Conjunctive queries. Many computational problems are much easier for conjunctive queries than for general first-order queries.
|
|
- Benjamin Wheeler
- 5 years ago
- Views:
Transcription
1 Conjunctive queries Relational calculus queries without negation and disjunction. Conjunctive queries have a normal form: ( y 1 ) ( y n )(p 1 (x 1,..., x m, y 1,..., y n ) p k (x 1,..., x m, y 1,..., y n )). They can also be expressed in Datalog: q(x 1,..., x m ) : p 1 (x 1,..., x m, y 1,..., y n ),..., p k (x 1,..., x m, y 1,..., y n ). Many computational problems are much easier for conjunctive queries than for general first-order queries. 1
2 Query containment For every query language, a query can be viewed as a mapping from the set of all possible database instances to all possible result instances. A query Q 1 is contained in a query Q 2 (Q 1 Q 2 ) if for every database instance D: Q 1 (D) Q 2 (D). Query containment is: undecidable for arbitrary first-order queries decidable (NP-complete) for conjunctive queries without built-in predicates decidable (Π p 2-complete) for conjunctive queries with built-in predicates Query equivalence can be determined using containment: Q 1 Q 2 iff Q 1 Q 2 Q 2 Q 1. 2
3 Checking conjunctive query containment Without built-in predicates. Assume Q 1 = A 0 : A 1,..., A n. Algorithm for checking Q 1 Q 2 : 1. to each goal A i, i = 1,..., n, in the body of Q 1 apply some ground substitution h that maps different variables to different (arbitrary) constants 2. apply T Q2 to the canonical database: the set of facts {A 1 h,..., A n h} 3. Q 1 Q 2 iff A 0 h is derived. This algorithm works also if Q 2 is an arbitrary Datalog program (the step 2 has to be repeated like in bottom-up evaluation) but not if Q 1 is an arbitrary Datalog program. 3
4 Queries with built-in predicates Arithmetic comparison predicates. Multiple canonical databases: all possible orderings for variables instantiate variables to integers For every canonical database D that makes the entire body of Q 1 true, T Q2 needs to derive the corresponding head of Q 1. 4
5 Integrity constraints A query Q 1 is contained in a query Q 2 under a set of integrity constraints F (Q 1 F Q 2 ) if for every database instance D satisfying F : Q 1 (D) Q 2 (D). Theorem: Q 1 F Q 2 iff chase F (Q 1 ) chase F (Q 2 ). 5
6 Chase A versatile tool, useful also for checking query containment under integrity constraints. Chase: apply chase steps to the body of a conjunctive query Q until no changes occur. Chase steps depend on the kind of constraints used. For functional dependencies: FD-step using X Y over P : if there are two P -goals in the body of Q that agree on X-attributes, apply to Q a substitution that will make them agree on Y -attributes (preferring the variables in the head). Chase terminates for FDs. 6
7 Views in data integration Basic model: many independent data sources containing all the data wrappers of data sources provide a single data model a single integrated database (virtual) relationships between the content of the sources and that of the integrated database: local-as-view global-as-view queries asked against the integrated database 7
8 Local-as-view Each data source is viewed as a goal G s and is defined using a query Q g over the integrated database. Notation: S is an instance of the source, D is a (virtual) instance of the integrated database. Source annotations: sound: S Q g (D) (the most common), complete: Q g (D) S, exact: Q g (D) = S. There may be more than one instance D satisfying the annotations, for a given S. 8
9 Global-as-view Each relation over the integrated database is defined using a goal G g as a view Q s over the data sources. Notation: S consists of instances of all the sources, D is a (virtual) instance of the integrated database. Source annotations: sound: Q s (S) G g (D), complete: G g (D) Q s (S), exact: G g (D) = Q s (S) (the most common). Under the exact annotations, there is only one satisfying instance D, for a given S. 9
10 Comparison Local-as-view: query evaluation rewriting in terms of views cannot be composed scalable Global-as-view: query evaluation view materialization (for exact annotations) can be composed (integrated database may be viewed as a data source) not scalable (adding sources requires the redefinition of the integrated database) 10
11 Query evaluation Semantics: a tuple t is a certain answer to a query Q given some source instances if it is in the answer to this query over every instance of the integrated database that satisfies all the source annotations. Computing certain answers is in most cases computationally hard. 11
12 Inverse rules An approach to query rewriting, used in Infomaster. Data source conjunctive query. Query a set of Datalog rules. Rewriting produces a set of nonrecursive Datalog rules with function symbols: EDB predicates: source relations IDB predicates: database relations Function symbols can be eliminated. 12
