scholarly journals Integrity Constraints Revisited: From Exact to Approximate Implication

2022 ◽  
Vol Volume 18, Issue 1 ◽  
Author(s):  
Batya Kenig ◽  
Dan Suciu
Keyword(s):  
Linear Inequality ◽  
Measure Theory ◽  
Probability Distributions ◽  
Integrity Constraints ◽  
Functional Dependencies ◽  
Data Dependencies ◽  
Relaxation Problem ◽  
Implication Problem ◽  
Schema Design ◽  
Degree Of Satisfaction

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". Then, we show that the implication problem for differential constraints in market basket analysis also admits a relaxation with a factor equal to 1. Finally, we show how some of the results in the paper can be derived using the I-measure theory, which relates between information theoretic measures and set theory. Our results recover, and sometimes extend, previously known results about the implication problem: the implication of MVDs and FDs can be checked by considering only 2-tuple relations.

scholarly journals On the Discovery of Semantically Meaningful SQL Constraints from Armstrong Samples: Foundations, Implementation, and Evaluation

2021 ◽  
Author(s):  
◽  
Van Tran Bao Le
Keyword(s):  
Database Design ◽  
Design Tool ◽  
Relational Model ◽  
Functional Dependencies ◽  
Data Dependencies ◽  
Design Choice ◽  
Implication Problem ◽  
Finite Set ◽  
Current Design ◽  
Class C

<p>A database is said to be C-Armstrong for a finite set Σ of data dependencies in a class C if the database satisfies all data dependencies in Σ and violates all data dependencies in C that are not implied by Σ. Therefore, Armstrong databases are concise, user-friendly representations of abstract data dependencies that can be used to judge, justify, convey, and test the understanding of database design choices. Indeed, an Armstrong database satisfies exactly those data dependencies that are considered meaningful by the current design choice Σ. Structural and computational properties of Armstrong databases have been deeply investigated in Codd’s Turing Award winning relational model of data. Armstrong databases have been incorporated in approaches towards relational database design. They have also been found useful for the elicitation of requirements, the semantic sampling of existing databases, and the specification of schema mappings. This research establishes a toolbox of Armstrong databases for SQL data. This is challenging as SQL data can contain null marker occurrences in columns declared NULL, and may contain duplicate rows. Thus, the existing theory of Armstrong databases only applies to idealized instances of SQL data, that is, instances without null marker occurrences and without duplicate rows. For the thesis, two popular interpretations of null markers are considered: the no information interpretation used in SQL, and the exists but unknown interpretation by Codd. Furthermore, the study is limited to the popular class C of functional dependencies. However, the presence of duplicate rows means that the class of uniqueness constraints is no longer subsumed by the class of functional dependencies, in contrast to the relational model of data. As a first contribution a provably-correct algorithm is developed that computes Armstrong databases for an arbitrarily given finite set of uniqueness constraints and functional dependencies. This contribution is based on axiomatic, algorithmic and logical characterizations of the associated implication problem that are also established in this thesis. While the problem to decide whether a given database is Armstrong for a given set of such constraints is precisely exponential, our algorithm computes an Armstrong database with a number of rows that is at most quadratic in the number of rows of a minimum-sized Armstrong database. As a second contribution the algorithms are implemented in the form of a design tool. Users of the tool can therefore inspect Armstrong databases to analyze their current design choice Σ. Intuitively, Armstrong databases are useful for the acquisition of semantically meaningful constraints, if the users can recognize the actual meaningfulness of constraints that they incorrectly perceived as meaningless before the inspection of an Armstrong database. As a final contribution, measures are introduced that formalize the term “useful” and it is shown by some detailed experiments that Armstrong tables, as computed by the tool, are indeed useful. In summary, this research establishes a toolbox of Armstrong databases that can be applied by database designers to concisely visualize constraints on SQL data. Such support can lead to database designs that guarantee efficient data management in practice.</p>

scholarly journals Approximate denial constraints

2020 ◽  
Vol 13 (10) ◽  
pp. 1682-1695
Author(s):  
Ester Livshits ◽  
Alireza Heidari ◽  
Ihab F. Ilyas ◽  
Benny Kimelfeld
Keyword(s):  
Integrity Constraints ◽  
Functional Dependencies ◽  
Approximation Function ◽  
Inconsistent Databases ◽  
The Past

