13 research outputs found
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
ΠΠ½Π°Π»ΠΈΠ· ΡΠΈΠΏΠΈΠ·ΠΈΡΠΎΠ²Π°Π½Π½ΡΡ Π·Π°Π²ΠΈΡΠΈΠΌΠΎΡΡΠ΅ΠΉ Π²ΠΊΠ»ΡΡΠ΅Π½ΠΈΡ Ρ Π½Π΅ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½Π½ΡΠΌΠΈ Π·Π½Π°ΡΠ΅Π½ΠΈΡΠΌΠΈ
Null values have become an urgent problem since the creation of the relational dataΒ model. The impact of the uncertainty aο¬ects all types of dependencies used in the design and operationΒ of the database. This fully applies to the inclusion dependencies, which are the theoretical basis forΒ referential integrity on the data. Attempts to solve this problem contain inaccuracy in the statementΒ of the problem and its solution. The errors in formulation of the problem can be associated with theΒ use in the deο¬nition of untyped inclusion dependencies, which leads to permutations of the attributes,Β although, the attributes in database technology are identiο¬ed by name and not by their place. In addition, linking with the use of the inclusion dependencies of heterogeneous attributes, even of the same type, is a sign of lost functional dependencies and leads to interaction of inclusion dependencies and non-trivial functional dependencies. Inaccuracies in the solution of the problem are contained in the statements of axioms and the proof of their properties, including completeness. In this paper we propose an original solution of this problem only for typed inclusion dependencies in the presence of Null values: a new axiom system is proposed, its completeness and soundness are proved. On the basis of inference rules we developed an algorithm for the construction of a not surplus set of typed inclusion dependencies. The correctness of the algorithm is proved.ΠΠ΅ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½Π½ΡΠ΅ Π·Π½Π°ΡΠ΅Π½ΠΈΡ ΡΡΠ°Π»ΠΈ Π°ΠΊΡΡΠ°Π»ΡΠ½ΠΎΠΉ ΠΏΡΠΎΠ±Π»Π΅ΠΌΠΎΠΉ Ρ ΠΌΠΎΠΌΠ΅Π½ΡΠ° ΡΠΎΠ·Π΄Π°Π½ΠΈΡ ΡΠ΅Π»ΡΡΠΈΠΎΠ½Π½ΠΎΠΉ ΠΌΠΎΠ΄Π΅Π»ΠΈ Π΄Π°Π½Π½ΡΡ
. ΠΠ»ΠΈΡΠ½ΠΈΠ΅ Π½Π΅ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½Π½ΠΎΡΡΠ΅ΠΉ ΡΠΊΠ°Π·ΡΠ²Π°Π΅ΡΡΡ Π½Π° Π²ΡΠ΅Ρ
Π²ΠΈΠ΄Π°Ρ
Π·Π°Π²ΠΈΡΠΈΠΌΠΎΡΡΠ΅ΠΉ,Β ΠΈΡΠΏΠΎΠ»ΡΠ·ΡΠ΅ΠΌΡΡ
ΠΏΡΠΈ ΠΏΡΠΎΠ΅ΠΊΡΠΈΡΠΎΠ²Π°Π½ΠΈΠΈ ΠΈ ΡΠΊΡΠΏΠ»ΡΠ°ΡΠ°ΡΠΈΠΈ Π±Π°Π·Ρ Π΄Π°Π½Π½ΡΡ
. Π ΠΏΠΎΠ»Π½ΠΎΠΉ ΠΌΠ΅ΡΠ΅ ΡΡΠΎ ΠΎΡΠ½ΠΎΡΠΈΡΡΡ ΠΈΒ ΠΊ Π·Π°Π²ΠΈΡΠΈΠΌΠΎΡΡΡΠΌ Π²ΠΊΠ»ΡΡΠ΅Π½ΠΈΡ, ΠΊΠΎΡΠΎΡΡΠ΅ ΡΠ²Π»ΡΡΡΡΡ ΡΠ΅ΠΎΡΠ΅ΡΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΎΡΠ½ΠΎΠ²ΠΎΠΉ ΡΡΡΠ»ΠΎΡΠ½ΠΎΠΉ ΡΠ΅Π»ΠΎΡΡΠ½ΠΎΡΡΠΈ Π½Π°Β Π΄Π°Π½Π½ΡΠ΅. ΠΠΎΠΏΡΡΠΊΠΈ ΡΠ΅ΡΠ΅Π½ΠΈΡ ΡΠΊΠ°Π·Π°Π½Π½ΠΎΠΉ ΠΏΡΠΎΠ±Π»Π΅ΠΌΡ ΡΠΎΠ΄Π΅ΡΠΆΠ°Ρ Π½Π΅ΡΠΎΡΠ½ΠΎΡΡΠΈ ΠΊΠ°ΠΊ Π² ΠΏΠΎΡΡΠ°Π½ΠΎΠ²ΠΊΠ΅ Π·Π°Π΄Π°ΡΠΈ,Β ΡΠ°ΠΊ ΠΈ Π² ΡΠ°ΠΌΠΎΠΌ Π΅Π΅ ΡΠ΅ΡΠ΅Π½ΠΈΠΈ. Π ΠΏΠΎΡΡΠ°Π½ΠΎΠ²ΠΎΡΠ½ΡΠΌ ΠΎΡΠΈΠ±ΠΊΠ°ΠΌ ΠΌΠΎΠΆΠ½ΠΎ ΠΎΡΠ½Π΅ΡΡΠΈ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΠ΅ Π² ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΠΈ Π½Π΅ΡΠΈΠΏΠΈΠ·ΠΈΡΠΎΠ²Π°Π½Π½ΡΡ
