bridging domain knowledge and its formalisation – and integrating services on top of that

Introduction Formalisation Bridging the Gap: Representation & Services Conclusion & Outlook

Bridging Domain Knowledgeand its Formalisation –

and Integrating Services on Top of ThatPresentation at the University of Birmingham, UK

Christoph Lange

University of Bremen, Germany

2011-12-19

Christoph Lange Bridging Domain Knowledge and its Formalisation – and Integrating Services on Top of That 2011-12-19 1

http://www.uni-bremen.de



‘Hello, World!’

Ph.D. from Jacobs University Bremen (withMichael Kohlhase)Enabling Collaborationon Semiformal Mathematical Knowledgeby Semantic Web IntegrationPostdoctoral researcher at the University ofBremen (with John Bateman, Till Mossakowski)Ontology Integration and Interoperability(OntoIOp) – Distributed Ontology Language(DOL)↝ ISO 17347




Why Formalise?

Take advantage of machine support for domain-relevant tasks⇒ teach the computer about your domainMachine support needed for

verifying assumptionsretrieving relevant informationautomating processes (while avoiding low-level coding)

How to formalise? – Use logic!




Machine Support (1): Mathematics Publishing

The author(s):

0 original idea (in one’smind)

1 formalise intostructured document

2 search existingknowledge to buildon

3 validate formalstructure

4 present in acomprehensible way

5 submit for review

The reader(s):

‘What does thatmean?’: missingbackground,used to differentnotation

‘How does thatwork?’

‘What is that goodfor?’

look up backgroundinformation in citedpublications

The reviewer(s):

1 read paper (←Ð)

2 verify claims

3 point out problemswith the paper andits formal concepts




Logical Formalisation (1): Math. Publishing

MathKnowledgeItem

StatementTheory

Type

ConstitutiveStatement

NonConstitutiveStatement

Import

SymbolDefinition

Axiom

Example AssertionProof

NotationDefinition

subClassOf

otherproperties

dependsOn,hasPart,verbalizes

imports,metaTheory

importsFrom

homeTheory

hasTyp

e

proveshasDefinition exemplifies

render

sSymbol




Machine Support (2): Ambient Assisted Living

Scenario

Clara instructs herwheelchair to get her to the kitchen (next doorto the living room). For dinner, she would like to take a pizza fromthe freezer and bake it in the oven. (Her diet is vegetarian.)Afterwards she needs to rest in bed.

Devices Involved, Simple to Complex:

kitchen light switch

freezer (aware of its contents)

wheelchair (with navigation)




Logical Formalisation (2): AAL

Light Switch: propositional logic‘light is switched on if and only if someone is in the room and itis dark outside’ – light_on ≡ person_in_room ∧ dark_outsideFreezer: description logic (Pizza ontology)‘a vegetarian pizza is a pizza whose toppings are all vegetarian’VegetarianPizza ≡ Pizza ⊓ ∀hasTopping.VegetarianWheelchair: first order logic (RCC-style spatial calculus)‘two areas in a house (e.g. a working area in a room) are eitherthe same, or intersecting, or bordering, or separated, or one ispart of the other’∀a1, a2.equal(a1, a2) ∨ overlapping(a1, a2) ∨ bordering(a1, a2) ∨disconnected(a1, a2) ∨ part_of(a1, a2) ∨ part_of(a2, a1)




What is Wrong with Formalisation?

The machine understands it ✓Logic experts understand it ✓Domain experts don’t understand it ☇

Recallwell-known software engineering disasterse.g. the 1998 Mars Polar Lander ($ 165 million)Loss: thenmoney, soon human lives?ICD-11 being formalised into an ontologyDomain experts don’t need to fully understand a formalisation,but they should be able to proof-read it!




Semiformal Mathematical Knowledge

Informal

x4−4x3+2x2+4x+4 = (x2−√

2±√

4 + 2√7)x+(1±

√4 + 2

√7+

√7)),

(1)whereabove thetwo factorscomefrom takingthe+ signeachtime,or the−

signeachtime. Note factoringa quarticinto two realquadraticsis differentthantrying to find four complexroots.Definition: A function f is analytic on an opensubsetR ⊂ C if f is complexdifferentiableeverywhereonR; f is entire if it is analyticonall of C.

