Alberto O. Mendelzon

Propositional knowledge base revision and minimal change

Abstract The semantics of revising knowledge bases represented by sets of propositional sentences is analyzed from a model-theoretic point of view. A characterization of all revision schemes that satisfy the Gardenfors rationality postulates is given in terms of minimal change with respect to an ordering among interpretations. Revision methods proposed by various authors are surveyed and analyzed in this framework. The correspondences between Gardenfors-like rationality postulates and minimal changes with respect to other orderings are also investigated.

Database techniques for the World-Wide Web: a survey

The popularity of the World-Wide Web (WWW) has made it a prime vehicle for disseminating information. The relevance of database concepts to the problems of managing and querying this information has led to a signi cant body of recent research addressing these problems. Even though the underlying challenge is the one that has been traditionally addressed by the database community { how to manage large volumes of data { the novel context of the WWW forces us to signi cantly extend previous techniques. The primary goal of this survey is to classify the di erent tasks to which database concepts have been applied, and to emphasize the technical innovations that were required to do so.

Answering queries using views (extended abstract)

We consider the problem of computing answers to queries by using materialized views. Aside from its potential in optimizing query evaluation, the problem also arises in applications such as Global Information Systems, Mobile Computing and maintaining physical data independence. We consider the problem of finding a rewriting of a query that uses the materialized views, the problem of finding minimal rewritings, and finding complete rewritings (i.e., rewritings that use only the views). We show that all the possible rewritings can be obtained by considering cent ainment mappings from the views to the query, and that the problems we consider are NP-complete when both the query and the views are conjunctive and don’t involve builtin comparison predicates. We show that the problem has two independent sources of complexity (the number of possible containment mappings, and the complexity of deciding which literals from the original query can be deleted). We describe a polynomial time algorithm for finding rewritings, and show that under certain conditions, it will find the minimal rewriting. Finally, we analyze the complexity of the problems when the queries and views may be disjunctive and involve built-in comparison predicates.

Similarity-based queries for time series data

We study a set of linear transformations on the Fourier series representation of a sequence that can be used as the basis for similarity queries on time-series data. We show that our set of transformations is rich enough to formulate operations such as moving average and time warping. We present a query processing algorithm that uses the underlying R-tree index of a multidimensional data set to answer similarity queries efficiently. Our experiments show that the performance of this algorithm is competitive to that of processing ordinary (exact match) queries using the index, and much faster than sequential scanning. We relate our transformations to the general framework for similarity queries of Jagadish et al.

Finding Regular Simple Paths in Graph Databases

We consider the following problem: given a labelled directed graph G and a regular expression R, find all pairs of nodes connected by a simple path such that the concatenation of the labels along the path satisfies R. The problem is motivated by the observation that many recursive queries can be expressed in this form, and by the implementation of a query language, G+, based on this observation. We show that the problem is in general intractable, but present an algorithm than runs in polynomial time in the size of the graph when the regular expression and the graph are free of conflicts. We also present a class of languages whose expressions can always be evaluated in time polynomial in the size of both the database and the expression, and characterize syntactically the expressions for such languages.

A graphical query language supporting recursion

We define a language G for querying data represented as a labeled graph G. By considering G as a relation, this graphical query language can be viewed as a relational query language, and its expressive power can be compared to that of other relational query languages. We do not propose G as an alternative to general purpose relational query languages, but rather as a complementary language in which recursive queries are simple to formulate. The user is aided in this formulation by means of a graphical interface. The provision of regular expressions in G allows recursive queries more general than transitive closure to be posed, although the language is not as powerful as those based on function-free Horn clauses. However, we hope to be able to exploit well-known graph algorithms in evaluating recursive queries efficiently, a topic which has received widespread attention recently.

Foundations of semantic web databases

The Semantic Web is based on the idea of adding more machine-readable semantics to web information via annotations written in a language called the Resource Description Framework (RDF). RDF resembles a subset of binary first-order logic including the ability to refer to anonymous objects. Its extended version, RDFS, supports reification, typing and inheritance. These features introduce new challenges into the formal study of sets of RDF/RDFS statements and languages for querying them. Although several such query languages have been proposed, there has been little work on foundational aspects. We investigate these, including computational aspects of testing entailment and redundancy. We propose a query language with well-defined semantics and study the complexity of query processing, query containment, and simplification of answers.

MERGING DATABASES UNDER CONSTRAINTS

The problem of integrating information from conflicting sources comes up in many current applications, such as cooperative information systems, heterogeneous databases, and multiagent systems. We model this by the operation of merging first-order theories. We propose a formal semantics for this operation and show that it has desirable properties, including abiding by majority rule in case of conflict and syntax independence. We apply our semantics to the special case when the theories to be merged represent relational databases under integrity constraints. We then present a way of merging databases that have different or conflicting schemas caused by problems such as synonyms, homonyms or type conflicts mentioned in the schema integration literature.

Tableau Techniques for Querying Information Sources through Global Schemas

The foundational homomorphism techniques introduced by Chandra and Merlin for testing containment of conjunctive queries have recently attracted renewed interest due to their central role in information integration applications. We show that generalizations of the classical tableau representation of conjunctive queries are useful for computing query answers in information integration systems where information sources are modeled as views defined on a virtual global schema. We consider a general situation where sources may or may not be known to be correct and complete. We characterize the set of answers to a global query and give algorithms to compute a finite representation of this possibly infinite set, as well as its certain and possible approximations. We show how to rewrite a global query in terms of the sources in two special cases, and show that one of these is equivalent to the Information Manifold rewriting of Levy et al.

Similarity-based queries

We develop a domain-independent framework for defining qneries in terms of similarity of objects. Our framework has three components: a pattern language, a transformation rule language, and a query language. The pattern language specifies classes of objects, the transformation rule language defines similarity by specifying the similarity-preserving transformations, and the whole package is wrapped in a general query language. The framework can be “tuned” to the needs of a specific application domain, such as time sequences, molecules, text strings or images, by the choice of these languages. We demonstrate the framework by presenting a specific instance on a specific domain – the domain of sequences. We start with sequences over a finite alphabet, and then consider sequences over infinite ordered domains. The basic pattern language weuseis regular expressions, and the query language is calculus-based. We show that even when the pattern/query languages chosen are not too powerful, the approximation framework obtained is very strong. We study the properties of the framework, and in particular present expressive power and complexity results.