Evaluation of Nonrecursive Datalog Queries
26.5.8 Evaluation of Nonrecursive Datalog Queries
In order to use Datalog as a deductive database system, it is appropriate to define an inference mechanism based on relational database query processing concepts. The inherent strategy involves a bottom-up evaluation, starting with base relations; the order of operations is kept flexible and subject to query optimization. In this section we discuss an inference mechanism based on relational operations that can be applied to nonrecursive Datalog queries. We use the fact and rule base shown in Figures 26.14 and 26.15 to illustrate our discussion.
If a query involves only fact-defined predicates, the inference becomes one of searching among the facts for the query result. For example, a query such as
DEPARTMENT (X, Research )? is a selection of all employee names X who work for the Research department. In
relational algebra, it is the query: π $1 ( σ $2 = “Research” ( DEPARTMENT )) which can be answered by searching through the fact-defined predicate
department (X,Y ). The query involves relational SELECT and PROJECT operations on a base relation, and it can be handled by the database query processing and opti-
982 Chapter 26 Enhanced Data Models for Advanced Applications
When a query involves rule-defined predicates, the inference mechanism must compute the result based on the rule definitions. If a query is nonrecursive and
involves a predicate p that appears as the head of a rule p :– p 1 ,p 2 , ... ,p n , the strategy is first to compute the relations corresponding to p 1 ,p 2 , ... ,p n and then to compute the relation corresponding to p. It is useful to keep track of the dependency among the predicates of a deductive database in a predicate dependency graph. Figure
26.17 shows the graph for the fact and rule predicates shown in Figures 26.14 and
26.15. The dependency graph contains a node for each predicate. Whenever a pred- icate A is specified in the body (RHS) of a rule, and the head (LHS) of that rule is the predicate B, we say that B depends on A, and we draw a directed edge from A to
B. This indicates that in order to compute the facts for the predicate B (the rule head), we must first compute the facts for all the predicates A in the rule body. If the dependency graph has no cycles, we call the rule set nonrecursive. If there is at least one cycle, we call the rule set recursive. In Figure 26.17, there is one recursively defined predicate—namely, SUPERIOR —which has a recursive edge pointing back to itself. Additionally, because the predicate subordinate depends on SUPERIOR , it also requires recursion in computing its result.
A query that includes only nonrecursive predicates is called a nonrecursive query. In this section we discuss only inference mechanisms for nonrecursive queries. In Figure 26.17, any query that does not involve the predicates SUBORDINATE or SUPERIOR is nonrecursive. In the predicate dependency graph, the nodes corre- sponding to fact-defined predicates do not have any incoming edges, since all fact- defined predicates have their facts stored in a database relation. The contents of a fact-defined predicate can be computed by directly retrieving the tuples in the cor- responding database relation.
UNDER_40K_SUPERVISOR SUBORDINATE Predicate dependency graph for Figures
MAIN_PRODUCT_EMP
OVER_40K_EMP
SUPERIOR
WORKS_ON
EMPLOYEE
SALARY
SUPERVISE
26.6 Summary 983
The main function of an inference mechanism is to compute the facts that corre- spond to query predicates. This can be accomplished by generating a relational expression involving relational operators as SELECT , PROJECT , JOIN , UNION , and SET DIFFERENCE (with appropriate provision for dealing with safety issues) that, when executed, provides the query result. The query can then be executed by utiliz- ing the internal query processing and optimization operations of a relational data- base management system. Whenever the inference mechanism needs to compute the fact set corresponding to a nonrecursive rule-defined predicate p, it first locates all the rules that have p as their head. The idea is to compute the fact set for each such rule and then to apply the UNION operation to the results, since UNION corre- sponds to a logical OR operation. The dependency graph indicates all predicates q on which each p depends, and since we assume that the predicate is nonrecursive, we can always determine a partial order among such predicates q. Before computing the fact set for p, first we compute the fact sets for all predicates q on which p depends, based on their partial order. For example, if a query involves the predicate UNDER_40K_SUPERVISOR , we must first compute both SUPERVISOR and OVER_40K_EMP . Since the latter two depend only on the fact-defined predicates EMPLOYEE , SALARY , and SUPERVISE , they can be computed directly from the stored database relations.
This concludes our introduction to deductive databases. Additional material may be found at the book’s Website, where the complete Chapter 25 from the third edition is available. This includes a discussion on algorithms for recursive query processing. We have included an extensive bibliography of work in deductive databases, recur- sive query processing, magic sets, combination of relational databases with deduc- tive rules, and GLUE-NAIL! System at the end of this chapter.
