Li Yan Yuan

A new normal form for nested relations

We consider nested relations whose schemes are structured as trees, called scheme trees, and introduce a normal form for such relations, called the nested normal form. Given a set of attributes <italic>U</italic>, and a set of multivalued dependencies (MVDs) <italic>M</italic> over these attributes, we present an algorithm to obtain a nested normal form decomposition of <italic>U</italic> with respect to <italic>M</italic>. Such a decomposition has several desirable properties, such as explicitly representing a set of full and embedded MVDs implied by <italic>M</italic>, and being a faithful and nonredundant representation of <italic>U</italic>. Moreover, if the given set of MVDs is conflict-free, then the nested normal form decomposition is also dependency-preserving. Finally, we show that if <italic>M</italic> is conflict-free, then the set of root-to-leaf paths of scheme trees in nested normal form decomposition is precisely the unique 4NF decomposition [9, 16] of <italic>U</italic> with respect to <italic>M</italic>.

On the equivalence of semantics for normal logic programs

Abstract Despite the frequent comment that there is no general agreement on the semantics of logic programs, this paper shows that a number of independently proposed extensions to the stable model semantics coincide: the regular model semantics proposed by You and Yuan, the partial stable model semantics by Sacca and Zaniolo, the preferential semantics by Dung, and a stronger version of the stable class semantics by Baral and Subrahmanian. We show that these equivalent semantics can be characterized simply as selecting a particular kind of stable classes, called normal alternating fixpoints . In addition, we indicate that almost all of the previously proposed semantic frameworks coincide with that of normal alternating fixpoints. Due to its simplicity and naturalness, the framework of normal alternating fixpoints offers great potential in the study of the semantics for various nonmonotonic systems.

A three-valued semantics for deductive databases and logic programs

This paper proposes two principles, justifiability and minimal undefinedness, for a three-valued model-theoretic approach to semantics of logic programs and deductive databases (also called disjunctive logic programs). The former is intimately related to the concept of labeling-based justification in Doyles truth maintenance system while the latter requires the use of the truth value undefined only when it is necessary. We examine the question why and in what circumstances the undefined is needed under these two principles. We show that these two principles yield a declarative semantics for deductive databases and logic programs, which is called the regular model semantics. Program properties in this semantics are analyzed and results obtained concerning the relationship among regular, stable, and well-founded semantics, which show that the regular model semantics is a natural extension of the latter two semantics.

Implementation of a Linear Tabling Mechanism

Delaying-based tabling mechanisms, such as the one adopted in XSB, are non-linear in the sense that the computation state of delayed calls has to be preserved. In this paper, we present the implementation of a linear tabling mechanism. The key idea is to let a call execute from the backtracking point of a former variant call if such a call exists. The linear tabling mechanism has the following advantages over non-linear ones: (1) it is relatively easy to implement; (2) it imposes no overhead on standard Prolog programs; and (3) the cut operator works as for standard Prolog programs and thus it is possible to use the cut operator to express negation-as-failure and conditionals in tabled programs. The weakness of the linear mechanism is the necessity of re-computation for computing fix-points. However, we have found that re-computation can be avoided for a large portion of calls of directly-recursive tabled predicates. We have implemented the linear tabling mechanism in B-Prolog. Experimental comparison shows that B-Prolog is close in speed to XSB and outperforms XSB when re-computation can be avoided. Concerning space efficiency, B-Prolog is an order of magnitude better than XSB for some programs.

Three-valued formalization of logic programming: is it needed?

The central issue of this paper concerns the truth value undefined in Przymusinsis 3-valued formalization of nonmonotonic reasoning and logic programming. We argue that this formalization can lead to the problem of unintended semantics and loss of disjunctive information. We modify the formalization by proposing two general principles for logic program semantics: justifiability and minimal undefinedness. The former is shown to be a general property for almost all logic program semantics, and the latter requires the use of the undefined only when it is necessary. We show that there are three types of information embedded in the undefined: the disjunctive, the factoring, and the “difficult-to-be-assigned”. In the modified formalization, the first two can be successfully identified and branched into multiple models. This leaves only the “difficult-to-be-assigned” as the undefined. It is shown that the truth value undefined is needed only for a very special type of programs whose practicality is yet to be evidenced.