Π·Π°Π²ΠΈΡΠΈΠΌΠΎΡΡΠ΅ΠΉ Π²ΠΊΠ»ΡΡΠ΅Π½ΠΈΡ, ΡΡΠΎ ΠΏΡΠΈΠ²ΠΎΠ΄ΠΈΡ ΠΊ ΠΏΠ΅ΡΠ΅ΡΡΠ°Π½ΠΎΠ²ΠΊΠ°ΠΌ Π°ΡΡΠΈΠ±ΡΡΠΎΠ², Ρ
ΠΎΡΡ Π²Β ΡΠ΅Ρ
Π½ΠΎΠ»ΠΎΠ³ΠΈΡΡ
Π±Π°Π· Π΄Π°Π½Π½ΡΡ
Π°ΡΡΠΈΠ±ΡΡΡ ΠΈΠ΄Π΅Π½ΡΠΈΡΠΈΡΠΈΡΡΡΡΡΡ ΠΏΠΎ ΠΈΠΌΠ΅Π½ΠΈ, Π° Π½Π΅ ΠΏΠΎ ΠΈΡ
ΠΏΠΎΠ·ΠΈΡΠΈΠΈ. ΠΡΠΎΠΌΠ΅ ΡΠΎΠ³ΠΎ,Β ΡΠ²ΡΠ·ΡΠ²Π°Π½ΠΈΠ΅ Π·Π°Π²ΠΈΡΠΈΠΌΠΎΡΡΡΡ Π²ΠΊΠ»ΡΡΠ΅Π½ΠΈΡ ΡΠ°Π·Π½ΠΎΡΠΎΠ΄Π½ΡΡ
, ΠΏΡΡΡΡ Π΄Π°ΠΆΠ΅ ΠΎΠ΄Π½ΠΎΡΠΈΠΏΠ½ΡΡ
, Π°ΡΡΠΈΠ±ΡΡΠΎΠ² ΡΠ²Π»ΡΠ΅ΡΡΡΒ ΠΏΡΠΈΠ·Π½Π°ΠΊΠΎΠΌ ΠΏΠΎΡΠ΅ΡΡΠ½Π½ΠΎΠΉ ΡΡΠ½ΠΊΡΠΈΠΎΠ½Π°Π»ΡΠ½ΠΎΠΉ Π·Π°Π²ΠΈΡΠΈΠΌΠΎΡΡΠΈ ΠΈ ΠΏΡΠΈΠ²ΠΎΠ΄ΠΈΡ ΠΊ Π²Π·Π°ΠΈΠΌΠΎΠ΄Π΅ΠΉΡΡΠ²ΠΈΡ Π½Π΅ΡΡΠΈΠ²ΠΈΠ°Π»ΡΠ½ΡΡ
Π·Π°Π²ΠΈΡΠΈΠΌΠΎΡΡΠ΅ΠΉ Π²ΠΊΠ»ΡΡΠ΅Π½ΠΈΡ ΠΈ ΡΡΠ½ΠΊΡΠΈΠΎΠ½Π°Π»ΡΠ½ΡΡ
Π·Π°Π²ΠΈΡΠΈΠΌΠΎΡΡΠ΅ΠΉ. ΠΠ°Π²ΠΈΡΠΈΠΌΠΎΡΡΠΈ Π²ΠΊΠ»ΡΡΠ΅Π½ΠΈΡ Π΄ΠΎΠ»ΠΆΠ½ΡΒ ΠΎΠΏΡΠ΅Π΄Π΅Π»ΡΡΡ ΠΊΠΎΠ»ΠΈΡΠ΅ΡΡΠ²Π΅Π½Π½ΠΎΠ΅ ΡΠΎΠΎΡΠ½Π΅ΡΠ΅Π½ΠΈΠ΅ ΠΎΠ±ΡΠ΅ΠΊΡΠΎΠ² Π΄ΡΡΠ³ Ρ Π΄ΡΡΠ³ΠΎΠΌ, Π° Π½Π΅ Π·Π½Π°ΡΠ΅Π½ΠΈΠΉ Π°ΡΡΠΈΠ±ΡΡΠΎΠ². ΠΠ΅ΡΠΎΡΠ½ΠΎΡΡΠΈ Π² ΡΠ΅ΡΠ΅Π½ΠΈΠΈ ΡΠΊΠ°Π·Π°Π½Π½ΠΎΠΉ ΠΏΡΠΎΠ±Π»Π΅ΠΌΡ ΡΠΎΠ΄Π΅ΡΠΆΠ°ΡΡΡ Π² ΡΠΎΡΠΌΡΠ»ΠΈΡΠΎΠ²ΠΊΠ°Ρ
Π°ΠΊΡΠΈΠΎΠΌ ΠΈ Π΄ΠΎΠΊΠ°Π·Π°ΡΠ΅Π»ΡΡΡΠ²Π΅ ΠΈΡ
Β ΡΠ²ΠΎΠΉΡΡΠ², Π² ΡΠΎΠΌ ΡΠΈΡΠ»Π΅ ΠΏΠΎΠ»Π½ΠΎΡΡ. Π ΡΡΠΎΠΉ ΡΡΠ°ΡΡΠ΅ ΠΏΡΠ΅Π΄Π»Π°Π³Π°Π΅ΡΡΡ ΠΎΡΠΈΠ³ΠΈΠ½Π°Π»ΡΠ½ΠΎΠ΅ ΡΠ΅ΡΠ΅Π½ΠΈΠ΅ ΡΡΠΎΠΉ ΠΏΡΠΎΠ±Π»Π΅ΠΌΡ ΡΠΎΠ»ΡΠΊΠΎ Π΄Π»Ρ ΡΠΈΠΏΠΈΠ·ΠΈΡΠΎΠ²Π°Π½Π½ΡΡ
Π·Π°Π²ΠΈΡΠΈΠΌΠΎΡΡΠ΅ΠΉ Π²ΠΊΠ»ΡΡΠ΅Π½ΠΈΡ ΠΏΡΠΈ Π½Π°Π»ΠΈΡΠΈΠΈ Π½Π΅ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½Π½ΡΡ
Π·Π½Π°ΡΠ΅Π½ΠΈΠΉ:Β ΠΏΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½Π° ΡΠΈΡΡΠ΅ΠΌΠ° Π°ΠΊΡΠΈΠΎΠΌ, Π΄ΠΎΠΊΠ°Π·Π°Π½Π° Π΅Π΅ ΠΏΠΎΠ»Π½ΠΎΡΠ° ΠΈ Π½Π΅ΠΏΡΠΎΡΠΈΠ²ΠΎΡΠ΅ΡΠΈΠ²ΠΎΡΡΡ. ΠΠ° ΠΎΡΠ½ΠΎΠ²Π΅ ΠΏΡΠ°Π²ΠΈΠ» Π²ΡΠ²ΠΎΠ΄Π° ΡΠ°Π·ΡΠ°Π±ΠΎΡΠ°Π½ Π°Π»Π³ΠΎΡΠΈΡΠΌ ΠΏΠΎΡΡΡΠΎΠ΅Π½ΠΈΡ Π½Π΅ ΠΈΠ·Π±ΡΡΠΎΡΠ½ΠΎΠ³ΠΎ ΠΌΠ½ΠΎΠΆΠ΅ΡΡΠ²Π° ΡΠΈΠΏΠΈΠ·ΠΈΡΠΎΠ²Π°Π½Π½ΡΡ
Π·Π°Π²ΠΈΡΠΈΠΌΠΎΡΡΠ΅ΠΉΒ Π²ΠΊΠ»ΡΡΠ΅Π½ΠΈΡ. ΠΠΎΠΊΠ°Π·Π°Π½Π° ΠΊΠΎΡΡΠ΅ΠΊΡΠ½ΠΎΡΡΡ ΡΡΠΎΠ³ΠΎ Π°Π»Π³ΠΎΡΠΈΡΠΌΠ°
A PC Chase
PC stands for path-conjunctive, the name of a class of queries and dependencies that we define over complex values with dictionaries. This class includes the relational conjunctive queries and embedded dependencies, as well as many interesting examples of complex value and oodb queries and integrity constraints. We show that some important classical results on containment, dependency implication, and chasing extend and generalize to this class
Static Analysis of Graph Database Transformations
We investigate graph transformations, defined using Datalog-like rules based
