suitability of a kr for obdm - university of...

Suitability of a KR for OBDM• Last time

– We explored how a KR (like OWL) can support• terminology development• schema development

– form and query expansion– debugging and integration

• Is OWL fit for these purposes?– Terminology?– Schema, query, etc?

• Shape?• Values?

• How do we work with standard datatypes?

1Friday, 28 March 14

Ontology Based Data Access (ODBA)• Ontology at run time?

– More, ontology for the end user!??!• By end user, I mean, “someone writing queries”

• Familiar– Controlled vocabulary– Query by example

• New– “Better” queries– Integrated views of data

Friday, 28 March 14

“Better” queries• Better how?

– Consider a simple schema– What does the logical schema look like?– Lots of variants

• Sane queries– SELECT hasAge FROM employee

WHERE hasSalary >= 50000;– SELECT hasAge FROM student

WHERE hasSalary >= 50000;– What about Persons?

• Union query?

• Rather write– SELECT hasAge FROM Person

WHERE hasSalary >= 50000;– no matter what kind of persons there are

Person

Student Employee

hasAge hasSalary

create table employee(id number(4) hasAge number(3), hasSalary number(6);create table student(id number(4) hasAge number(3), hasSalary number(5);

Friday, 28 March 14

What do we need?• Richer query language!

– Need at least conjunctive queries• I.e., patterns with explicit varibles• Increases complexity!

– Ontology sensitive!• The queries should respect the semantics

• Data access!– ETL...populate an ABox from a Database– Distributed

• Leave my database ALOOOOOONNNNNEE!!!!!

– Need mappings

• Good computation– Some fragments of OWL tuned for this

• Cf OWL QL and OWL EL• Polynomial; OWL QL has pure query expansion implementations

Friday, 28 March 14

OWL and Data (Properties)

Sebastian Brandt [email protected]

(Slides by Bijan Parsia, [email protected])

Friday, 28 March 14

mailto:[email protected]




OWL Has Two “Worlds”• The world of logic

– Classes, individuals, (object) object properties– Java analogue:

• Classes, instances, and object valued instance variables

• The world of “data”– Datatypes, data values, data properties

(well, these span worlds)– Java analogue:

• Primitive types, primitive data values, primitively-valued instance vars


The World of Logic: “Abstract”• Individuals are members of classes• We know nothing about them except what the ontology

says– Individual: Bijan Types: Person.– Individual: Sean Types: Person.– Class: Instructor SubClassOf: Person– What do we know about Bijan, Sean, Instructor, and Person?

• Individuals (etc.) are characterized entirely by the user axioms– Ok, mostly. Tautologies: Bijan Types: owl:Thing.– What’s left unsaid may or may not hold

• Open world assumption (and no unique name assumption)• Think of the various models

• Remember: the interpretation domain is arbitrary7

Friday, 28 March 14

The World of Data: “Concrete”

8

• Just as with primitive types, we have predefined names:– For individuals:

• 1, 2, 0, 1.0, “I’m a string!”, "51"^^xsd:integer– For sets of individuals (aka types)

• integer, xsd:string, xsd:nonNegativeInteger, xsd:decimal, etc.

• These names have a fixed interpretation!– That is, (“1”^^xsd:integer)I is always the integer 1.– xsd:integer is always the set of integers– The atomic names (singular and plural) have built-in meaning

• On the abstract side, this is only true for owl:Thing, owl:Nothing, owl:topObjectProperty, owl:bottomObjectProperty, owl:topDataProperty, owl:bottomDataProperty, and the logical connectives

• The actual meanings for the tops vary with the interpretation domain

Friday, 28 March 14

Fixed meaning!• There is a lot we know about integers

– DataProperty: Height Characteristics: Functional– Individual: Bijan Facts: height “6”^^xsd:integer

• We know that my height cannot be equal to 2, 4, or 8–Bijan Facts: height 6, height 2

» Inconsistent!• We know that my height cannot be a xsd:string

• Compare with:– ObjectProperty: Height Characteristics: Functional– Individual: Bijan height Six, height Two– What follows?

• We can replicate the inequality on the abstract side– Just add Individual: Six DifferentFrom: Two– For all integers… (DifferentIndividuals helps only a little)– Many more entailments to formalize... 9

Friday, 28 March 14

What Can We Define?• We have an “expression language” for data

– We can derive new types from our primitives•integer[>= 0 , <=150]• This is a restriction on integer (a DataRestriction)

– The subset of integers between 0 and 150, inclusive• “<=” and “>=” have built in meaning

– That the values respect, e.g., 1<=2 but not 2 <=1– We can name these expressions

• In a limited way•Datatype: personAge EquivalentTo: integer[>= 0 , <=150]

– We can express boolean combinations of expressions•not personAge•integer[>=0] or integer[<=150]•(integer[>=0] or integer[<=150]) and not personAge• (And enumerations, e.g., {1, 2, 3})

10

“facet”

Friday, 28 March 14

Between Two Worlds• DataProperties

– Disjoint from ObjectProperties– ObjectProperties are interpreted into the crossproduct of the

(abstract) domain (i.e., Δ⨯Δ)– DataProperties are interpreted into the crossproduct of the

abstract and data domains (i.e., Δ⨯Δd)– Δ and Δd are disjoint– Δd is a (large) superset of the union of the value spaces

• DataProperty Axioms– Most of the usual: Sub/Equivalent/Disjoint, etc.