13 Query rewriting: 1. for every source rule A : B 1,..., B n, produce n inverse rules B 1 : A,..., B n : A 2. B i is like B i, except that each variable that occur only in the body of the source rule is replaced by the (Skolem) term f(x 1,..., X n ) where: f is a unique function symbol X 1,..., X n are all the variables in the head of the source rule 3. all the occurrences of the same variable are replaced by the same term Query evaluation: the query rule and the inverse rules are evaluated bottom-up the evaluation terminates only the substitutions that do not contain Skolem terms are returned to the user 13
14 Bucket algorithm An approach to query rewriting, used in Information Manifold. Data source a view defined as a conjunctive query. Query a conjunctive query Q D 0 : D 1,..., D n Rewriting of the query Q produces a set S, initially empty, of conjunctive queries. 14
15 Buckets: 1. create a bucket for every goal D 1,..., D n in Q 2. if A : B 1,..., B n is a data source definition such that for some j, B j unifies with D i, if D i has a head variable in some argument, then B j also has a head variable in the same argument, then Aσ (with new variables substituted for those variables that do not occur in B j ) is added to the bucket D i where σ is a most general unifier of B j and D i preferring the variables in the query Query rewriting: for each query rewriting Q which is a conjunction of one subgoal from each bucket: if the expansion of Q is contained in Q, then add Q to S the final rewriting is the union of the queries in S. 15
16 Constraints in the query and the views To prevent irrelevant goals from being placed in the buckets: if the constraints in the data source definition together with the constraints in the query are unsatisfiable after applying σ limited to the head variables of the view, then the source is useless for the query. To help pass the containment test: constraints may be added to a query rewriting. 16
17 Properties Not always a rewriting equivalent to the original query exists: data sources are insufficient data sources are incomplete. If the query does not contain any constraints, and there are only sound annotations, then the inverse rules and bucket algorithms are guaranteed to produce the maximally contained rewriting (in terms of the given sources) and the given query language. The rewriting computes exactly the certain answers. 17
18 Source limitations Sometimes data sources impose limitations on access paths to the data: some arguments have to be provided as inputs. This is represented by adorning each data source with a string of b and f: each argument is labelled with a b or an f b stands for mandatory input f stands for input or output To obtain a maximally-contained rewriting sometimes a recursive Datalog program is necessary. 18
Foundations of AI. 9. Predicate Logic. Syntax and Semantics, Normal Forms, Herbrand Expansion, Resolution
Foundations of AI 9. Predicate Logic Syntax and Semantics, Normal Forms, Herbrand Expansion, Resolution Wolfram Burgard, Andreas Karwath, Bernhard Nebel, and Martin Riedmiller 09/1 Contents Motivation
More informationOPTIMIZING RECURSIVE INFORMATION GATHERING PLANS. Eric M. Lambrecht
OPTIMIZING RECURSIVE INFORMATION GATHERING PLANS by Eric M. Lambrecht A Thesis Presented in Partial Fulfillment of the Requirements for the Degree Master of Science ARIZONA STATE UNIVERSITY December 1998
More informationRange Restriction for General Formulas
Range Restriction for General Formulas 1 Range Restriction for General Formulas Stefan Brass Martin-Luther-Universität Halle-Wittenberg Germany Range Restriction for General Formulas 2 Motivation Deductive
More informationIntegrity Constraints (Chapter 7.3) Overview. Bottom-Up. Top-Down. Integrity Constraint. Disjunctive & Negative Knowledge. Proof by Refutation
CSE560 Class 10: 1 c P. Heeman, 2010 Integrity Constraints Overview Disjunctive & Negative Knowledge Resolution Rule Bottom-Up Proof by Refutation Top-Down CSE560 Class 10: 2 c P. Heeman, 2010 Integrity
More informationDatabase Theory: Beyond FO
Database Theory: Beyond FO CS 645 Feb 11, 2010 Some slide content based on materials of Dan Suciu, Ullman/Widom 1 TODAY: Coming lectures Limited expressiveness of FO Adding recursion (Datalog) Expressiveness
More informationResolution (14A) Young W. Lim 6/14/14
Copyright (c) 2013-2014. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free
More informationFoundations of Databases
Foundations of Databases Free University of Bozen Bolzano, 2004 2005 Thomas Eiter Institut für Informationssysteme Arbeitsbereich Wissensbasierte Systeme (184/3) Technische Universität Wien http://www.kr.tuwien.ac.at/staff/eiter
More informationDatalog. Rules Programs Negation
Datalog Rules Programs Negation 1 Review of Logical If-Then Rules body h(x, ) :- a(y, ) & b(z, ) & head subgoals The head is true if all the subgoals are true. 2 Terminology Head and subgoals are atoms.
