Algebraic classifications for fragments of first-order logic and beyond

Complexity and decidability of logics is a major research area involving a huge range of different logical systems. This calls for a unified and systematic approach for the field. We introduce a research program based on an algebraic approach to complexity classifications of fragments of first-order logic (FO) and beyond. Our base system GRA, or general relation algebra, is equiexpressive with FO. It resembles cylindric algebra but employs a finite signature with only seven different operators. We provide a comprehensive classification of the decidability and complexity of the systems obtained by limiting the allowed sets of operators. We also give algebraic characterizations of the best known decidable fragments of FO. Furthermore, to move beyond FO, we introduce the notion of a generalized operator and briefly study related systems.Comment: Significantly updates the first version. The principal set of operations change

Work-Efficient Query Evaluation with PRAMs

The paper studies query evaluation in parallel constant time in the PRAM model. While it is well-known that all relational algebra queries can be evaluated in constant time on an appropriate CRCW-PRAM, this paper is interested in the efficiency of evaluation algorithms, that is, in the number of processors or, asymptotically equivalent, in the work. Naive evaluation in the parallel setting results in huge (polynomial) bounds on the work of such algorithms and in presentations of the result sets that can be extremely scattered in memory. The paper first discusses some obstacles for constant time PRAM query evaluation. It presents algorithms for relational operators that are considerably more efficient than the naive approaches. Further it explores three settings, in which efficient sequential query evaluation algorithms exist: acyclic queries, semi-join algebra queries, and join queries - the latter in the worst-case optimal framework. Under natural assumptions on the representation of the database, the work of the given algorithms matches the best sequential algorithms in the case of semi-join queries, and it comes close in the other two settings. An important tool is the compaction technique from Hagerup (1992)

Queries with Guarded Negation (full version)

A well-established and fundamental insight in database theory is that negation (also known as complementation) tends to make queries difficult to process and difficult to reason about. Many basic problems are decidable and admit practical algorithms in the case of unions of conjunctive queries, but become difficult or even undecidable when queries are allowed to contain negation. Inspired by recent results in finite model theory, we consider a restricted form of negation, guarded negation. We introduce a fragment of SQL, called GN-SQL, as well as a fragment of Datalog with stratified negation, called GN-Datalog, that allow only guarded negation, and we show that these query languages are computationally well behaved, in terms of testing query containment, query evaluation, open-world query answering, and boundedness. GN-SQL and GN-Datalog subsume a number of well known query languages and constraint languages, such as unions of conjunctive queries, monadic Datalog, and frontier-guarded tgds. In addition, an analysis of standard benchmark workloads shows that most usage of negation in SQL in practice is guarded negation

Complexity Classifications via Algebraic Logic

Complexity and decidability of logics is an active research area involving a wide range of different logical systems. We introduce an algebraic approach to complexity classifications of computational logics. Our base system GRA, or general relation algebra, is equiexpressive with first-order logic FO. It resembles cylindric algebra but employs a finite signature with only seven different operators, thus also giving a very succinct characterization of the expressive capacities of first-order logic. We provide a comprehensive classification of the decidability and complexity of the systems obtained by limiting the allowed sets of operators of GRA. We also discuss variants and extensions of GRA, and we provide algebraic characterizations of a range of well-known decidable logics

Generalized quantifiers in distributed databases.

Optimizing queries in a distributed database is quite difficult. This work proposes defining new generalized quantifiers which operate on sets rather than tuples. These quantifiers would allow for easier optimization in a horizontally distributed database. These operators are scalable with respect to both the number of hosts in the environment and the size of the data used

Principles of Guarded Structural Indexing

We present a new structural characterization of the expressive power of the acyclic conjunctive queries in terms of guarded simulations, and give a finite preservation theorem for the guarded simulation invariant fragment of first order logic. We discuss the relevance of these results as a formal basis for constructing so-called guarded structural indexes. Structural indexes were first proposed in the context of semistructured query languages and later successfully applied as an XML indexation mechanism for XPath-like queries on trees and graphs. Guarded structural indexes provide a generalization of structural indexes from graph databases to relational databases

Evaluating Datalog via Tree Automata and Cycluits

We investigate parameterizations of both database instances and queries that make query evaluation fixed-parameter tractable in combined complexity. We show that clique-frontier-guarded Datalog with stratified negation (CFG-Datalog) enjoys bilinear-time evaluation on structures of bounded treewidth for programs of bounded rule size. Such programs capture in particular conjunctive queries with simplicial decompositions of bounded width, guarded negation fragment queries of bounded CQ-rank, or two-way regular path queries. Our result is shown by translating to alternating two-way automata, whose semantics is defined via cyclic provenance circuits (cycluits) that can be tractably evaluated.Comment: 56 pages, 63 references. Journal version of "Combined Tractability of Query Evaluation via Tree Automata and Cycluits (Extended Version)" at arXiv:1612.04203. Up to the stylesheet, page/environment numbering, and possible minor publisher-induced changes, this is the exact content of the journal paper that will appear in Theory of Computing Systems. Update wrt version 1: latest reviewer feedbac

Trial for RDF: adapting graph query languages for RDF data

Querying RDF data is viewed as one of the main applications of graph query languages, and yet the standard model of graph databases – essentially labeled graphs – is different from the triples-based model of RDF. While encodings of RDF databases into graph data exist, we show that even the most natural ones are bound to lose somefunctionalitywhenused inconjunctionwith graph query languages. The solution is to work directly with triples, but then many properties taken for granted in the graphdatabasecontext(e.g., reachability)losetheir natural meaning. Our goal is to introduce languages that work directly over triples and are closed, i.e., they produce sets of triples, ratherthan graphs. Our basiclanguageis called TriAL, or Triple Algebra: it guarantees closure properties by replacing the product with a family of join operations. We extend TriAL with recursion, and explain why such an extension is more intricate for triples than for graphs. We present a declarative language, namely a fragment of datalog, capturing the recursive algebra. For both languages, the combined complexity of query evaluation is given by low-degree polynomials. We compare our languages with relational languages, such as finite-variable logics, and previously studied graph query languages such as adaptations of XPath, regular path queries, and nested regular expressions; many of these languages are subsumed by the recursive triple algebra. We also provide examples of the usefulness of TriAL in querying graph, RDF, and social networks data