Datalog and Data Integration

Zachary G. IvesUniversity of Pennsylvania

CIS 550 – Database & Information Systems

November 12, 2007

LSD Slides courtesy AnHai Doan

2

An Important Set of Questions

Views are incredibly powerful formalisms for describing how data relates: fn: rel … rel rel

(Or XML XML XML, or rel rel XML, ...)

Can I define a view recursively? Why might this be useful in the XML construction case?

When should the recursion stop?

Suppose we have two views, v1 and v2

How do I know whether they represent the same data? If v1 is materialized, can we use it to compute v2?

This is fundamental to query optimization and data integration, as we’ll see later

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Reasoning about Queries and Views

SQL or XQuery are a bit too complex to reason about directly Some aspects of it make reasoning about SQL

queries undecidable

We need an elegant way of describing views (let’s assume a relational model for now) Should be declarative Should be less complex than SQL Doesn’t need to support all of SQL –

aggregation, for instance, may be more than we need

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Let’s Go Back a Few Weeks…Domain Relational Calculus

Queries have form:

{<x1,x2, …, xn>| p }

Predicate: boolean expression over x1,x2, …, xn We have the following operations:

<xi,xj,…> R xi op xj xi op const const op xi

xi. p xj. p pq, pq p, pqwhere op is , , , , , and

xi,xj,… are domain variables; p,q are predicates Recall that this captures the same

expressiveness as the relational algebra

domain variables predicate

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A Similar Logic-Based Language:Datalog

Borrows the flavor of the relational calculus but is a “real” query language Based on the Prolog logic-programming

language A “datalog program” will be a series of if-then

rules (Horn rules) that define relations from predicates

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Datalog Terminology

An example datalog rule:idb(x,y) r1(x,z), r2(z,y), z < 10

Irrelevant variables can be replaced by _ (anonymous var)

Extensional relations or database schemas (edbs) are relations only occurring in rules’ bodies, or as base relations:

Ground facts only have constants, e.g., r1(“abc”, 123) Intensional relations (idbs) appear in the heads – these

are basically views Distinguished variables are the ones output in the head

head subgoals

body

7

Datalog in Action

As in DRC, the output (head) consists of a tuple for each possible assignment of variables that satisfies the predicate We typically avoid “” in Datalog queries:

variables in the body are existential, ranging over all possible values

Multiple rules with the same relation in the head represent a union

We often try to avoid disjunction (“”) within rules

Let’s see some examples of datalog queries (which consist of 1 or more rules): Given Professor(fid, name), Teaches(fid, serno, sem),

Courses(serno, cid, desc), Student(sid, name) Return course names other than CIS 550 Return the names of all people (professors or students)

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Datalog is Relationally Complete

We can map RA Datalog: Selection p: p becomes a datalog subgoal

Projection A: we drop projected-out variables from head Cross-product r s: q(A,B,C,D) r(A,B),s(C,D) Join r ⋈ s: q(A,B,C,D) r(A,B),s(C,D), condition Union r U s: q(A,B) r(A,B) ; q(C, D) :- s(C,D) Difference r – s: q(A,B) r(A,B), : s(A,B)

(If you think about it, DRC Datalog is even easier)

Great… But then why do we care about Datalog?

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A Query We Can’tAnswer in RA/TRC/DRC…

Recall our example of a binary relation for graphs or trees (similar to an XML Edge relation):

edge(from, to)

If we want to know what nodes are reachable:

reachable(F, T, 1) :- edge(F, T)distance 1

reachable(F, T, 2) :- edge(F, X), edge(X, T) dist. 2reachable(F, T, 3) :- reachable(F, X, 2), edge(X, T) dist. 3

But how about all reachable paths? (Note this was easy in XPath over an XML representation -- //edge)

(another way of writing )

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Recursive Datalog Queries

Define a recursive query in datalog:reachable(F, T, 1) :- edge(F, T) distance 1reachable(F, T, D + 1) :- reachable(F, X, D),

edge(X, T) distance >1

What does this mean, exactly, in terms of logic? There are actually three different (equivalent) definitions

of semantics; we will use that of fixpoint: We start with an instance of data, then derive all immediate

consequences We repeat as long as we derive new facts

In the RA, this requires a (restricted) while loop! “Inflationary semantics”

(which terminates in time polynomial in the size of the database!)