More informationData Integration: A Theoretical Perspective
Data Integration: A Theoretical Perspective Maurizio Lenzerini Dipartimento di Informatica e Sistemistica Università di Roma La Sapienza Via Salaria 113, I 00198 Roma, Italy lenzerini@dis.uniroma1.it ABSTRACT
More informationRewriting Ontology-Mediated Queries. Carsten Lutz University of Bremen
Rewriting Ontology-Mediated Queries Carsten Lutz University of Bremen Data Access and Ontologies Today, data is often highly incomplete and very heterogeneous Examples include web data and large-scale
More informationOutline. q Database integration & querying. q Peer-to-Peer data management q Stream data management q MapReduce-based distributed data management
Outline n Introduction & architectural issues n Data distribution n Distributed query processing n Distributed query optimization n Distributed transactions & concurrency control n Distributed reliability
More informationDatalog Evaluation. Linh Anh Nguyen. Institute of Informatics University of Warsaw
Datalog Evaluation Linh Anh Nguyen Institute of Informatics University of Warsaw Outline Simple Evaluation Methods Query-Subquery Recursive Magic-Set Technique Query-Subquery Nets [2/64] Linh Anh Nguyen
More informationLocal Stratiæcation. Instantiate rules; i.e., substitute all. possible constants for variables, but reject. instantiations that cause some EDB subgoal
Local Stratication Instantiate rules; i.e. substitute all possible constants for variables but reject instantiations that cause some EDB subgoal to be false. Ground atom = atom with no variables. Build
More informationMathematical Logic Prof. Arindama Singh Department of Mathematics Indian Institute of Technology, Madras. Lecture - 37 Resolution Rules
Mathematical Logic Prof. Arindama Singh Department of Mathematics Indian Institute of Technology, Madras Lecture - 37 Resolution Rules If some literals can be unified, the same algorithm should be able
More informationData integration lecture 2
PhD course on View-based query processing Data integration lecture 2 Riccardo Rosati Dipartimento di Informatica e Sistemistica Università di Roma La Sapienza {rosati}@dis.uniroma1.it Corso di Dottorato
More informationModule 6. Knowledge Representation and Logic (First Order Logic) Version 2 CSE IIT, Kharagpur
Module 6 Knowledge Representation and Logic (First Order Logic) 6.1 Instructional Objective Students should understand the advantages of first order logic as a knowledge representation language Students
More informationComplexity of Answering Queries Using Materialized Views
Complexity of Answering Queries Using Materialized Views Serge Abiteboul, Olivier Duschka To cite this version: Serge Abiteboul, Olivier Duschka. Complexity of Answering Queries Using Materialized Views.
More informationComputing Query Answers with Consistent Support
Computing Query Answers with Consistent Support Jui-Yi Kao Advised by: Stanford University Michael Genesereth Inconsistency in Databases If the data in a database violates the applicable ICs, we say the
More information(i.e., produced only a subset of the possible answers). We describe the novel class
Recursive Query Plans for Data Integration Oliver M. Duschka Michael R. Genesereth Department of Computer Science, Stanford University, Stanford, CA 94305, USA Alon Y. Levy 1 Department of Computer Science
More informationPCP and Hardness of Approximation
PCP and Hardness of Approximation January 30, 2009 Our goal herein is to define and prove basic concepts regarding hardness of approximation. We will state but obviously not prove a PCP theorem as a starting
More informationDATABASE THEORY. Lecture 11: Introduction to Datalog. TU Dresden, 12th June Markus Krötzsch Knowledge-Based Systems
DATABASE THEORY Lecture 11: Introduction to Datalog Markus Krötzsch Knowledge-Based Systems TU Dresden, 12th June 2018 Announcement All lectures and the exercise on 19 June 2018 will be in room APB 1004
More informationAnswering Queries with Useful Bindings
Answering Queries with Useful Bindings CHEN LI University of California at Irvine and EDWARD CHANG University of California, Santa Barbara In information-integration systems, sources may have diverse and
More informationLOGIC AND DISCRETE MATHEMATICS
LOGIC AND DISCRETE MATHEMATICS A Computer Science Perspective WINFRIED KARL GRASSMANN Department of Computer Science University of Saskatchewan JEAN-PAUL TREMBLAY Department of Computer Science University
More informationKnowledge Representation. CS 486/686: Introduction to Artificial Intelligence
Knowledge Representation CS 486/686: Introduction to Artificial Intelligence 1 Outline Knowledge-based agents Logics in general Propositional Logic& Reasoning First Order Logic 2 Introduction So far we
More informationA Retrospective on Datalog 1.0
A Retrospective on Datalog 1.0 Phokion G. Kolaitis UC Santa Cruz and IBM Research - Almaden Datalog 2.0 Vienna, September 2012 2 / 79 A Brief History of Datalog In the beginning of time, there was E.F.
