429,370 research outputs found
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
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
Path constraints in semistructured databases
AbstractWe investigate a class of path constraints that is of interest in connection with both semistructured and structured data. In standard database systems, constraints are typically expressed as part of the schema, but in semistructured data there is no explicit schema and path constraints provide a natural alternative. As with structured data, path constraints on semistructured data express integrity constraints associated with the semantics of data and are important in query optimization. We show that in semistructured databases, despite the simple syntax of the constraints, their associated implication problem is r.e. complete and finite implication problem is co-r.e. complete. However, we establish the decidability of the implication and finite implication problems for several fragments of the path constraint language and demonstrate that these fragments suffice to express important semantic information such as extent constraints, inverse relationships, and local database constraints commonly found in object-oriented databases
Distribution Constraints: The Chase for Distributed Data
This paper introduces a declarative framework to specify and reason about distributions of data over computing nodes in a distributed setting. More specifically, it proposes distribution constraints which are tuple and equality generating dependencies (tgds and egds) extended with node variables ranging over computing nodes. In particular, they can express co-partitioning constraints and constraints about range-based data distributions by using comparison atoms. The main technical contribution is the study of the implication problem of distribution constraints. While implication is undecidable in general, relevant fragments of so-called data-full constraints are exhibited for which the corresponding implication problems are complete for EXPTIME, PSPACE and NP. These results yield bounds on deciding parallel-correctness for conjunctive queries in the presence of distribution constraints
Enhancing Reuse of Constraint Solutions to Improve Symbolic Execution
Constraint solution reuse is an effective approach to save the time of
constraint solving in symbolic execution. Most of the existing reuse approaches
are based on syntactic or semantic equivalence of constraints; e.g. the Green
framework is able to reuse constraints which have different representations but
are semantically equivalent, through canonizing constraints into syntactically
equivalent normal forms. However, syntactic/semantic equivalence is not a
necessary condition for reuse--some constraints are not syntactically or
semantically equivalent, but their solutions still have potential for reuse.
Existing approaches are unable to recognize and reuse such constraints.
In this paper, we present GreenTrie, an extension to the Green framework,
which supports constraint reuse based on the logical implication relations
among constraints. GreenTrie provides a component, called L-Trie, which stores
constraints and solutions into tries, indexed by an implication partial order
graph of constraints. L-Trie is able to carry out logical reduction and logical
subset and superset querying for given constraints, to check for reuse of
previously solved constraints. We report the results of an experimental
assessment of GreenTrie against the original Green framework, which shows that
our extension achieves better reuse of constraint solving result and saves
significant symbolic execution time.Comment: this paper has been submitted to conference ISSTA 201
A cognitive view of relevant implication
Relevant logics provide an alternative to classical implication
that is capable of accounting for the relationship between the antecedent
and the consequence of a valid implication. Relevant implication is usually
explained in terms of information required to assess a proposition.
By doing so, relevant implication introduces a number of cognitively relevant
aspects in the denition of logical operators. In this paper, we
aim to take a closer look at the cognitive feature of relevant implication.
For this purpose, we develop a cognitively-oriented interpretation of the
semantics of relevant logics. In particular, we provide an interpretation
of Routley-Meyer semantics in terms of conceptual spaces and we show
that it meets the constraints of the algebraic semantics of relevant logic
Dark energy, Ricci-nonflat spaces, and the Swampland
It was recently pointed out that the existence of dark energy imposes highly
restrictive constraints on effective field theories that satisfy the Swampland
conjectures. We provide a critical confrontation of these constraints with the
cosmological framework emerging from the Salam-Sezgin model and its string
realization by Cvetic, Gibbons, and Pope. We also discuss the implication of
the constraints for string model building.Comment: Matching version to be published in PL
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