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.     

A sound and complete chase procedure for constrained tuple-generating dependencies

We present a chase procedure for solving the implication problem of constrained tuple-generating dependencies (ctgds), a general class of database dependencies that is also able to handle data and predicates on interpreted domains. Current chase procedures for ctgds are sound but not complete, in the sense that they are unguaranteed to stop successfully whenever implication is true. The procedure we present is sound and complete, the first to our knowledge. It follows a linear reasoning over constraint domains that have the Independence of Negative Constraints property. We then soundly extend this procedure by a disjunctive reasoning over unrestricted constraint domains. To achieve these results, we used a different approach. Previous chases act like a closure operator, whereas we used a goal-directed design.     

A proof procedure for the logic of hereditary Harrop formulas

A proof procedure is presented for a class of formulas in intuitionistic logic. These formulas are the so-calledgoal formulas in the theory of hereditary Harrop formulas. Proof search in intuitionistic logic is complicated by the nonexistence of a Herbrand-like theorem for this logic: formulas cannot in general be preprocessed into a form such as the clausal form, and the construction of a proof is often sensitive to the order in which the connectives and quantifiers are analyzed. An interesting aspect of the formulas we consider here is that this analysis can be carried out in a relatively controlled manner in their context. In particular, the task of finding a proof can be reduced to one of demonstrating that a formula follows from a set of assumptions, with the next step in this process being determined by the structure of the conclusion formula. An acceptable implementation of this observation must utilize unification. However, since our formulas may contain universal and existential quantifiers in mixed order, care must be exercised to ensure the correctness of unification. One way of realizing this requirement involves labelling constants and variables and then using these labels to constrain unification. This form of unification is presented and used in a proof procedure for goal formulas in a first-order version of hereditary Harrop formulas. Modifications to this procedure for the relevant formulas in a higher-order logic are also described. The proof procedure that we present has a practical value in that it provides the basis for an implementation of the logic programming language Prolog.     

A new reduction rule for the connection graph proof procedure

A new reduction rule is introduced for the connection graph proof procedure proposed by Kowalski in 1975. The new rule considers sets of values which clause variables may take. Application of the rule often leads to massive removals of links. A proof system in which the new rule is included has successfully been implemented in PROLOG. The performance of this system is compared to other resolution based proof systems. Also, the new rule is related to order-sorted logic.     

Comparable dependencies over heterogeneous data

To study the data dependencies over heterogeneous data in dataspaces, we define a general dependency form, namely comparable dependencies (CDS), which specifies constraints on comparable attributes. It covers the semantics of a broad class of dependencies in databases, including functional dependencies (FDS), metric functional dependencies (MFDS), and matching dependencies (MDS). As we illustrated, comparable dependencies are useful in real practice of dataspaces, such as semantic query optimization. Due to heterogeneous data in dataspaces, the first question, known as the validation problem, is to tell whether a dependency (almost) holds in a data instance. Unfortunately, as we proved, the validation problem with certain error or confidence guarantee is generally hard. In fact, the confidence validation problem is also NP-hard to approximate to within any constant factor. Nevertheless, we develop several approaches for efficient approximation computation, such as greedy and randomized approaches with an approximation bound on the maximum number of violations that an object may introduce. Finally, through an extensive experimental evaluation on real data, we verify the superiority of our methods.     

Mining functional dependencies from data

In this paper, we propose an efficient rule discovery algorithm, called FD_Mine, for mining functional dependencies from data. By exploiting Armstrong’s Axioms for functional dependencies, we identify equivalences among attributes, which can be used to reduce both the size of the dataset and the number of functional dependencies to be checked. We first describe four effective pruning rules that reduce the size of the search space. In particular, the number of functional dependencies to be checked is reduced by skipping the search for FDs that are logically implied by already discovered FDs. Then, we present the FD_Mine algorithm, which incorporates the four pruning rules into the mining process. We prove the correctness of FD_Mine, that is, we show that the pruning does not lead to the loss of useful information. We report the results of a series of experiments. These experiments show that the proposed algorithm is effective on 15 UCI datasets and synthetic data.     