More informationChapter 9: Constraint Logic Programming
9. Constraint Logic Programming 9-1 Deductive Databases and Logic Programming (Winter 2007/2008) Chapter 9: Constraint Logic Programming Introduction, Examples Basic Query Evaluation Finite Domain Constraint
More informationChapter 10 Part 1: Reduction
//06 Polynomial-Time Reduction Suppose we could solve Y in polynomial-time. What else could we solve in polynomial time? don't confuse with reduces from Chapter 0 Part : Reduction Reduction. Problem X
More informationPlan of the lecture. G53RDB: Theory of Relational Databases Lecture 14. Example. Datalog syntax: rules. Datalog query. Meaning of Datalog rules
Plan of the lecture G53RDB: Theory of Relational Databases Lecture 14 Natasha Alechina School of Computer Science & IT nza@cs.nott.ac.uk More Datalog: Safe queries Datalog and relational algebra Recursive
More informationImplementing mapping composition
The VLDB Journal (2008) 17:333 353 DOI 10.1007/s00778-007-0059-9 SPECIAL ISSUE PAPER Implementing mapping composition Philip A. Bernstein Todd J. Green Sergey Melnik Alan Nash Received: 17 February 2007
More informationDATABASE THEORY. Lecture 15: Datalog Evaluation (2) TU Dresden, 26th June Markus Krötzsch Knowledge-Based Systems
DATABASE THEORY Lecture 15: Datalog Evaluation (2) Markus Krötzsch Knowledge-Based Systems TU Dresden, 26th June 2018 Review: Datalog Evaluation A rule-based recursive query language father(alice, bob)
More informationQuery Containment for Data Integration Systems
Query Containment for Data Integration Systems Todd Millstein University of Washington Seattle, Washington todd@cs.washington.edu Alon Levy University of Washington Seattle, Washington alon@cs.washington.edu
More informationLecture 1: Conjunctive Queries
CS 784: Foundations of Data Management Spring 2017 Instructor: Paris Koutris Lecture 1: Conjunctive Queries A database schema R is a set of relations: we will typically use the symbols R, S, T,... to denote
More informationCSL105: Discrete Mathematical Structures. Ragesh Jaiswal, CSE, IIT Delhi
is another way of showing that an argument is correct. Definitions: Literal: A variable or a negation of a variable is called a literal. Sum and Product: A disjunction of literals is called a sum and a
More informationCSE-6490B Assignment #1
29 October 2008 CSE-6490B Assignment #1 p. 1 of 5 CSE-6490B Assignment #1 1. Queries in Datalog. Enroll now in Datalog U.! (5 points) Consider the following schema. student(s#, sname, dob, d#) FK (d#)
More informationModule 6. Knowledge Representation and Logic (First Order Logic) Version 2 CSE IIT, Kharagpur
Module 6 Knowledge Representation and Logic (First Order Logic) Lesson 15 Inference in FOL - I 6.2.8 Resolution We have introduced the inference rule Modus Ponens. Now we introduce another inference rule
More informationCOMP718: Ontologies and Knowledge Bases
1/35 COMP718: Ontologies and Knowledge Bases Lecture 9: Ontology/Conceptual Model based Data Access Maria Keet email: keet@ukzn.ac.za home: http://www.meteck.org School of Mathematics, Statistics, and
More informationAn Evolution of Mathematical Tools
An Evolution of Mathematical Tools From Conceptualization to Formalization Here's what we do when we build a formal model (or do a computation): 0. Identify a collection of objects/events in the real world.
More informationThe Formal Semantics of Programming Languages An Introduction. Glynn Winskel. The MIT Press Cambridge, Massachusetts London, England
The Formal Semantics of Programming Languages An Introduction Glynn Winskel The MIT Press Cambridge, Massachusetts London, England Series foreword Preface xiii xv 1 Basic set theory 1 1.1 Logical notation
More informationOn the Hardness of Counting the Solutions of SPARQL Queries
On the Hardness of Counting the Solutions of SPARQL Queries Reinhard Pichler and Sebastian Skritek Vienna University of Technology, Faculty of Informatics {pichler,skritek}@dbai.tuwien.ac.at 1 Introduction
More informationThe Inverse of a Schema Mapping
The Inverse of a Schema Mapping Jorge Pérez Department of Computer Science, Universidad de Chile Blanco Encalada 2120, Santiago, Chile jperez@dcc.uchile.cl Abstract The inversion of schema mappings has
More informationDATABASE THEORY. Lecture 18: Dependencies. TU Dresden, 3rd July Markus Krötzsch Knowledge-Based Systems
DATABASE THEORY Lecture 18: Dependencies Markus Krötzsch Knowledge-Based Systems TU Dresden, 3rd July 2018 Review: Databases and their schemas Lines: Line Type 85 bus 3 tram F1 ferry...... Stops: SID Stop
More information8.1 Polynomial-Time Reductions
8.1 Polynomial-Time Reductions Classify Problems According to Computational Requirements Q. Which problems will we be able to solve in practice? A working definition. Those with polynomial-time algorithms.
