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.     

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.     

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.     

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.     

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.     

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.     

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．     

Feature space theory in data mining: transformations between extensions and intensions in knowledge representation

Knowledge representation is one of the important topics in data mining research. In this paper, based on the feature space theory in data mining, the transformation between extensions and intensions of concepts is discussed in detail. First, inner projections of fuzzy relations, as a basic mathematical tool, are defined, and properties of inner projections are discussed. Then inner transformation of fuzzy relations, inverse inner transformations, and related properties are introduced. The concept structure is shown by feature spaces. Lastly, transformations between extensions and intensions are discussed.     

Binary input,output, and manipulation extensions of conversational programming with some biological applications

This paper presents details of how the conversational programming system may be extended to allow input, output, and manipulation in binary and how these extensions may be used in various applications.     

Decision field theory extensions for behavior modeling in dynamic environment using Bayesian belief network

Decision field theory (DFT), widely known in the field of mathematical psychology, provides a mathematical model for the evolution of the preferences among options of a human decision-maker. The evolution is based on the subjective evaluation for the options and his/her attention on an attribute (interest). In this paper, we extend DFT to cope with the dynamically changing environment. The proposed extended DFT (EDFT) updates the subjective evaluation for the options and the attention on the attribute, where Bayesian belief network (BBN) is employed to infer these updates under the dynamic environment. Four important theorems are derived regarding the extension, which enhance the usability of EDFT by providing the minimum time steps required to obtain the stabilized results before running the simulation (under certain assumptions). A human-in-the-loop experiment is conducted for the virtual stock market to illustrate and validate the proposed EDFT. The preliminary result is quite promising.     

Computer-generated interval extensions of factorable functions and their derivatives

A simple method for obtaining computer-generated interval extensions of a real rational factorable function and its first and second partial derivatives is described, Extensions for irrational factorable functions and several applications of the techniques are discussed     

Nonextensive lattice gauge theories: Algorithms and methods

High-energy phenomena presenting strong dynamical correlations, long-range interactions and microscopic memory effects are well described by nonextensive versions of the canonical Boltzmann–Gibbs statistical mechanics. After a brief theoretical review, we introduce a class of generalized heat-bath algorithms that enable Monte Carlo lattice simulations of gauge fields on the nonextensive statistical ensemble of Tsallis. The algorithmic performance is evaluated as a function of the Tsallis parameter q$q$ in equilibrium and nonequilibrium setups. Then, we revisit short-time dynamic techniques, which in contrast to usual simulations in equilibrium present negligible finite-size effects and no critical slowing down. As an application, we investigate the short-time critical behaviour of the nonextensive hot Yang–Mills theory at q$q$-values obtained from heavy-ion collision experiments. Our results imply that, when the equivalence of statistical ensembles is obeyed, the long-standing universality arguments relating gauge theories and spin systems hold also for the nonextensive framework.     

Nonstandard set theories and information management

The merits of set theory as a foundational tool in mathematics stimulate its use in various areas of artificial intelligence, in particular intelligent information systems. In this paper, a study of various nonstandard treatments of set theory from this perspective is offered. Applications of these alternative set theories to information or knowledge management are surveyed.     

Interface theories for concurrency and data

We present a compositional approach for specifying concurrent behavior of components with data states on the basis of interface theories. The dynamic aspects of a system are specified by modal input/output automata, whereas changing data states are specified by pre- and postconditions. The combination of the two formalisms leads to our notion of modal input/output automata with data constraints (MIODs). In this setting we study refinement and behavioral compatibility of MIODs. We show that compatibility is preserved by refinement and that refinement is compositional w.r.t. synchronous composition, thus satisfying basic requirements of an interface theory. We propose a semantic foundation of interface specifications where any MIOD is equipped with a model-theoretic semantics describing the class of its correct implementation models. Implementation models are formalized in terms of guarded input/output transition systems and the correctness notion is based on a simulation relation between an MIOD and an implementation model which relates not only abstract and concrete control states but also (abstract) data constraints and concrete data states. We show that our approach is compositional in the sense that locally correct implementation models of compatible MIODs compose to globally correct implementations, thus ensuring independent implementability.     

Theories of initial segments of standard models of arithmetics and their complete extensions

We investigate families of finite initial segments of standard models for various arithmetics. We give an axiomatization of the theory of sentences true in almost all finite models with addition. We also characterize its complete extensions and relate its infinite models to models of Presburger arithmetic.We also estimate the complexity of complete extensions of the arithmetic with addition and multiplication.