Membership problems for data dependencies in relational expressions

In relational databases, a query can be formulated in terms of a relational algebra expression using projection, selection, restriction, cross product and union. In this paper, we consider a problem, called the membership problem, of determining whether a given dependency d is valid in a given relational expression E over a given database scheme R that is, whether every instance of the view scheme defined by E satisfies d (assuming that the underlying constraints in R are always satisfied).Consider the case where each relation scheme in R is associated with functional dependencies (FDs) as constraints, and d is an FD. Then the complement of the membership problem is NP-complete. However, if E contains no union, then the membership problem can be solved in polynomial time. Furthermore, if E contains neither a union nor a projection, then we can construct in polynomial time a cover for valid FDs in E, that is, a set of FDs which implies every valid FD in E.Consider the case where each relation scheme in R is associated with multivalued dependencies (MVDs) as well as FDs, and d is an FD or an MVD. Even if E consists of selections and cross products only, the membership problem is NP-hard. However, if E contains no union, and each relation scheme name in R occurs in E at most once, then the membership problem can be solved in polynomial time. As a corollary of this result, it can be determined in polynomial time whether a given FD or MVD is valid in $\text{R}{}_1\text{???R}{}_{\mathrm{s}}$, where R₁,…,R_s are relation schemes with FDs and MVDs, and $\text{R}{}_{\mathrm{i}}\text{?R}{}_{\mathrm{j}}$ is the natural join of R_i and R_j.     

Fast in-place verification of data dependencies

Several fast and space-optimal sequential and parallel algorithms for solving the satisfaction problem of functional and multivalued dependencies (FDs and MVDs) are presented. Two frameworks to verify an MVD for a relation and their implementation by exploring the existing fast space-optimal sorting techniques are described. The space optimality means that only a constant amount of extra memory space is needed for the sequential implementations, and O(M) amount of extra memory space for parallel algorithms that use M processors. This feature makes the algorithms attractive whenever space is a critical resource and I/O transfers should be reduced to the minimal, as is often the case for relational database systems. The time requirements for in-place FD and MVD verification are given in terms of M and of N, which is the number of tuples in a relation. The effect of relation modification on FD and MVD verification is examined     

A data mining algorithm for generalized Web prefetching

Predictive Web prefetching refers to the mechanism of deducing the forthcoming page accesses of a client based on its past accesses. In this paper, we present a new context for the interpretation of Web prefetching algorithms as Markov predictors. We identify the factors that affect the performance of Web prefetching algorithms. We propose a new algorithm called WM,,, which is based on data mining and is proven to be a generalization of existing ones. It was designed to address their specific limitations and its characteristics include all the above factors. It compares favorably with previously proposed algorithms. Further, the algorithm efficiently addresses the increased number of candidates. We present a detailed performance evaluation of WM, with synthetic and real data. The experimental results show that WM/sub o/ can provide significant improvements over previously proposed Web prefetching algorithms.     

A generalized Waring regression model for count data

A regression model for count data based on the generalized Waring distribution is developed. This model allows the observed variability to be split into three components: randomness, internal differences between individuals and the presence of other external factors that have not been included as covariates in the model. An application in the field of sports illustrates its capacity for modelling data sets with great accuracy. Moreover, this yields more information than a model based on the negative binomial distribution.     

A shared memory algorithm and proof for the generalized alternative construct in CSP

Communicating Sequential Processes (CSP) is a paradigm for communication and synchronization among distributed processes. The alternative construct is a key feature of CSP that allows nondeterministic selection of one among several possible communicants. A generalized version of Hoare's original alternative construct that allows output commands to be included in guards has been proposed. Previous algorithms for this construct assume a message passing architecture and are not appropriate for multiprocessor systems that feature shared memory. This paper describes a distributed algorithm for the generalized alternative construct that exploits the capabilities of a parallel computer with shared memory. A correctness proof of the proposed algorithm is presented to show that the algorithm conforms to somesatefy andliveness criteria. Extensions to allow termination of processes and to ensure fairness in guard selection are also given.This work was supported by ONR Contract Number N00014-87-K-0184.     

