Guaranteeing no interaction between functional dependencies and tree-like inclusion dependencies

Functional dependencies (FDs) and inclusion dependencies (INDs) are the most fundamental integrity constraints that arise in practice in relational databases. A given set of FDs does not interact with a given set of INDs if logical implication of any FD can be determined solely by the given set of FDs, and logical implication of any IND can be determined solely by the given set of INDs. The set of tree-like INDs constitutes a useful subclass of INDs whose implication problem is polynomial time decidable. We exhibit a necessary and sufficient condition for a set of FDs and tree-like INDs not to interact; this condition can be tested in polynomial time

On Independence Atoms and Keys

Uniqueness and independence are two fundamental properties of data. Their enforcement in database systems can lead to higher quality data, faster data service response time, better data-driven decision making and knowledge discovery from data. The applications can be effectively unlocked by providing efficient solutions to the underlying implication problems of keys and independence atoms. Indeed, for the sole class of keys and the sole class of independence atoms the associated finite and general implication problems coincide and enjoy simple axiomatizations. However, the situation changes drastically when keys and independence atoms are combined. We show that the finite and the general implication problems are already different for keys and unary independence atoms. Furthermore, we establish a finite axiomatization for the general implication problem, and show that the finite implication problem does not enjoy a k-ary axiomatization for any k

Reasoning about embedded dependencies using inclusion dependencies

The implication problem for the class of embedded dependencies is undecidable. However, this does not imply lackness of a proof procedure as exemplified by the chase algorithm. In this paper we present a complete axiomatization of embedded dependencies that is based on the chase and uses inclusion dependencies and implicit existential quantification in the intermediate steps of deductions

Inclusion and Exclusion Dependencies in Team Semantics: On Some Logics of Imperfect Information

We introduce some new logics of imperfect information by adding atomic formulas corresponding to inclusion and exclusion dependencies to the language of first order logic. The properties of these logics and their relationships with other logics of imperfect information are then studied. Furthermore, a game theoretic semantics for these logics is developed. As a corollary of these results, we characterize the expressive power of independence logic, thus answering an open problem posed in (Gr\"adel and V\"a\"an\"anen, 2010)

Querying Schemas With Access Restrictions

We study verification of systems whose transitions consist of accesses to a Web-based data-source. An access is a lookup on a relation within a relational database, fixing values for a set of positions in the relation. For example, a transition can represent access to a Web form, where the user is restricted to filling in values for a particular set of fields. We look at verifying properties of a schema describing the possible accesses of such a system. We present a language where one can describe the properties of an access path, and also specify additional restrictions on accesses that are enforced by the schema. Our main property language, AccLTL, is based on a first-order extension of linear-time temporal logic, interpreting access paths as sequences of relational structures. We also present a lower-level automaton model, Aautomata, which AccLTL specifications can compile into. We show that AccLTL and A-automata can express static analysis problems related to "querying with limited access patterns" that have been studied in the database literature in the past, such as whether an access is relevant to answering a query, and whether two queries are equivalent in the accessible data they can return. We prove decidability and complexity results for several restrictions and variants of AccLTL, and explain which properties of paths can be expressed in each restriction.Comment: VLDB201

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

On Variants of Dependence Logic : Axiomatizability and Expressiveness

Dependence logic is a novel logical formalism that has connections to database theory, statistics, linguistics, social choice theory, and physics. Its aim is to provide a systematic and mathematically rigorous tool for studying notions of dependence and independence in different areas. Recently many variants of dependence logic have been studied in the contexts of first-order, modal, and propositional logic. In this thesis we examine independence and inclusion logic that are variants of dependence logic extending first-order logic with so-called independence or inclusion atoms, respectively. The work consists of two parts in which we study either axiomatizability or expressivity hierarchies regarding these logics. In the first part we examine whether there exist some natural parameters of independence and inclusion logic that give rise to infinite expressivity or complexity hierarchies. Two main parameters are considered. These are arity of a dependency atom and number of universal quantifiers. We show that for both logics, the notion of arity gives rise to strict expressivity hierarchies. With respect to number of universal quantifiers however, strictness or collapse of the corresponding hierarchies turns out to be relative to the choice of semantics. In the second part we turn attention to axiomatizations. Due to their complexity, dependence and independence logic cannot have a complete recursively enumerable axiomatization. Hence, restricting attention to partial solutions, we first axiomatize all first-order consequences of independence logic sentences, thus extending an analogous result for dependence logic. We also consider the class of independence and inclusion atoms, and show that it can be axiomatized using implicit existential quantification. For relational databases this implies a sound and complete axiomatization of embedded multivalued and inclusion dependencies taken together. Lastly, we consider keys together with so-called pure independence atoms and prove both positive and negative results regarding their finite axiomatizability.Riippuvuuslogiikka on formalismi, joka tutkii muodollisen logiikan viitekehyksessä riippuvuuden ja riippumattomuuden käsitteitä. Koska nämä käsitteet ilmenevät myös monilla muilla eri tieteenaloilla, riippuvuuslogiikan tutkimus kytkeytyy muun muassa tietokantateoriaan, tilastotieteeseen, kielitieteeseen, sosiaalisen valinnan teoriaan ja fysiikkaan. Ideana riippuvuuslogiikassa on laajentaa tunnettuja muodollisen logiikan kieliä erilaisilla riippuvuuden käsitteillä. Propositio-, modaali- ja predikaattilogiikoille voidaan kaikille määritellä laajennoksia, joissa riippuvuuksia ilmaistaan uusien atomikaavojen avulla. Tämä väitöskirja tarkastelee kahta tällaista ensimmäisen kertaluvun predikaattilogiikan laajennosta. Toisessa uudet atomikaavat kuvaavat riippumattomuuden, ja toisessa sisältyvyyden käsitteitä. Saatuja laajennoksia kutsutaan riippumattomuuslogiikaksi ja inkluusiologiikaksi. Tutkielma jakautuu kahteen osaan. Ensimmäisessä osassa tarkastellaan edellä mainittujen logiikoiden ilmaisuvoimaan ja laskennalliseen vaativuuteen liittyviä hierarkioita. Kyseiset hierarkiat saadaan rajoittamalla joko uusien atomikaavojen kokoa tai universaalikvanttorien lukumäärää. Toisessa osassa tutkitaan riippumattomuus- ja inkluusiologiikan muodollista päättelyä. Tarkastelun kohteena on muodollisen päättelyn kehittäminen riippumattomuuslogiikan ensimmäisen kertaluvun seurauksille sekä erilaisille kokoelmille uusia atomikaavoja. Jälkimmäiseen tapaukseen kehitetty muodollisen päättelyn teoria soveltuu erityisesti relationaalisten tietokantojen riippuvuuskäsitteiden implikaatio-ongelmiin