More informationChapter 5: Other Relational Languages
Chapter 5: Other Relational Languages Database System Concepts, 5th Ed. See www.db-book.com for conditions on re-use Chapter 5: Other Relational Languages Tuple Relational Calculus Domain Relational Calculus
More informationData Integration: Logic Query Languages
Data Integration: Logic Query Languages Jan Chomicki University at Buffalo Datalog Datalog A logic language Datalog programs consist of logical facts and rules Datalog is a subset of Prolog (no data structures)
More informationDATABASE THEORY. Lecture 12: Evaluation of Datalog (2) TU Dresden, 30 June Markus Krötzsch
DATABASE THEORY Lecture 12: Evaluation of Datalog (2) Markus Krötzsch TU Dresden, 30 June 2016 Overview 1. Introduction Relational data model 2. First-order queries 3. Complexity of query answering 4.
More informationChapter 5: Other Relational Languages.! Query-by-Example (QBE)! Datalog
Chapter 5: Other Relational Languages! Query-by-Example (QBE)! Datalog 5.1 Query-by by-example (QBE)! Basic Structure! Queries on One Relation! Queries on Several Relations! The Condition Box! The Result
More informationOn the Computational Complexity of Minimal-Change Integrity Maintenance in Relational Databases
On the Computational Complexity of Minimal-Change Integrity Maintenance in Relational Databases Jan Chomicki 1 and Jerzy Marcinkowski 2 1 Dept. of Computer Science and Engineering University at Buffalo
More informationDatalog. Susan B. Davidson. CIS 700: Advanced Topics in Databases MW 1:30-3 Towne 309
Datalog Susan B. Davidson CIS 700: Advanced Topics in Databases MW 1:30-3 Towne 309 http://www.cis.upenn.edu/~susan/cis700/homepage.html 2017 A. Alawini, S. Davidson Homework for this week Sign up to present
More informationMulti-event IDS Categories. Introduction to Misuse Intrusion Detection Systems (IDS) Formal Specification of Intrusion Signatures and Detection Rules
Formal Specification of Intrusion Signatures and Detection Rules By Jean-Philippe Pouzol and Mireille Ducassé 15 th IEEE Computer Security Foundations Workshop 2002 Presented by Brian Kellogg CSE914: Formal
More informationFOUNDATIONS OF DATABASES AND QUERY LANGUAGES
FOUNDATIONS OF DATABASES AND QUERY LANGUAGES Lecture 14: Database Theory in Practice Markus Krötzsch TU Dresden, 20 July 2015 Overview 1. Introduction Relational data model 2. First-order queries 3. Complexity
More informationOverview. CS389L: Automated Logical Reasoning. Lecture 6: First Order Logic Syntax and Semantics. Constants in First-Order Logic.
Overview CS389L: Automated Logical Reasoning Lecture 6: First Order Logic Syntax and Semantics Işıl Dillig So far: Automated reasoning in propositional logic. Propositional logic is simple and easy to
More informationFoundations of Databases
Foundations of Databases Free University of Bozen Bolzano, 2004 2005 Thomas Eiter Institut für Informationssysteme Arbeitsbereich Wissensbasierte Systeme (184/3) Technische Universität Wien http://www.kr.tuwien.ac.at/staff/eiter
More informationCS 3512, Spring Instructor: Doug Dunham. Textbook: James L. Hein, Discrete Structures, Logic, and Computability, 3rd Ed. Jones and Barlett, 2010
CS 3512, Spring 2011 Instructor: Doug Dunham Textbook: James L. Hein, Discrete Structures, Logic, and Computability, 3rd Ed. Jones and Barlett, 2010 Prerequisites: Calc I, CS2511 Rough course outline:
More informationProcessing Regular Path Queries Using Views or What Do We Need for Integrating Semistructured Data?
Processing Regular Path Queries Using Views or What Do We Need for Integrating Semistructured Data? Diego Calvanese University of Rome La Sapienza joint work with G. De Giacomo, M. Lenzerini, M.Y. Vardi
More information! Greed. O(n log n) interval scheduling. ! Divide-and-conquer. O(n log n) FFT. ! Dynamic programming. O(n 2 ) edit distance.