on acyclic conjunctive two-way regular path queries (acyclic C2RPQs), and we
study two fundamental static analysis problems: type checking and equivalence
of transformations in the presence of graph schemas. Additionally, we
investigate the problem of target schema elicitation, which aims to construct a
schema that closely captures all outputs of a transformation over graphs
conforming to the input schema. We show all these problems are in EXPTIME by
reducing them to C2RPQ containment modulo schema; we also provide matching
lower bounds. We use cycle reversing to reduce query containment to the problem
of unrestricted (finite or infinite) satisfiability of C2RPQs modulo a theory
expressed in a description logic
Finite Open-World Query Answering with Number Restrictions (Extended Version)
Open-world query answering is the problem of deciding, given a set of facts,
conjunction of constraints, and query, whether the facts and constraints imply
the query. This amounts to reasoning over all instances that include the facts
and satisfy the constraints. We study finite open-world query answering (FQA),
which assumes that the underlying world is finite and thus only considers the
finite completions of the instance. The major known decidable cases of FQA
derive from the following: the guarded fragment of first-order logic, which can
express referential constraints (data in one place points to data in another)
but cannot express number restrictions such as functional dependencies; and the
guarded fragment with number restrictions but on a signature of arity only two.
In this paper, we give the first decidability results for FQA that combine both
referential constraints and number restrictions for arbitrary signatures: we
show that, for unary inclusion dependencies and functional dependencies, the
finiteness assumption of FQA can be lifted up to taking the finite implication
closure of the dependencies. Our result relies on new techniques to construct
finite universal models of such constraints, for any bound on the maximal query
size.Comment: 59 pages. To appear in LICS 2015. Extended version including proof
When Can We Answer Queries Using Result-Bounded Data Interfaces?
We consider answering queries on data available through access methods, that
provide lookup access to the tuples matching a given binding. Such interfaces
are common on the Web; further, they often have bounds on how many results they
can return, e.g., because of pagination or rate limits. We thus study
result-bounded methods, which may return only a limited number of tuples. We