Parts
» Fundamentals_of_Database_Systems,_6th_Edition
» Characteristics of the Database Approach
» Advantages of Using the DBMS Approach
» A Brief History of Database Applications
» Schemas, Instances, and Database State
» The Three-Schema Architecture
» The Database System Environment
» Centralized and Client/Server Architectures for DBMSs
» Classification of Database Management Systems
» Domains, Attributes, Tuples, and Relations
» Key Constraints and Constraints on NULL Values
» Relational Databases and Relational Database Schemas
» Integrity, Referential Integrity, and Foreign Keys
» Update Operations, Transactions, and Dealing with Constraint Violations
» SQL Data Definition and Data Types
» Specifying Constraints in SQL
» The SELECT-FROM-WHERE Structure of Basic SQL Queries
» Ambiguous Attribute Names, Aliasing, Renaming, and Tuple Variables
» Substring Pattern Matching and Arithmetic Operators
» INSERT, DELETE, and UPDATE Statements in SQL
» Comparisons Involving NULL and Three-Valued Logic
» Nested Queries, Tuples, and Set/Multiset Comparisons
» The EXISTS and UNIQUE Functions in SQL
» Joined Tables in SQL and Outer Joins
» Grouping: The GROUP BY and HAVING Clauses
» Discussion and Summary of SQL Queries
» Specifying General Constraints as Assertions in SQL
» Introduction to Triggers in SQL
» Specification of Views in SQL
» View Implementation, View Update, and Inline Views
» Schema Change Statements in SQL
» Sequences of Operations and the RENAME Operation
» The UNION, INTERSECTION, and MINUS Operations
» The CARTESIAN PRODUCT (CROSS PRODUCT) Operation
» Variations of JOIN: The EQUIJOIN and NATURAL JOIN
» Additional Relational Operations
» Examples of Queries in Relational Algebra
» The Tuple Relational Calculus
» The Domain Relational Calculus
» Using High-Level Conceptual Data Models
» Entity Types, Entity Sets, Keys, and Value Sets
» Relationship Types, Relationship Sets, Roles, and Structural Constraints
» ER Diagrams, Naming Conventions, and Design Issues
» Example of Other Notation: UML Class Diagrams
» Relationship Types of Degree Higher than Two
» Subclasses, Superclasses, and Inheritance
» Constraints on Specialization and Generalization
» Specialization and Generalization Hierarchies
» Modeling of UNION Types Using Categories
» A Sample UNIVERSITY EER Schema, Design Choices, and Formal Definitions
» Data Abstraction, Knowledge Representation, and Ontology Concepts
» ER-to-Relational Mapping Algorithm
» Discussion and Summary of Mapping for ER Model Constructs
» Mapping EER Model Constructs
» The Role of Information Systems
» The Database Design and Implementation Process
» Use of UML Diagrams as an Aid to Database Design Specification 6
» Rational Rose: A UML-Based Design Tool
» Automated Database Design Tools
» Introduction to Object-Oriented Concepts and Features
» Object Identity, and Objects versus Literals
» Complex Type Structures for Objects and Literals
» Encapsulation of Operations and Persistence of Objects
» Type Hierarchies and Inheritance
» Other Object-Oriented Concepts
» Object-Relational Features: Object Database Extensions to SQL
» Overview of the Object Model of ODMG
» Built-in Interfaces and Classes in the Object Model
» Atomic (User-Defined) Objects
» Extents, Keys, and Factory Objects
» The Object Definition Language ODL
» Differences between Conceptual Design of ODB and RDB
» Mapping an EER Schema to an ODB Schema
» Query Results and Path Expressions
» Overview of the C++ Language Binding in the ODMG Standard
» Structured, Semistructured, and Unstructured Data
» XML Hierarchical (Tree) Data Model
» Well-Formed and Valid XML Documents and XML DTD
» XPath: Specifying Path Expressions in XML
» XQuery: Specifying Queries in XML
» Extracting XML Documents from
» Database Programming: Techniques
» Retrieving Single Tuples with Embedded SQL
» Retrieving Multiple Tuples with Embedded SQL Using Cursors
» Specifying Queries at Runtime Using Dynamic SQL
» SQLJ: Embedding SQL Commands in Java
» Retrieving Multiple Tuples in SQLJ Using Iterators
» Database Programming with SQL/CLI Using C
» JDBC: SQL Function Calls for Java Programming
» Database Stored Procedures and SQL/PSM
» PHP Variables, Data Types, and Programming Constructs
» Overview of PHP Database Programming
» Imparting Clear Semantics to Attributes in Relations
» Redundant Information in Tuples and Update Anomalies
» Normal Forms Based on Primary Keys
» General Definitions of Second and Third Normal Forms
» Multivalued Dependency and Fourth Normal Form
» Join Dependencies and Fifth Normal Form
» Inference Rules for Functional Dependencies
» Minimal Sets of Functional Dependencies
» Properties of Relational Decompositions
» Dependency-Preserving Decomposition
