions postulate new information that is likely believed by the user and is necessary to make sense of his or her argument, and explanatory extensions postulate information the user may have implicitly considered when constructing his or her argument. Our system receives as input an argument entered through a web interface, and produces an interpretation in terms of its underlying knowledge representation—a Bayesian network. Our evaluations show that suppositions and explanatory extensions are necessary components of interpretations, and that users consider appropriate the suppositions and explanatory extensions postulated by our system. This article integrates and extends research described in George et al., 2004; Zukerman et al., 2004; Zukerman and George, 2005; George et al., 2005. The research described in this article was conducted while Sarah George was employed at Monash University and was supported in part by the ARC Centre for Perceptive and Intelligent Machines in Complex Environments.     

Stable and extension class theory for logic programs and default logics

The stable model semantics (cf. Gelfond and Lifschitz [1]) for logic programs suffers from the problem that programs may not always have stable models. Likewise, default theories suffer from the problem that they do not always have extensions. In such cases, both these formalisms for non-monotonic reasoning have an inadequate semantics. In this paper, we propose a novel idea-that of extension classes for default logics, and of stable classes for logic programs. It is shown that the extension class and stable class semantics extend the extension and stable model semantics respectively. This allows us to reason about inconsistent default theories, and about logic programs with inconsistent completions. Our work extends the results of Marek and Truszczynski [2] relating logic programming and default logics.     

Characterizations and algorithms of extensions for CADL and QDL

Recently,Giordano and Martelli (1994) proposed two new cumulative variants of Reiter‘s default logic(DL):Commitment to Assumptions Default Logic (CADL) and Quasi-Default Logic(QDL).They have only given quasi-inductive characterizations of extensions for the two variants.In this paper,finite characterizations of extensions for CADL and QDL by applying notions of(joint) compatibility are presented respectively.And corresponding algorithms and complexity resuts for reasoning are obtained.     

Sequent calculi for skeptical reasoning in predicate default logic and other nonmonotonic logics

Sequent calculi for skeptical consequence in predicate default logic, predicate stable model logic programming, and infinite autoepistemic theories are presented and proved sound and complete. While skeptical consequence is decidable in the finite propositional case of all three formalisms, the move to predicate or infinite theories increases the complexity of skeptical reasoning to being ₁¹-complete. This implies the need for sequent rules with countably many premises, and such rules are employed. AMS subject classification 03B42, 68N17, 68T27This paper grew directly out of the authors dissertation, written under the direction of Anil Nerode.     

基于TF-IDF算法的P2P贷款违约预测模型

针对目前P2P贷款违约预测模型受限于借贷双方信息不对称性,未考虑投资人之间差异性的问题,提出了基于信息检索词频-逆文本频率（TF-IDF）算法的P2P贷款违约预测模型。首先以投资效用理论为基础,利用投资人历史投资收益率、贷款利率出价等信息,建立基于投资人效用的贷款违约预测模型;然后,借鉴信息检索TF-IDF算法,构造投资人逆向投资比例因子,对投资人差异性进行量化度量,优化模型中投资人权重计算因子。实验结果表明,该模型预测准确度与其他模型相比平均提高了6%左右,并在不同的测试数据集上都保持最优。     

可能性缺省逻辑及其应用

本文分析了Yager用可能性理论框架来表示缺省知识的形式化方法,并测试了三类不同的应用方案,得到的结果与Reiter的缺省逻辑得到的结果相比较,表明只在具有严格的约束的缺省逻辑下,Yager的形式化方法才与Reiter的缺省逻辑具有一定的相关性,我们指出了它们在一般缺省理论下的不匹配处,并给出了以不动点机制抽改进方来消除这
些不匹配。     

Rough Sets, Their Extensions and Applications

Rough set theory provides a useful mathematical foundation for developing automated computational systems that can help understand and make use of imperfect knowledge.Despite its recency,the theory and its extensions have been widely applied to many problems,including decision analysis,data mining,intelligent control and pattern recognition.This paper presents an outline of the basic concepts of rough sets and their major extensions,covering variable precision,tolerance and fuzzy rough sets.It also shows the diversity of successful applications these theories have entailed,ranging from financial and business,through biological and medicine,to physical,art,and meteorological.     

对Etherington并行网络推理算法不完整性问题的探讨

网络缺省推理中扩展的计算需要进行并行性处理．Ｅｔｈｅｒｉｎｇｔｏｎ的并行网络推理算法（ＰＮＩＡ）为缺省推理提供了一条有效的途径．但它存在不能穷尽所有扩展的不完整性问题．本文提出了一个解决这一不完整性间题的并行网络推理算法．