study how to decide if a query is answerable using result-bounded methods,
i.e., how to compute a plan that returns all answers to the query using the
methods, assuming that the underlying data satisfies some integrity
constraints. We first show how to reduce answerability to a query containment
problem with constraints. Second, we show "schema simplification" theorems
describing when and how result bounded services can be used. Finally, we use
these theorems to give decidability and complexity results about answerability
for common constraint classes.Comment: 65 pages; journal version of the PODS'18 paper arXiv:1706.0793
When Can We Answer Queries Using Result-Bounded Data Interfaces?
We consider answering queries where the underlying data is available only
over limited interfaces which provide lookup access to the tuples matching a
given binding, but possibly restricting the number of output tuples returned.
Interfaces imposing such "result bounds" are common in accessing data via the
web. Given a query over a set of relations as well as some integrity
constraints that relate the queried relations to the data sources, we examine
the problem of deciding if the query is answerable over the interfaces; that
is, whether there exists a plan that returns all answers to the query, assuming
the source data satisfies the integrity constraints.
The first component of our analysis of answerability is a reduction to a
query containment problem with constraints. The second component is a set of
"schema simplification" theorems capturing limitations on how interfaces with
result bounds can be useful to obtain complete answers to queries. These
results also help to show decidability for the containment problem that
captures answerability, for many classes of constraints. The final component in
our analysis of answerability is a "linearization" method, showing that query
containment with certain guarded dependencies -- including those that emerge
from answerability problems -- can be reduced to query containment for a
well-behaved class of linear dependencies. Putting these components together,
we get a detailed picture of how to check answerability over result-bounded
services.Comment: 45 pages, 2 tables, 43 references. Complete version with proofs of
the PODS'18 paper. The main text of this paper is almost identical to the
PODS'18 except that we have fixed some small mistakes. Relative to the
earlier arXiv version, many errors were corrected, and some terminology has
change