The problem of mining integrity constraints from data has been extensively studied over the past two decades for commonly used types of constraints, including the classic Functional Dependencies (FDs) and the more general Denial Constraints (DCs). In this paper, we investigate the problem of mining from data approximate DCs, that is, DCs that are "almost" satisfied. Approximation allows us to discover more accurate constraints in inconsistent databases and detect rules that are generally correct but may have a few exceptions. It also allows to avoid overfitting and obtain constraints that are more general, more natural, and less contrived. We introduce the algorithm ADCMiner for mining approximate DCs. An important feature of this algorithm is that it does not assume any specific approximation function for DCs, but rather allows for arbitrary approximation functions that satisfy some natural axioms that we define in the paper. We also show how our algorithm can be combined with sampling to return highly accurate results considerably faster.

Towards a Normal Form and a Query Language for Extended Relations Defined by Regular Expressions

2016 ◽  
Vol 27 (2) ◽  
pp. 27-48
Author(s):  
András Benczúr ◽  
Gyula I. Szabó
Keyword(s):  
Normal Form ◽  
Data Base ◽  
Data Model ◽  
Query Language ◽  
Xml Schema ◽  
Relational Model ◽  
Regular Expressions ◽  
Functional Dependencies ◽  
Decision Algorithm ◽  
Implication Problem

This paper introduces a generalized data base concept that unites relational and semi structured data models. As an important theoretical result we could find a quadratic decision algorithm for the implication problem of functional and join dependencies defined on the united data model. As practical contribution we presented a normal form for the new data model as a tool for data base design. With our novel representations of regular expressions, a more effective searching method could be developed. XML elements are described by XML schema languages such as a DTD or an XML Schema definition. The instances of these elements are semi-structured tuples. A semi-structured tuple is an ordered list of (attribute: value) pairs. We may think of a semi-structured tuple as a sentence of a formal language, where the values are the terminal symbols and the attribute names are the non-terminal symbols. In the authors' former work (Szabó and Benczúr, 2015) they introduced the notion of the extended tuple as a sentence from a regular language generated by a grammar where the non-terminal symbols of the grammar are the attribute names of the tuple. Sets of extended tuples are the extended relations. The authors then introduced the dual language, which generates the tuple types allowed to occur in extended relations. They defined functional dependencies (regular FD - RFD) over extended relations. In this paper they rephrase the RFD concept by directly using regular expressions over attribute names to define extended tuples. By the help of a special vertex labeled graph associated to regular expressions the specification of substring selection for the projection operation can be defined. The normalization for regular schemas is more complex than it is in the relational model, because the schema of an extended relation can contain an infinite number of tuple types. However, the authors can define selection, projection and join operations on extended relations too, so a lossless-join decomposition can be performed. They extended their previous model to deal with XML schema indicators too, e.g., with numerical constraints. They added line and set constructors too, in order to extend their model with more general projection and selection operators. This model establishes a query language with table join functionality for collected XML element data.

Data Dependencies in Codd's Relational Model with Similarities

2011 ◽  
pp. 634-657
Author(s):  
Radim Belohlavek ◽  
Vilem Vychodil
Keyword(s):  
Fuzzy Logic ◽  
Classical Logic ◽  
Reference Model ◽  
Relational Model ◽  
Future Research ◽  
Functional Dependencies ◽  
Narrow Sense ◽  
Data Dependencies ◽  
Similarity Relations ◽  
Conceptual Clarity

This chapter deals with data dependencies in Codd’s relational model of data. In particular, we deal with fuzzy logic extensions of the relational model that consist of adding similarity relations to domains and consider functional dependencies in these extensions. We present a particular extension and functional dependencies in this extension that follow the principles of fuzzy logic in a narrow sense. We present selected features and results regarding this extension. Then, we use this extension as a reference model and compare it to several other extensions proposed in the literature. We argue that following the principles of fuzzy logic in a narrow sense, the same way we can follow the principles of classical logic in the case of the ordinary Codd relational model, helps achieve transparency, versatility, conceptual clarity, and theoretical and computational tractability of the extension. We outline several topics for future research.