Algorithm Design Patterns and Anti-Patterns Chapter 8 NP and Computational Intractability Algorithm design patterns. Ex.! Greed. O(n log n) interval scheduling.! Divide-and-conquer. O(n log n) FFT.! Dynamic
More informationOptimization of logical query plans Eliminating redundant joins
Optimization of logical query plans Eliminating redundant joins 66 Optimization of logical query plans Query Compiler Execution Engine SQL Translation Logical query plan "Intermediate code" Logical plan
More informationCSE 20 DISCRETE MATH. Fall
CSE 20 DISCRETE MATH Fall 2017 http://cseweb.ucsd.edu/classes/fa17/cse20-ab/ Final exam The final exam is Saturday December 16 11:30am-2:30pm. Lecture A will take the exam in Lecture B will take the exam
More informationRelational Databases
Relational Databases Jan Chomicki University at Buffalo Jan Chomicki () Relational databases 1 / 49 Plan of the course 1 Relational databases 2 Relational database design 3 Conceptual database design 4
More informationReconcilable Differences
Theory of Computing Systems manuscript No. (will be inserted by the editor) Reconcilable Differences Todd J. Green Zachary G. Ives Val Tannen Received: date / Accepted: date Abstract In this paper we study
More informationFinite Model Generation for Isabelle/HOL Using a SAT Solver
Finite Model Generation for / Using a SAT Solver Tjark Weber webertj@in.tum.de Technische Universität München Winterhütte, März 2004 Finite Model Generation for / p.1/21 is a generic proof assistant: Highly
More informationAccess Patterns (Extended Version) Chen Li. Department of Computer Science, Stanford University, CA Abstract
Computing Complete Answers to Queries in the Presence of Limited Access Patterns (Extended Version) Chen Li Department of Computer Science, Stanford University, CA 94305 chenli@db.stanford.edu Abstract
More informationPositive higher-order queries
Positive higher-order queries Michael Benedikt, Gabriele Puppis, Huy u To cite this version: Michael Benedikt, Gabriele Puppis, Huy u. Positive higher-order queries. Proceedings of PODS 2010, 2010, Indianapolis,
More informationFinding Equivalent Rewritings in the Presence of Arithmetic Comparisons
Finding Equivalent Rewritings in the Presence of Arithmetic Comparisons Foto Afrati 1, Rada Chirkova 2, Manolis Gergatsoulis 3, and Vassia Pavlaki 1 1 Department of Electrical and Computing Engineering,
More informationA SQL-Middleware Unifying Why and Why-Not Provenance for First-Order Queries
A SQL-Middleware Unifying Why and Why-Not Provenance for First-Order Queries Seokki Lee Sven Köhler Bertram Ludäscher Boris Glavic Illinois Institute of Technology. {slee95@hawk.iit.edu, bglavic@iit.edu}
More informationCSE 344 JANUARY 26 TH DATALOG
CSE 344 JANUARY 26 TH DATALOG ADMINISTRATIVE MINUTIAE HW3 and OQ3 out HW3 due next Friday OQ3 due next Wednesday HW4 out next week: on Datalog Midterm reminder: Feb 9 th RELATIONAL ALGEBRA Set-at-a-time
More informationChapter 8. NP and Computational Intractability. Slides by Kevin Wayne. Copyright 2005 Pearson-Addison Wesley. All rights reserved.
Chapter 8 NP and Computational Intractability Slides by Kevin Wayne. Copyright 2005 Pearson-Addison Wesley. All rights reserved. 1 Algorithm Design Patterns and Anti-Patterns Algorithm design patterns.
More informationHarvard School of Engineering and Applied Sciences CS 152: Programming Languages. Lambda calculus
Harvard School of Engineering and Applied Sciences CS 152: Programming Languages Tuesday, February 19, 2013 The lambda calculus (or λ-calculus) was introduced by Alonzo Church and Stephen Cole Kleene in
More informationMidterm. Introduction to Data Management CSE 344. Datalog. What is Datalog? Why Do We Learn Datalog? Why Do We Learn Datalog? Lecture 13: Datalog
Midterm Introduction to Data Management CSE 344 Lecture 13: Datalog Guest lecturer: Laurel Orr Monday, February 8 th in class Content Lectures 1 through 13 Homework 1 through 4 (due Feb 10) Webquiz 1 through
More informationLogical Query Languages. Motivation: 1. Logical rules extend more naturally to. recursive queries than does relational algebra. Used in SQL recursion.
Logical Query Languages Motivation: 1. Logical rules extend more naturally to recursive queries than does relational algebra. Used in SQL recursion. 2. Logical rules form the basis for many information-integration
More informationMidterm. Database Systems CSE 414. What is Datalog? Datalog. Why Do We Learn Datalog? Why Do We Learn Datalog?
