Jia-Huai You

Unfolding partiality and disjunctions in stable model semantics

This article studies an implementation methodology for partial and disjunctive stable models where partiality and disjunctions are unfolded from a logic program so that an implementation of stable models for normal (disjunction-free) programs can be used as the core inference engine. The unfolding is done in two separate steps. First, it is shown that partial stable models can be captured by total stable models using a simple linear and modular program transformation. Hence, reasoning tasks concerning partial stable models can be solved using an implementation of total stable models. Disjunctive partial stable models have been lacking implementations which now become available as the translation handles also the disjunctive case. Second, it is shown how total stable models of disjunctive programs can be determined by computing stable models for normal programs. Thus an implementation of stable models of normal programs can be used as a core engine for implementing disjunctive programs. The feasibility of the approach is demonstrated by constructing a system for computing stable models of disjunctive programs using the SMODELS system as the core engine. The performance of the resulting system is compared to that of DLV, which is a state-of-the-art system for disjunctive programs.

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.

Abduction in logic programming: a new definition and an abductive procedure based on rewriting

A long outstanding problem for abduction in logic programming has been on how minimality might be defined. Without minimality, an abductive procedure is often required to generate exponentially many subsumed explanations for a given observation. In this paper, we propose a new definition of abduction in logic programming where the set of minimal explanations can be viewed as a succinct representation of the set of all explanations. We then propose an abductive procedure where the problem of generating explanations is formalized as rewriting with confluent and terminating rewrite systems. We show that these rewrite systems are sound and complete under the partial stable model semantics, and sound and complete under the answer set semantics when the underlying program is so-called odd-loop free. We discuss an application of abduction in logic programming to a problem in reasoning about actions and provide some experimental results.

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.

Quartet-Based Phylogeny Reconstruction with Answer Set Programming

In this paper, a new representation is presented for the Maximum Quartet Consistency (MQC) problem, where solving the MQC problem becomes searching for an ultrametric matrix that satisfies a maximum number of given quartet topologies. A number of structural properties of the MQC problem in this new representation are characterized through formulating into answer set programming, a recent powerful logic programming tool for modeling and solving search problems. Using these properties, a number of optimization techniques are proposed to speed up the search process. The experimental results on a number of simulated data sets suggest that the new representation, combined with answer set programming, presents a unique perspective to the MQC problem.

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.

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.