• Restrictions on DataProperties– In general no “chaining”:

• No transitive, inverse, reflexive, etc.• Anything that would potentially “merge” the domains


Between Two Worlds

6

12

ΔI Δinteger

b

-1 10

2-2a

Example interpretation I

......

different type or sort

Bijan Facts: height “6”^^xsd:integer

•I•I•I

Fixed for any interpretationFriday, 28 March 14

Between Two Worlds• Class: To3 EquivalentTo: P min 3 Thing

• Individual: Bijan Facts: P X, P Y, P Z (*)

de

c

13

Δ Δ

Interpretation I

b

Bijan Bijan

b

Z

X

Y

•I

•I

•I

•J

•J•I

f

P•I

•J

•J

Interpretation JI ⊨ (*)

I ⊨ Bijan :Types To3

J ⊨ (*)

J ⊭ Bijan :Types To3

•J

object property

Friday, 28 March 14

Between Two Worlds• Class: To3 EquivalentTo: DP min 3 integer

• Individual: Bijan Facts: DP 1, DP 2, DP 3 (*)

14

Bijan

3ΔIΔinteger

DP

b-1

1

0

2

-2a

•I •I

Example interpretation I

I ⊨ (*) implies I ⊨ Bijan :Types To3 for any interpretation I

data property

Friday, 28 March 14

Two World Philosophy • OWL is for developing theories about the world

– Very blank slate– We’re cautious about what we conclude

• Pedantry is critical!

• We have excellent theories about integers– And strings! As well as how to compute with them

• There’s no point in trying to formalize integers– Integers should be a standard part of our language

• Very hard to recognize a half baked integer theory– As a theory of integers


The Standard Datatype Map: Types“Maths” Numbers String Misc

owl:realowl:rationalxsd:decimalxsd:integerxsd:nonNegativeIntegerxsd:nonPositiveIntegerxsd:positiveIntegerxsd:negativeIntegerxsd:longxsd:intxsd:shortxsd:bytexsd:unsignedLongxsd:unsignedIntxsd:unsignedShortxsd:unsignedByte

rdf:plainLiteralxsd:IRIxsd:stringxsd:normalizedStringxsd:tokenxsd:languagexsd:Namexsd:NCNamexsd:NMTOKEN

rdf:XMLLiteralxsd:boolean



Date and Time



xsd:dateTimexsd:dateTimeStamp


rdf:plainLiteralxsd:IRIxsd:stringxsd:normalizedStringxsd:tokenxsd:languagexsd:Namexsd:NCNamexsd:NMTOKEN Binary



xsd:hexBinaryxsd:hex64Binary


“Computer” Numbers xsd:hexBinaryxsd:hex64Binary


xsd:doublexsd:float

xsd:hexBinaryxsd:hex64Binary


The Standard Datatype Map: Facets“Maths” Numbers String Misc

xsd:minInclusivexsd:maxInclusexsd:minExclusivexsd:maxExclusive

xsd:lengthxsd:minLengthxsd:maxLengthxsd:pattern

(for rdf:plainLiteralrdf:langRange)

Nonexsd:minInclusivexsd:maxInclusexsd:minExclusivexsd:maxExclusive



Date and Time








Binary




xsd:lengthxsd:minLengthxsd:maxLength


“Computer” Numbers xsd:lengthxsd:minLengthxsd:maxLength



xsd:lengthxsd:minLengthxsd:maxLength

17

integer[<= 0

, >= 150]

Friday, 28 March 14

The Standard Datatype Map“Maths” Numbers String Misc

Everything derived from owl:Real. Note that there area many elements of owl:Real which have no lexical form.

Everything derived from rdf:plainLiteral except xsd:IRI (which is disjoint from the rest)

Mutually DisjointEverything derived from owl:Real. Note that there area many elements of owl:Real which have no lexical form.


Date and Time



Mutually disjoint



Binary



Mutually disjoint


“Computer” Numbers Mutually disjoint


Disjoint from owl:Real (and the other categories) and each other

Mutually disjoint


Key Restrictions• Restrictions on datatypes: “admissible”

– Support top predicate– Closed under negation– Satisfiability of conjunctions is decidable

• integer[<=0] and integer[>=10] is unsatisfiable

• We consider only unary predicates

• Benefits– Admissible datatypes + OWL(DL) = decidable KR formalism– Can be implemented using a “datatype oracle”

• Simply extend existing reasoner by solvers for datatypes• No need to build new reasoner from scratch


Robustness of Datatypes• Semantically robust

– Ontologies don’t change when you add or remove non-used datatypes

• Computationally robust– Very robust for decidability– Complexity is a bit trickier

• Implementably robust– Highly modular implementation

• Expressively limited– Can’t even say “a square’s height equals its width”!– Can’t talk about the whole data domain

• We trade off expressivity for robustness


Two World Philosophy BenefitsFrom a user perspective:• + Integers "Just Work"

• So do strings, floats, decimals, etc.• Powerful constructors

• + Normal syntax• + Clean separation

(data and objects; user theory and builtin theory)• May be a -

• - Limits on user extensibility• And transparency, explorability

• - Expressivity restrictions (no addition!)• From a theory perspective:

• + Analyzable• From an implementation perspective:

• + Modular implementation• - Must extend implementation to accommodate new types, facets


Liberalization• Our restrictions are overstrict

– Simple generalisation: Allow n-ary comparisons• Not just age some integer[>=5]• Compare values on different properties

– age only integer[<= height] (made up syntax!)– Bijan Facts: age 42, height 6

• Note that these still must be path free!– No, Person that hasCar hasAge

» only integer[= hasHouse hasAge]– People whose cars are only as old as their houses

– We can liberalize this a bit further• Allow for (linear) (in)equations as “predicates”

22

EquivalentClasses(SafelyDosedPatient DataAllValuesFrom(tookDrugInAmount weight DataComparison(Arguments(totalDoseInMg weightinKg) leq(totalDoseInMg times(2, weightInKg)))))

Friday, 28 March 14

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