Midterm Database Systems CSE 414 Lecture 13: Datalog Guest lecturer: Jay Garlapati Friday, April 29, in class Content Lectures 1 through 13 Homework 1 through 3 Webquiz 1 through 4 (due Thursday) Closed
More informationFunctional Logic Programming. Kristjan Vedel
Functional Logic Programming Kristjan Vedel Imperative vs Declarative Algorithm = Logic + Control Imperative How? Explicit Control Sequences of commands for the computer to execute Declarative What? Implicit
More informationFigure 5.1: Query processing in a data integration system. This chapter focuses on the reformulation step, highlighted in the dashed box.
Chapter 5 Describing Data Sources In order for a data integration system to process a query over a set of data sources, the system must know which sources are available, what data exists in each source
More information! Greed. O(n log n) interval scheduling. ! Divide-and-conquer. O(n log n) FFT. ! Dynamic programming. O(n 2 ) edit distance.
Algorithm Design Patterns and Anti-Patterns 8. NP and Computational Intractability Algorithm design patterns. Ex.! Greed. O(n log n) interval scheduling.! Divide-and-conquer. O(n log n) FFT.! Dynamic programming.
More informationRelational Algebra and Relational Calculus. Pearson Education Limited 1995,
Relational Algebra and Relational Calculus 1 Objectives Meaning of the term relational completeness. How to form queries in relational algebra. How to form queries in tuple relational calculus. How to
More informationQuery Rewriting Using Views in the Presence of Inclusion Dependencies
Query Rewriting Using Views in the Presence of Inclusion Dependencies Qingyuan Bai Jun Hong Michael F. McTear School of Computing and Mathematics, University of Ulster at Jordanstown, Newtownabbey, Co.
More information2.2.2.Relational Database concept
Foreign key:- is a field (or collection of fields) in one table that uniquely identifies a row of another table. In simpler words, the foreign key is defined in a second table, but it refers to the primary
More informationData Integration: Datalog
Data Integration: Datalog Jan Chomicki University at Buffalo and Warsaw University Feb. 22, 2007 Jan Chomicki (UB/UW) Data Integration: Datalog Feb. 22, 2007 1 / 12 Plan of the course 1 Datalog 2 Negation
More informationFormal Predicate Calculus. Michael Meyling
Formal Predicate Calculus Michael Meyling May 24, 2013 2 The source for this document can be found here: http://www.qedeq.org/0_04_07/doc/math/qedeq_formal_logic_v1.xml Copyright by the authors. All rights
More informationAn Algorithm for Answering Queries Efficiently Using Views Prasenjit Mitra Infolab, Stanford University Stanford, CA, 94305, U.S.A.
An Algorithm for Answering Queries Efficiently Using Views Prasenjit Mitra Infolab, Stanford University Stanford, CA, 94305, U.S.A. mitra@db.stanford.edu September, 1999 Abstract Algorithms for answering
More informationDatabase Theory: Datalog, Views
Database Theory: Datalog, Views CS 645 Mar 8, 2006 Some slide content courtesy of Ramakrishnan & Gehrke, Dan Suciu, Ullman & Widom 1 TODAY: Coming lectures Adding recursion: datalog Summary of Containment
More informationFoundations of Schema Mapping Management
Foundations of Schema Mapping Management Marcelo Arenas Jorge Pérez Juan Reutter Cristian Riveros PUC Chile PUC Chile University of Edinburgh Oxford University marenas@ing.puc.cl jperez@ing.puc.cl juan.reutter@ed.ac.uk
More informationCSE 20 DISCRETE MATH. Winter
CSE 20 DISCRETE MATH Winter 2017 http://cseweb.ucsd.edu/classes/wi17/cse20-ab/ Final exam The final exam is Saturday March 18 8am-11am. Lecture A will take the exam in GH 242 Lecture B will take the exam
More informationIntroduction to Data Management CSE 344. Lecture 14: Datalog (guest lecturer Dan Suciu)
Introduction to Data Management CSE 344 Lecture 14: Datalog (guest lecturer Dan Suciu) CSE 344 - Winter 2017 1 Announcements WQ 4 and HW 4 due on Thursday Midterm next Monday in class This week: Today:
More informationExpressive capabilities description languages and query rewriting algorithms q
The Journal of Logic Programming 43 (2000) 75±122 www.elsevier.com/locate/jlpr Expressive capabilities description languages and query rewriting algorithms q Vasilis Vassalos a, *, Yannis Papakonstantinou
More informationLecture 17 of 41. Clausal (Conjunctive Normal) Form and Resolution Techniques
Lecture 17 of 41 Clausal (Conjunctive Normal) Form and Resolution Techniques Wednesday, 29 September 2004 William H. Hsu, KSU http://www.kddresearch.org http://www.cis.ksu.edu/~bhsu Reading: Chapter 9,
More informationDatabase Theory VU , SS Codd s Theorem. Reinhard Pichler
Database Theory Database Theory VU 181.140, SS 2011 3. Codd s Theorem Reinhard Pichler Institut für Informationssysteme Arbeitsbereich DBAI Technische Universität Wien 29 March, 2011 Pichler 29 March,
More informationOutline. Forward chaining Backward chaining Resolution. West Knowledge Base. Forward chaining algorithm. Resolution-Based Inference.