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Our Query in RA + while(inflationary semantics, no negation)

Datalog:reachable(F, T, 1) :- edge(F, T)reachable(F, T, D+1) :- reachable(F, X, D), edge(X, T)

RA procedure with while:reachable += edge ⋈ literal1

while change {reachable += F, T, D(F X(edge) ⋈ T X,D D0(reachable) ⋈ add1)

}

Note literal1(F,1) and add1(D0,D) are actually arithmetic and literal functions modeled here as relations.

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A Special Type of Query: Conjunctive Queries

A single Datalog rule with no “,” “,” “” can express select, project, and join – a conjunctive query

Conjunctive queries are possible to reason about statically (Note that we can write CQ’s in other languages, e.g., SQL!)

We know how to “minimize” conjunctive queriesAn important simplification that can’t be done for general SQL

We can test whether one conjunctive query’s answers always contain another conjunctive query’s answers (for ANY instance)

Why might this be useful?

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Example of Containment

Suppose we have two queries:

q1(S,C) :- Student(S, N), Takes(S, C), Course(C, X), inCIS(C), Course(C, “DB & Info Systems”)

q2(S,C) :- Student(S, N), Takes(S, C), Course(C, X)

Intuitively, q1 must contain the same or fewer answers vs. q2: It has all of the same conditions, except one extra conjunction

(i.e., it’s more restricted) There’s no union or any other way it can add more data

We can say that q2 contains q1 because this holds for any instance of our DB {Student, Takes, Course}

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Wrapping up Datalog…

We’ve seen a new language, Datalog It’s basically a glorified DRC with a special feature,

recursion It’s much cleaner than SQL for reasoning about … But negation (as in the DRC) poses some

challenges

We’ve seen that a particular kind of query, the conjunctive query, is written naturally in Datalog Conjunctive queries are possible to reason about We can minimize them, or check containment Conjunctive queries are very commonly used in our

next problem, data integration

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A Problem

We’ve seen that even with normalization and the same needs, different people will arrive at different schemas

In fact, most people also have different needs! Often people build databases in isolation, then want

to share their data Different systems within an enterprise Different information brokers on the Web Scientific collaborators Researchers who want to publish their data for others to

use This is the goal of data integration: tie together

different sources, controlled by many people, under a common schema

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Building a Data Integration System

Create a middleware “mediator” or “data integration system” over the sources Can be warehoused (a data warehouse) or virtual Presents a uniform query interface and schema Abstracts away multitude of sources; consults them for

relevant data Unifies different source data formats (and possibly schemas) Sources are generally autonomous, not designed to be

integrated Sources may be local DBs or remote web sources/services Sources may require certain input to return output (e.g.,

web forms): “binding patterns” describe these

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Data Integration System / Mediator

Typical Data Integration Components

Mediated Schema

Wrapper Wrapper Wrapper

SourceRelations

Mappingsin Catalog

SourceCatalog

Query Results

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Typical Data Integration Architecture

Reformulator

QueryProcessor

SourceCatalog

Wrapper Wrapper Wrapper

Query

Query over sources

SourceDescrs.

Queries +bindings Data in mediated format

Results

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Challenges of Mapping Schemas

In a perfect world, it would be easy to match up items from one schema with another Every table would have a similar table in the other schema Every attribute would have an identical attribute in the other

schema Every value would clearly map to a value in the other schema

Real world: as with human languages, things don’t map clearly! May have different numbers of tables – different

decompositions Metadata in one relation may be data in another Values may not exactly correspond It may be unclear whether a value is the same

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Different Aspects to Mapping

Schema matching / ontology alignmentHow do we find correspondences between attributes?

Entity matching / deduplication / record linking / etc.

How do we know when two records refer to the same thing?

