21 research outputs found
Complete Axiomatizations of Fragments of Monadic Second-Order Logic on Finite Trees
We consider a specific class of tree structures that can represent basic
structures in linguistics and computer science such as XML documents, parse
trees, and treebanks, namely, finite node-labeled sibling-ordered trees. We
present axiomatizations of the monadic second-order logic (MSO), monadic
transitive closure logic (FO(TC1)) and monadic least fixed-point logic
(FO(LFP1)) theories of this class of structures. These logics can express
important properties such as reachability. Using model-theoretic techniques, we
show by a uniform argument that these axiomatizations are complete, i.e., each
formula that is valid on all finite trees is provable using our axioms. As a
backdrop to our positive results, on arbitrary structures, the logics that we
study are known to be non-recursively axiomatizable
Containment of Pattern-Based Queries over Data Trees
International audienceWe study static analysis, in particular the containment problem, for analogs of conjunctive queries over XML documents. The problem has been studied for queries based on arbitrary patterns, not necessarily following the tree structure of documents. However, many applications force the syntactic shape of queries to be tree-like, as they are based on proper tree patterns. This renders previous results, crucially based on having non-tree-like features, inapplicable. Thus, we investigate static analysis of queries based on proper tree patterns. We go beyond simple navigational conjunctive queries in two ways: we look at unions and Boolean combinations of such queries as well and, crucially, all our queries handle data stored in documents, i.e., we deal with containment over data trees. We start by giving a general \Pi^p_2 upper bound on the containment of conjunctive queries and Boolean combinations for patterns that involve all types of navigation through documents. We then show matching hardness for conjunctive queries with all navigation, or their Boolean combinations with the simplest form of navigation. After that we look at cases when containment can be witnessed by homomorphisms of analogs of tableaux. These include conjunctive queries and their unions over child and next-sibling axes; however, we show that not all cases of containment can be witnessed by homomorphisms. We look at extending tree patterns used in queries in three possible ways: with wildcard, with schema information, and with data value comparisons. The first one is relatively harmless, the second one tends to increase complexity by an exponential, and the last one quickly leads to undecidability
Querying Incomplete Data : Complexity and Tractability via Datalog and First-Order Rewritings
To answer database queries over incomplete data the gold standard is finding
certain answers: those that are true regardless of how incomplete data is
interpreted. Such answers can be found efficiently for conjunctive queries and
their unions, even in the presence of constraints. With negation added, the
problem becomes intractable however. We concentrate on the complexity of
certain answers under constraints, and on effficiently answering queries
outside the usual classes of (unions) of conjunctive queries by means of
rewriting as Datalog and first-order queries. We first notice that there are
three different ways in which query answering can be cast as a decision
problem. We complete the existing picture and provide precise complexity bounds
on all versions of the decision problem, for certain and best answers. We then
study a well-behaved class of queries that extends unions of conjunctive
queries with a mild form of negation. We show that for them, certain answers
can be expressed in Datalog with negation, even in the presence of functional
dependencies, thus making them tractable in data complexity. We show that in
general Datalog cannot be replaced by first-order logic, but without
constraints such a rewriting can be done in first-order. The paper is under
consideration in Theory and Practice of Logic Programming (TPLP).Comment: Under consideration in Theory and Practice of Logic Programming
(TPLP
Certain Answers of Extensions of Conjunctive Queries by Datalog and First-Order Rewriting
International audienc
Reasoning About Pattern-Based XML Queries
Abstract. We survey results about static analysis of pattern-based queries over XML documents. These queries are analogs of conjunctive queries, their unions and Boolean combinations, in which tree patterns play the role of atomic formulae. As in the relational case, they can be viewed as both queries and incomplete documents, and thus static analysis problems can also be viewed as finding certain answers of queries over such documents. We look at satisfiability of patterns under schemas, containment of queries for various features of XML used in queries, finding certain answers, and applications of pattern-based queries in reasoning about schema mappings for data exchange.
A Researcherâs Digest of GQL
International audienceGQL (Graph Query Language) is being developed as a new ISO standard for graph query languages to play the same role for graph databases as SQL plays for relational. In parallel, an extension of SQL for querying property graphs, SQL/PGQ, is added to the SQL standard; it shares the graph pattern matching functionality with GQL. Both standards (not yet published) are hard-to-understand specifications of hundreds of pages. The goal of this paper is to present a digest of the language that is easy for the research community to understand, and thus to initiate research on these future standards for querying graphs. The paper concentrates on pattern matching features shared by GQL and SQL/PGQ, as well as querying facilities of GQL