Vine copulas for mixed data : multi-view clustering for mixed data beyond meta-Gaussian dependencies

Copulas enable flexible parameterization of multivariate distributions in terms of constituent marginals and dependence families. Vine copulas, hierarchical collections of bivariate copulas, can model a wide variety of dependencies in multivariate data including asymmetric and tail dependencies which the more widely used Gaussian copulas, used in Meta-Gaussian distributions, cannot. However, current inference algorithms for vines cannot fit data with mixed—a combination of continuous, binary and ordinal—features that are common in many domains. We design a new inference algorithm to fit vines on mixed data thereby extending their use to several applications. We illustrate our algorithm by developing a dependency-seeking multi-view clustering model based on Dirichlet Process mixture of vines that generalizes previous models to arbitrary dependencies as well as to mixed marginals. Empirical results on synthetic and real datasets demonstrate the performance on clustering single-view and multi-view data with asymmetric and tail dependencies and with mixed marginals.     

On the expressive power of data dependencies

Summary The class of data dependencies is a class of first-order sentences that seem to be suitable to express semantic constraints for relational databases. We deal with the question of which classes of databases are axiomatizable by data dependencies. (A class of databases is said to be axiomatizable by sentences of a certain kind if there exists a set of sentences of that kind such that is the class of all models of that set.) Our results characterize, by algebraic closure conditions, classes of databases that are axiomatizable by dependencies of different kinds. Our technique is model-theoretic, and the characterization easily entails all previously known results on axiomatizability by dependencies.Research partially supported by Swiss National Science Foundation Grant No. 82.820.0.80 (1980–1982), revision of the paper was done while visiting the Mathematisches Forschungsinstitut at the Swiss Federal Institute of Technology (Summer 1985)Part of the research reported here was done while the author was at Stanford University and supported by a Weizmann Post-Doctoral Fellowship and AFOSR grant 80-0212     

Contexts and data dependencies: a synthesis

Two data-organization devices that have come out of AI re-search are data pools (``contexts') and data dependencies. The latter are more flexible than the former, and have supplanted them. Data pools offer certain advantages of efficiency, however, so it is worth trying to make the two mechanisms compatible. Doing this requires generalizing the mark-and-sweep algorithms that maintain consistency in a data-dependency network, so that the labels passed around do not simply say whether a datum is IN or OUT, but say which data pools it is present in. The revised algorithm is essentially an algorithm for solving simultaneous Boolean equations. Other mechanisms are needed for per-forming useful chores like maintaining well-founded support links and orchestrating demon calls.     

A generalized histogram clustering scheme for multidimensional image data

A clustering procedure called HICAP (HIstogram Cluster Analysis Procedure) was developed to perform an unsupervised classification of multidimensional image data. The clustering approach used in HICAP is based upon an algorithm described by Narendra and Goldberg to classify four-dimensional Landsat Multispectral Scanner data. HICAP incorporates two major modifications to the scheme by Narendra and Goldberg. The first modification is that HICAP is generalized to process up to 32-bit data with an arbitrary number of dimensions. The second modification is that HICAP uses more efficient algorithms to implement the clustering approach described by Narendra and Goldberg.(¹) This means that the HICAP classification requires less computation, although it is otherwise identical to the original classification. The computational savings afforded by HICAP increases with the number of dimensions in the data.     

MRPPS—An interactive refutation proof procedure system for question-answering

In this paper a system termed the Maryland refutation proof procedure system (MRPPS) is described. MRPPS is an interactive system which gives the user the ability to create and maintain a core-bound data base and to input queries either as well-formed formulas in the first-order predicate calculus or as clauses. MRPPS consists of three basic components: (1) a set of inference rules for making logical deductions, many of which are based on the resolution principle; (2) a search strategy for heuristically determining the sequence in which to select base clauses and to perform deductions on clauses already generated; and (3) a base clause selection strategy that uses heuristic and semantic information for determining which data axioms and general axioms are to be brought to bear on the problem. These three components are described and MRPPS is compared to related work.     

A top-down methodology for microprocessor validation

A major challenge in today's functional verification is the lack of a formal specification with which to compare the RTL model. We propose a novel top-down verification approach that allows specification of a design above the RTL. From this specification, it is possible to automatically generate assertion models and RTL reference models. We also demonstrate that symbolic simulation and equivalence checking can be applied to verify an RTL design against its specification.