Mapping definition How do we specify the constraints or

transformations that let us reason about when to create an entry in one schema, given an entry in another schema?Let’s see one influential approach to schema matching…

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The LSD (Learning Source Descriptions) System

Suppose user wants to integrate 100 data sources1. User:

manually creates mappings for a few sources, say 3 shows LSD these mappings

2. LSD learns from the mappings “Multi-strategy” learning incorporates many types of

info in a general way Knowledge of constraints further helps

3. LSD proposes mappings for remaining 97 sources

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listed-price $250,000 $110,000 ...

address price agent-phone description

Example

location Miami, FL Boston, MA ...

phone(305) 729 0831(617) 253 1429 ...

commentsFantastic houseGreat location ...

realestate.com

location listed-price phone comments

Schema of realestate.com

If “fantastic” & “great”

occur frequently in data values =>

description

Learned hypotheses

price $550,000 $320,000 ...

contact-phone(278) 345 7215(617) 335 2315 ...

extra-infoBeautiful yardGreat beach ...

homes.com

If “phone” occurs in the name =>

agent-phone

Mediated schema

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LSD’s Multi-Strategy Learning

Use a set of base learners Each exploits well certain types of information:

Name learner looks at words in the attribute names Naïve Bayes learner looks at patterns in the data values Etc.

Match schema elements of a new source Apply the base learners

Each returns a score For different attributes one learner is more useful than

another Combine their predictions using a meta-learner

Meta-learner Uses training sources to measure base learner

accuracy Weighs each learner based on its accuracy

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<location> Boston, MA </> <listed-price> $110,000</> <phone> (617) 253 1429</> <comments> Great location </>

<location> Miami, FL </> <listed-price> $250,000</> <phone> (305) 729 0831</> <comments> Fantastic house </>

Training the Learners

Naive Bayes Learner

(location, address)(listed-price, price)(phone, agent-phone)(comments, description) ...

(“Miami, FL”, address)(“$ 250,000”, price)(“(305) 729 0831”, agent-phone)(“Fantastic house”, description) ...

realestate.com

Name Learner

address price agent-phone description

Schema of realestate.com

Mediated schema

location listed-price phone comments

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<extra-info>Beautiful yard</><extra-info>Great beach</><extra-info>Close to Seattle</>

<day-phone>(278) 345 7215</><day-phone>(617) 335 2315</><day-phone>(512) 427 1115</>

<area>Seattle, WA</><area>Kent, WA</><area>Austin, TX</>

Applying the Learners

Name LearnerNaive Bayes

Meta-Learner

(address,0.8), (description,0.2)(address,0.6), (description,0.4)(address,0.7), (description,0.3)

(address,0.6), (description,0.4)

Meta-LearnerName LearnerNaive Bayes

(address,0.7), (description,0.3)

(agent-phone,0.9), (description,0.1)

address price agent-phone description

Schema of homes.com Mediated schema

area day-phone extra-info

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Putting It All Together: LSD System

L1 L2 Lk

Mediated schema

Source schemas

Data listings

Training datafor base learners Constraint Handler

Mapping Combination

User Feedback

Domain Constraints

Matching PhaseTraining Phase

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Mappings between Schemas

LSD provides attribute correspondences, but not complete mappings

Mappings generally are posed as views: define relations in one schema (typically either the mediated schema or the source schema), given data in the other schema This allows us to “restructure” or “recompose + decompose”

our data in a new way

We can also define mappings between values in a view We use an intermediate table defining correspondences – a

“concordance table” It can be filled in using some type of code, and corrected by

hand

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A Few Mapping Examples

Movie(Title, Year, Director, Editor, Star1, Star2)

Movie(Title, Year, Director, Editor, Star1, Star2)

PieceOfArt(ID, Artist, Subject, Title, TypeOfArt)

MotionPicture(ID, Title, Year)Participant(ID, Name, Role)

CustID

CustName

1234 Smith, J.

PennID

EmpName

46732 John Smith

PieceOfArt(I, A, S, T, “Movie”) :- Movie(T, Y, A, _, S1, S2),ID = T || Y, S = S1 || S2

Movie(T, Y, D, E, S1, S2) :- MotionPicture(I, T, Y), Participant(I, D, “Dir”), Participant(I, E, “Editor”), Participant(I, S1, “Star1”), Participant(I, S2, “Star2”)

T1 T2

Need a concordance table from CustIDs to PennIDs

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Two Important Approaches

TSIMMIS [Garcia-Molina+97] – Stanford Focus: semistructured data (OEM), OQL-based language

(Lorel) Creates a mediated schema as a view over the sources Spawned a UCSD project called MIX, which led to a

company now owned by BEA Systems Other important systems of this vein: Kleisli/K2 @ Penn

Information Manifold [Levy+96] – AT&T Research Focus: local-as-view mappings, relational model Sources defined as views over mediated schema

Requires a special Led to peer-to-peer integration approaches (Piazza, etc.)