» Dependency-Preserving and Nonadditive (Lossless) Join Decomposition into 3NF Schemas
» Problems with NULL Values and Dangling Tuples
» Discussion of Normalization Algorithms and Alternative Relational Designs
» Further Discussion of Multivalued Dependencies and 4NF
» Other Dependencies and Normal Forms
» Memory Hierarchies and Storage Devices
» Hardware Description of Disk Devices
» Magnetic Tape Storage Devices
» Placing File Records on Disk
» Files of Unordered Records (Heap Files)
» Files of Ordered Records (Sorted Files)
» External Hashing for Disk Files
» Hashing Techniques That Allow Dynamic File Expansion
» Other Primary File Organizations
» Parallelizing Disk Access Using RAID Technology
» Types of Single-Level Ordered Indexes
» Some General Issues Concerning Indexing
» Algorithms for External Sorting
» Implementing the SELECT Operation
» Implementing the JOIN Operation
» Algorithms for PROJECT and Set
» Notation for Query Trees and Query Graphs
» Heuristic Optimization of Query Trees
» Catalog Information Used in Cost Functions
» Examples of Cost Functions for SELECT
» Examples of Cost Functions for JOIN
» Example to Illustrate Cost-Based Query Optimization
» Factors That Influence Physical Database Design
» Physical Database Design Decisions
» An Overview of Database Tuning in Relational Systems
» Transactions, Database Items, Read and Write Operations, and DBMS Buffers
» Why Concurrency Control Is Needed
» Transaction and System Concepts
» Desirable Properties of Transactions
» Serial, Nonserial, and Conflict-Serializable Schedules
» Testing for Conflict Serializability of a Schedule
» How Serializability Is Used for Concurrency Control
» View Equivalence and View Serializability
» Types of Locks and System Lock Tables
» Guaranteeing Serializability by Two-Phase Locking
» Dealing with Deadlock and Starvation
» Concurrency Control Based on Timestamp Ordering
» Multiversion Concurrency Control Techniques
» Validation (Optimistic) Concurrency
» Granularity of Data Items and Multiple Granularity Locking
» Using Locks for Concurrency Control in Indexes
» Other Concurrency Control Issues
» Recovery Outline and Categorization of Recovery Algorithms
» Caching (Buffering) of Disk Blocks
» Write-Ahead Logging, Steal/No-Steal, and Force/No-Force
» Transaction Rollback and Cascading Rollback
» NO-UNDO/REDO Recovery Based on Deferred Update
» Recovery Techniques Based on Immediate Update
» The ARIES Recovery Algorithm
» Recovery in Multidatabase Systems
» Introduction to Database Security Issues 1
» Discretionary Access Control Based on Granting and Revoking Privileges
» Mandatory Access Control and Role-Based Access Control for Multilevel Security
» Introduction to Statistical Database Security
» Introduction to Flow Control
» Encryption and Public Key Infrastructures
» Challenges of Database Security
» Distributed Database Concepts 1
» Types of Distributed Database Systems
» Distributed Database Architectures
» Data Replication and Allocation
» Example of Fragmentation, Allocation, and Replication
» Query Processing and Optimization in Distributed Databases
» Overview of Transaction Management in Distributed Databases
» Overview of Concurrency Control and Recovery in Distributed Databases
» Current Trends in Distributed Databases
» Distributed Databases in Oracle 13
» Generalized Model for Active Databases and Oracle Triggers
» Design and Implementation Issues for Active Databases
» Examples of Statement-Level Active Rules
» Time Representation, Calendars, and Time Dimensions
» Incorporating Time in Relational Databases Using Tuple Versioning
» Incorporating Time in Object-Oriented Databases Using Attribute Versioning
» Temporal Querying Constructs and the TSQL2 Language
» Spatial Database Concepts 24
» Multimedia Database Concepts
» Clausal Form and Horn Clauses
» Datalog Programs and Their Safety
» Evaluation of Nonrecursive Datalog Queries
» Introduction to Information Retrieval
» Types of Queries in IR Systems
» Evaluation Measures of Search Relevance
» Web Analysis and Its Relationship to Information Retrieval
» Analyzing the Link Structure of Web Pages
» Approaches to Web Content Analysis
» Trends in Information Retrieval
» Data Mining as a Part of the Knowledge
» Goals of Data Mining and Knowledge Discovery
» Types of Knowledge Discovered during Data Mining
» Market-Basket Model, Support, and Confidence
» Frequent-Pattern (FP) Tree and FP-Growth Algorithm
» Other Types of Association Rules
» Approaches to Other Data Mining Problems
» Commercial Data Mining Tools
» Data Modeling for Data Warehouses
» Difficulties of Implementing Data Warehouses
» Grouping, Aggregation, and Database Modification in QBE
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