Resolution-Based Inference Outline R&N: 9.3-9.6 Michael Rovatsos University of Edinburgh Forward chaining Backward chaining Resolution 10 th February 2015 Forward chaining algorithm West Knowledge Base
More informationInverting Schema Mappings: Bridging the Gap between Theory and Practice
Inverting Schema Mappings: Bridging the Gap between Theory and Practice Marcelo Arenas Jorge Pérez Juan Reutter Cristian Riveros PUC Chile PUC Chile PUC Chile R&M Tech marenas@ing.puc.cl jperez@ing.puc.cl
More informationLecture 9: Datalog with Negation
CS 784: Foundations of Data Management Spring 2017 Instructor: Paris Koutris Lecture 9: Datalog with Negation In this lecture we will study the addition of negation to Datalog. We start with an example.
More informationSQL, DLs, Datalog, and ASP: comparison
SQL, DLs, Datalog, and ASP: comparison Riccardo Rosati Knowledge Representation and Semantic Technologies Corso di Laurea in Ingegneria informatica Sapienza Università di Roma 2014/2015 CWA vs. OWA DLs
More informationEfficiently Computing Provenance Graphs for Queries with Negation
Efficiently Computing Provenance Graphs for Queries with Negation Seokki Lee, Sven Köhler, Bertram Ludäscher, Boris Glavic IIT DB Group Technical Report IIT/CS-DB-26-3 26- http://www.cs.iit.edu/ dbgroup/
More informationLogic Languages. Hwansoo Han
Logic Languages Hwansoo Han Logic Programming Based on first-order predicate calculus Operators Conjunction, disjunction, negation, implication Universal and existential quantifiers E A x for all x...
More informationNP and computational intractability. Kleinberg and Tardos, chapter 8
NP and computational intractability Kleinberg and Tardos, chapter 8 1 Major Transition So far we have studied certain algorithmic patterns Greedy, Divide and conquer, Dynamic programming to develop efficient
More information. Relation and attribute names: The relation and attribute names in the mediated. Describing Data Sources. 3.1 Overview and Desiderata
3 Describing Data Sources In order for a data integration system to process a query over a set of data sources, the system must know which sources are available, what data exist in each source, and how
More informationDeductive Databases. Motivation. Datalog. Chapter 25
Deductive Databases Chapter 25 1 Motivation SQL-92 cannot express some queries: Are we running low on any parts needed to build a ZX600 sports car? What is the total component and assembly cost to build
More informationEssential Gringo (Draft)
Essential Gringo (Draft) Vladimir Lifschitz, University of Texas 1 Introduction The designers of the Abstract Gringo language AG [Gebser et al., 2015a] aimed at creating a relatively simple mathematical
More informationContext-free Grammars
1 contents of Context-free Grammars Phrase Structure Everyday Grammars for Programming Language Formal Definition of Context-free Grammars Definition of Language Left-to-right Application cfg ects Transforming
More informationNotes. Notes. Introduction. Notes. Propositional Functions. Slides by Christopher M. Bourke Instructor: Berthe Y. Choueiry.
Slides by Christopher M. Bourke Instructor: Berthe Y. Choueiry Spring 2006 1 / 1 Computer Science & Engineering 235 Introduction to Discrete Mathematics Sections 1.3 1.4 of Rosen cse235@cse.unl.edu Introduction
More informationDatalog. Susan B. Davidson. CIS 700: Advanced Topics in Databases MW 1:30-3 Towne 309
Datalog Susan B. Davidson CIS 700: Advanced Topics in Databases MW 1:30-3 Towne 309 http://www.cis.upenn.edu/~susan/cis700/homepage.html 2017 A. Alawini, S. Davidson References Textbooks Ramakrishnan and
More informationCS 512, Spring 2017: Take-Home End-of-Term Examination
CS 512, Spring 2017: Take-Home End-of-Term Examination Out: Tuesday, 9 May 2017, 12:00 noon Due: Wednesday, 10 May 2017, by 11:59 am Turn in your solutions electronically, as a single PDF file, by placing
More information