Focus: Web-based queriable sources

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TSIMMIS

One of the first systems to support semi-structured data, which predated XML by several years: “OEM”

An instance of a “global-as-view” mediation system We define our global schema as views over the

sources

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XML vs. Object Exchange Model<book> <author>Bernstein</author> <author>Newcomer</author> <title>Principles of TP</title></book>

<book> <author>Chamberlin</author> <title>DB2 UDB</title></book>

O1: book { O2: author { Bernstein } O3: author { Newcomer } O4: title { Principles of TP }

}

O5: book { O6: author { Chamberlin } O7: title { DB2 UDB }}

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Queries in TSIMMIS

Specified in OQL-style language called Lorel OQL was an object-oriented query language that looks like

SQL Lorel is, in many ways, a predecessor to XQuery

Based on path expressions over OEM structures: select book where book.title = “DB2 UDB” and book.author = “Chamberlin”

This is basically like XQuery, which we’ll use in place of Lorel and the MSL template language. Previous query restated =

for $b in AllData()/bookwhere $b/title/text() = “DB2 UDB” and $b/author/text() = “Chamberlin”return $b

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Query Answering in TSIMMIS

Basically, it’s view unfolding, i.e., composing a query with a view

The query is the one being asked The views are the MSL templates for the

wrappers Some of the views may actually require

parameters, e.g., an author name, before they’ll return answers Common for web forms (see Amazon, Google, …) XQuery functions (XQuery’s version of views) support

parameters as well, so we’ll see these in action

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A Wrapper Definition in MSL

Wrappers have templates and binding patterns ($X) in MSL:

B :- B: <book {<author $X>}> // $$ = “select * from book where author=“ $X //

This reformats a SQL query over Book(author, year, title)

In XQuery, this might look like:define function GetBook($x AS xsd:string) as book {

for $b in sql(“Amazon.DB”, “select * from book where author=‘” + $x

+”’”)return <book>{$b/title}<author>$x</author></book>

}

book

title author

… …

…

The union of GetBook’s results is unioned with others to form the view Mediator()

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How to Answer the Query

Given our query:for $b in Mediator()/bookwhere $b/title/text() = “DB2 UDB” and $b/author/text() = “Chamberlin”return $b

Find all wrapper definitions that: Contain output enough “structure” to match

the conditions of the query Or have already tested the conditions for us!

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Query Composition with Views

We find all views that define book with author and title, and we compose the query with each:

define function GetBook($x AS xsd:string) as book {for $b in

sql(“Amazon.DB”, “select * from book where author=‘” + $x + “’”)

return <book> {$b/title} <author>{$x}</author></book>}for $b in Mediator()/book

where $b/title/text() = “DB2 UDB” and $b/author/text() = “Chamberlin”return $b

book

title author

… …

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Matching View Output to Our Query’s Conditions

Determine that $b/book/author/text() $x by matching the pattern on the function’s output:define function GetBook($x AS xsd:string) as book {

for $b in sql(“Amazon.DB”, “select * from book where author=‘” + $x +

“’”)return <book>{ $b/title } <author>{$x}</author></book>

}

let $x := “Chamberlin”for $b in GetBook($x)/bookwhere $b/title/text() = “DB2 UDB” return $b

book

title author

… …

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The Final Step: Unfolding

let $x := “Chamberlin”for $b in (

for $b’ in sql(“Amazon.com”,

“select * from book where author=‘” + $x + “’”) return <book>{ $b/title }<author>{$x}</author></book> )/bookwhere $b/title/text() = “DB2 UDB” return $b

How do we simplify further to get to here?for $b in sql(“Amazon.com”,

“select * from book where author=‘Chamberlin’”)where $b/title/text() = “DB2 UDB” return $b

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Virtues of TSIMMIS

Early adopter of semistructured data, greatly predating XML Can support data from many different kinds of

sources Obviously, doesn’t fully solve heterogeneity

problem

Presents a mediated schema that is the union of multiple views Query answering based on view unfolding

Easily composed in a hierarchy of mediators

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Limitations of TSIMMIS’ Approach

Some data sources may contain data with certain ranges or properties

“Books by Aho”, “Students at UPenn”, … If we ask a query for students at Columbia, don’t

want to bother querying students at Penn… How do we express these?

Mediated schema is basically the union of the various MSL templates – as they change, so may the mediated schema