437 research outputs found
Efficient Discovery of Ontology Functional Dependencies
Poor data quality has become a pervasive issue due to the increasing
complexity and size of modern datasets. Constraint based data cleaning
techniques rely on integrity constraints as a benchmark to identify and correct
errors. Data values that do not satisfy the given set of constraints are
flagged as dirty, and data updates are made to re-align the data and the
constraints. However, many errors often require user input to resolve due to
domain expertise defining specific terminology and relationships. For example,
in pharmaceuticals, 'Advil' \emph{is-a} brand name for 'ibuprofen' that can be
captured in a pharmaceutical ontology. While functional dependencies (FDs) have
traditionally been used in existing data cleaning solutions to model syntactic
equivalence, they are not able to model broader relationships (e.g., is-a)
defined by an ontology. In this paper, we take a first step towards extending
the set of data quality constraints used in data cleaning by defining and
discovering \emph{Ontology Functional Dependencies} (OFDs). We lay out
theoretical and practical foundations for OFDs, including a set of sound and
complete axioms, and a linear inference procedure. We then develop effective
algorithms for discovering OFDs, and a set of optimizations that efficiently
prune the search space. Our experimental evaluation using real data show the
scalability and accuracy of our algorithms.Comment: 12 page
Integrity Constraints Revisited: From Exact to Approximate Implication
Integrity constraints such as functional dependencies (FD), and multi-valued dependencies (MVD) are fundamental in database schema design. Likewise, probabilistic conditional independences (CI) are crucial for reasoning about multivariate probability distributions. The implication problem studies whether a set of constraints (antecedents) implies another constraint (consequent), and has been investigated in both the database and the AI literature, under the assumption that all constraints hold exactly. However, many applications today consider constraints that hold only approximately. In this paper we define an approximate implication as a linear inequality between the degree of satisfaction of the antecedents and consequent, and we study the relaxation problem: when does an exact implication relax to an approximate implication? We use information theory to define the degree of satisfaction, and prove several results. First, we show that any implication from a set of data dependencies (MVDs+FDs) can be relaxed to a simple linear inequality with a factor at most quadratic in the number of variables; when the consequent is an FD, the factor can be reduced to 1. Second, we prove that there exists an implication between CIs that does not admit any relaxation; however, we prove that every implication between CIs relaxes "in the limit". Finally, we show that the implication problem for differential constraints in market basket analysis also admits a relaxation with a factor equal to 1. Our results recover, and sometimes extend, several previously known results about the implication problem: implication of MVDs can be checked by considering only 2-tuple relations, and the implication of differential constraints for frequent item sets can be checked by considering only databases containing a single transaction
Using concept lattices to mine functional dependencies
Concept Lattices have been proved to be a valuable tool to represent
the knowlegde in a database.
In this paper we show how functional dependencies in databases
can be extracted using Concept Lattices, not preprocessing the original
database,
but providing a new closure operator. We also prove that this method
generalizes the previous methods and
closure operators that are being used to find association rules in binary
databases.Postprint (published version
Integrity Constraints Revisited: From Exact to Approximate Implication
Integrity constraints such as functional dependencies (FD), and multi-valued
dependencies (MVD) are fundamental in database schema design. Likewise,
probabilistic conditional independences (CI) are crucial for reasoning about
multivariate probability distributions. The implication problem studies whether
a set of constraints (antecedents) implies another constraint (consequent), and
has been investigated in both the database and the AI literature, under the
assumption that all constraints hold exactly. However, many applications today
consider constraints that hold only approximately. In this paper we define an
approximate implication as a linear inequality between the degree of
satisfaction of the antecedents and consequent, and we study the relaxation
problem: when does an exact implication relax to an approximate implication? We
use information theory to define the degree of satisfaction, and prove several
results. First, we show that any implication from a set of data dependencies
(MVDs+FDs) can be relaxed to a simple linear inequality with a factor at most
quadratic in the number of variables; when the consequent is an FD, the factor
can be reduced to 1. Second, we prove that there exists an implication between
CIs that does not admit any relaxation; however, we prove that every
implication between CIs relaxes "in the limit". Finally, we show that the
implication problem for differential constraints in market basket analysis also
admits a relaxation with a factor equal to 1. Our results recover, and
sometimes extend, several previously known results about the implication
problem: implication of MVDs can be checked by considering only 2-tuple
relations, and the implication of differential constraints for frequent item
sets can be checked by considering only databases containing a single
transaction
Fundamentals and applications of order dependencies
Business-intelligence queries often involve SQL functions and algebraic expressions. There can be clear semantic relationships between a column's values and the values of a function over that column. A common property is monotonicity: as the column's values ascend, so do the function's values (or the other column's values). This we call an order dependency (OD). Queries can be evaluated more efficiently when the query optimizer uses order dependencies. They can be run even faster when the optimizer can also reason over known ODs to infer new ones.
Order dependencies can be declared as integrity constraints, and they can be detected automatically for many types of SQL functions and algebraic expressions. We present optimization techniques using ODs for queries that involve join, order by, group by, partition by, and distinct. Essentially, ODs can further exploit interesting orders to eliminate or simplify potentially expensive sorts in the query plan. We evaluate these techniques over our prototype implementation in IBM® DB2® using the TPC-DS® benchmark schema and some customer inspired queries. Our experimental results demonstrate a significant performance gain.
Dependencies have played an important role in database theory. We study the theoretical aspects of order dependencies-and unidirectional order dependencies (UODs), a proper sub-class of ODs-which describe the relationships among lexicographical orderings of sets of tuples. We investigate the inference problem for order dependencies. We establish the following: (i) a sound and complete axiomatization for UODs which is sound for ODs; (ii) a hierarchy of order dependency classes; (iii) a proof of co-NP-completeness of the inference problem for ODs and for the subclass of UODs; (iv) a proof of co-NP-completeness of the inference problem of functional dependencies (FDs) from ODs in general, but demonstrate linear time complexity for the inference of FDs from UODs; (v) a sound and complete elimination procedure for testing logical implication over ODs; and (vi) a sound and complete polynomial inference algorithm for sets of UODs over natural domains
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
Fuzzy inequational logic
We present a logic for reasoning about graded inequalities which generalizes
the ordinary inequational logic used in universal algebra. The logic deals with
atomic predicate formulas of the form of inequalities between terms and
formalizes their semantic entailment and provability in graded setting which
allows to draw partially true conclusions from partially true assumptions. We
follow the Pavelka approach and define general degrees of semantic entailment
and provability using complete residuated lattices as structures of truth
degrees. We prove the logic is Pavelka-style complete. Furthermore, we present
a logic for reasoning about graded if-then rules which is obtained as
particular case of the general result
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