Autoepistemic Circumscription and Logic Programming

We propose a framework of autoepistemic reasoning in which the underlying semantics is determined by the choice of a nonmonotonic inference mechanism and by specifying abelief constraint. While the latter makes the approach flexible in meeting possibly different applications, the former links the resulting semantics to a nonmonotonic reasoning formalism and thus allows adoption of existing techniques. In this paper we choosecircumscription as the underlying inference mechanism and use two different belief constraints to define two semantics,the stable circumscriptive semantics andthe well-founded circumscriptive semantics, for autoepistemic theories. The former coincides with Moores autoepistemic logic for logic programs and is arguably more desirable in handling disjunctive autoepistemic theories. The latter is a reconstruction and extension of Przymusinskis iterative method for computing the leastAEL(circ) expansions for logic programs. We show that for logic programs the two construction methods coincide. However, while Przymusinskis construction method is restricted to logic programs only, the well-founded circumscriptive semantics is applicable to more general autoepistemic theories.

Linear tabulated resolution based on Prolog control strategy

Infinite loops and redundant computations are long recognized open problems in Prolog. Two methods have been explored to resolve these problems: loop checking and tabling. Loop checking can cut infinite loops, but it cannot be both sound and complete even for function-free logic programs. Tabling seems to be an effective way to resolve infinite loops and redundant computations. However, existing tabulated resolutions, such as OLDT-resolution, SLG-resolution and Tabulated SLS-resolution, are non-linear because they rely on the solution-lookup mode in formulating tabling. The principal disadvantage of non-linear resolutions is that they cannot be implemented using a simple stack-based memory structure like that in Prolog. Moreover, some strictly sequential operators such as cuts may not be handled as easily as in Prolog. In this paper, we propose a hybrid method to resolve infinite loops and redundant computations. We combine the ideas of loop checking and tabling to establish a linear tabulated resolution called TP-resolution. TP-resolution has two distinctive features: (1) it makes linear tabulated derivations in the same way as Prolog except that infinite loops are broken and redundant computations are reduced. It handles cuts as effectively as Prolog; and (2) it is sound and complete for positive logic programs with the bounded-term-size property. The underlying algorithm can be implemented by an extension to any existing Prolog abstract machines such as WAM or ATOAM.

A sound and complete query evaluation algorithm for relational databases with disjunctive information

There have been numerous attempts to represent incomplete information in relational databases ince the very beginning of the rehuional dambase theory [Co79, IL%, Re841. Two manifestations of the problem of representing incomplete information are disjunctive information and null value. The null value is a special symbol with some unknown properties, while disjunctive information represents disjunctive facts of the form: “P is the case, or Q is, or . . . . but I do not know which”.

Survey of Large-Scale Data Management Systems for Big Data Applications

Today, data is flowing into various organizations at an unprecedented scale. The ability to scale out for processing an enhanced workload has become an important factor for the proliferation and popularization of database systems. Big data applications demand and consequently lead to the developments of diverse large-scale data management systems in different organizations, ranging from traditional database vendors to new emerging Internet-based enterprises. In this survey, we investigate, characterize, and analyze the large-scale data management systems in depth and develop comprehensive taxonomies for various critical aspects covering the data model, the system architecture, and the consistency model. We map the prevailing highly scalable data management systems to the proposed taxonomies, not only to classify the common techniques but also to provide a basis for analyzing current system scalability limitations. To overcome these limitations, we predicate and highlight the possible principles that future efforts need to be undertaken for the next generation large-scale data management systems.

A dynamic approach to characterizing termination of general logic programs

We present a new characterization of termination of general logic programs. Most existing termination analysis approaches rely on some static information about the structure of the source code of a logic program, such as modes/types, norms/level mappings, models/interargument relations, and the like. We propose a dynamic approach that employs some key dynamic features of an infinite (generalized) SLDNF-derivation, such as repetition of selected subgoals and recursive increase in term size. We also introduce a new formulation of SLDNF-trees, called generalized SLDNF-trees. Generalized SLDNF-trees deal with negative subgoals in the same way as Prolog and exist for any general logic programs.