Consistent Queries over Databases with Integrity Constraints

2009 ◽  
pp. 2051-2058
Author(s):  
Luciano Caroprese ◽  
Cristian Molinaro ◽  
Irina Trubitsyna ◽  
Ester Zumpano
Keyword(s):  
Integrity Constraints ◽  
Database Integration ◽  
Functional Dependencies ◽  
Distributed Information ◽  
Semantic Query ◽  
Cooperative Query Answering ◽  
Semantic Query Optimization ◽  
Integration Architecture ◽  
Source Of Information ◽  
Different Sources

Integrating data from different sources consists of two main steps, the first in which the various relations are merged together, and the second in which some tuples are removed (or inserted) from the resulting database in order to satisfy integrity constraints. There are several ways to integrate databases or possibly distributed information sources, but whatever integration architecture we choose, the heterogeneity of the sources to be integrated causes subtle problems. In particular, the database obtained from the integration process may be inconsistent with respect to integrity constraints, that is, one or more integrity constraints are not satisfied. Integrity constraints represent an important source of information about the real world. They are usually used to define constraints on data (functional dependencies, inclusion dependencies, etc.) and have, nowadays, a wide applicability in several contexts such as semantic query optimization, cooperative query answering, database integration, and view update.

Managing Inconsistent Databases Using Active Integrity Constraints

2005 ◽  
pp. 345-350
Author(s):  
Sergio Flesca ◽  
Sergio Greco ◽  
Ester Zumpano
Keyword(s):  
Data Warehousing ◽  
Integrity Constraints ◽  
Database Integration ◽  
Functional Dependencies ◽  
Minimal Set ◽  
Federated Databases ◽  
Inconsistent Databases ◽  
Conflicting Information ◽  
Integration Data ◽  
Inconsistent Database

Integrity constraints are a fundamental part of a database schema. They are generally used to define constraints on data (functional dependencies, inclusion dependencies, exclusion dependencies, etc.), and their enforcement ensures a semantically correct state of a database. As the presence of data inconsistent with respect to integrity constraints is not unusual, its management plays a key role in all the areas in which duplicate or conflicting information is likely to occur, such as database integration, data warehousing, and federated databases (Bry, 1997; Lin, 1996; Subrahmanian, 1994). It is well known that the presence of inconsistent data can be managed by “repairing” the database, that is, by providing consistent databases, obtained by a minimal set of update operations on the inconsistent original environment, or by consistently answering queries posed over the inconsistent database.

scholarly journals Planning and managing resources of transport enterprises

2018 ◽  
Vol 239 ◽  
pp. 04023
Author(s):  
Viktor Terskikh ◽  
Vladimir Katargin ◽  
Natalia Morozova
Keyword(s):  
System Reliability ◽  
Probability Distributions ◽  
Road Transport ◽  
Spare Parts ◽  
Target Level ◽  
Management Effectiveness ◽  
New Approach ◽  
Degree Of Satisfaction ◽  
The Cost ◽  
Statistical Indicators

The paper considers a new approach to planning and forming a stock of spare parts necessary for the smooth functioning of transport enterprises. The basis of the author's approach is the developed simulation model of the warehouse adapted for any type of enterprise that serves and (or) operates road transport. The need for spare parts in this model is defined as a mixture of probability distributions of demand of various kinds, which makes it universal. The model was based on the new patterns of influence of following factors on the size of the stock revealed by the authors: the statistical indicators of the need for spare parts, the type and location of the enterprise, the target level of reliability of the supply system, etc. The proposed approach allows connecting the main indicators of the resource management effectiveness: the shortage rate, the cost of stock, the level of system reliability. It allows planning and forming a stock of spare parts reasonably. It is expected that the proposed approach will increase the efficiency of transport enterprises and the degree of satisfaction of consumers of their services.

scholarly journals Satisfaction and Implication of Integrity Constraints in Ontology-based Data Access

2019 ◽  
Author(s):  
Charalampos Nikolaou ◽  
Bernardo Cuenca Grau ◽  
Egor V. Kostylev ◽  
Mark Kaminski ◽  
Ian Horrocks
Keyword(s):  
Constraint Satisfaction ◽  
Data Access ◽  
Integrity Constraints ◽  
Functional Dependencies ◽  
Complexity Bounds ◽  
Decidability And Complexity

We extend ontology-based data access with integrity constraints over both the source and target schemas. The relevant reasoning problems in this setting are constraint satisfaction—to check whether a database satisfies the target constraints given the mappings and the ontology—and source-to-target (resp., target-to-source) constraint implication, which is to check whether a target constraint (resp., a source constraint) is satisfied by each database satisfying the source constraints (resp., the target constraints). We establish decidability and complexity bounds for all these problems in the case where ontologies are expressed in DL-LiteR and constraints range from functional dependencies to disjunctive tuple-generating dependencies.

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