2 Proof of the FundamentalTheoremvia Liouville

Theorem 2.1 (Liouville). If f(z) is analyticandboundedin thecomplex plane,thenf(z) is constant.

Wenow prove

Theorem 2.2 (Fundamental Theorem of Algebra). Let p(z) be a polynomialwith complex coefficientsof degreen. Thenp(z) hasn roots.

Proof. It is sufficient to show any p(z) hasoneroot, for by division we canthenwrite p(z) = (z − z0)g(z), with g of lowerdegree.

Notethatif

p(z) = anzn + an−1z

n−1 + · · ·+ a0, (2)

thenas|z| → ∞, |p(z)| → ∞. This followsas

p(z) = zn ·∣∣∣an +

an−1

z+ · · ·+ a0

zn

∣∣∣ . (3)

Assumep(z) is non-zeroeverywhere.Then 1p(z)

is boundedwhen |z| ≥ R.

Also, p(z) 6= 0, so 1p(z)

is boundedfor |z| ≤ R by continuity. Thus, 1p(z)

isa bounded,entire function, which must be constant. Thus, p(z) is constant,acontradictionwhich impliesp(z) musthave azero(ourassumption).

[Lev]

2

Formalised = Computerised

Semiformal – a pragmatic and practical compromiseanything informal that is intended to or could in principle beformalisedcombinations of informal and formal for both human andmachine audience




Services (1): Look up Background Knowledge

Authored in STEX, output to XHTML+MathML

\begin{definition}[for=subSet]...

\end{definition}...\subSet{R}{\cartProd{A,B}}




Services (2): Adaptive Presentation

Authored in LATEX, output to XHTML+MathML

\usepackage{siunitx}\DeclareSIUnit \foot { ft }...\SI{9144}{\feet}




Services (3): Ontology Documentation




Services (4): Localised Peer Review

`

discussion page

knowledgeitems

(OMDoc ontology)on wiki pages

definitionforum1

example

post1: Issue(UnclearWh.Useful)

post7: Decision

post2: Elaboration

post4: Idea(ProvideExample)

post3: Position

post5: Evaluation

exemplifies

hasDiscussion(IkeWiki ontology)

has_container

has_reply

resolvesInto

physical structure(SIOC Core)

argumentativestructure

(SIOC Arg.)

elaborates_on

agrees_with

proposes_solution_for

supports

post6: Position

agrees_with

decides

supported_by

Position

Decision

Issue

Inappropriatefor Domain

Wrong Incomprehensible

subClassOf

Idea

ProvideExample

Keep asBad Example

Delete

subClassOfproposes_solution_for

agrees_with/disagrees_with

agrees_with/disagrees_with

decides decides

supported_by

OntologyEntity

resolves_into

Math. Know-ledge Item

Theorem Example

subClassOf

subClassOf

SIOCargumentationmodule (partly shown)

Domain-specificargumentationclasses (partly shown)

OMDoc ontology

……




Services (5): Software Eng. Expert Finding

The V-Model introduces relationsbetween document fragments

Formalise V-Model vocabulary:refines, implements, describesUseMark up these secondary(non-logical) relations as metadata

STEX supports flexibly extensible metadata in RDFa stylespecify their semantics in vocabularies; once more in STEX

Example (Refining a Specification)

\SemVMrel[module=reqspec,refid=R12,rel=refines]




Services (5): Software Eng. Expert Finding (2)# application-specific dimensions:PREFIX ver: <http://www.sams-projekt.de/ontologies/VersionManagement#> # versioningPREFIX sp: <http://www.sams-projekt.de/ontologies/V-model#> # software process# prefixes for logical/functional structures (OMDoc), administrative metadata (DCMES),# and user profiles (FOAF) omitted

SELECT ?potentialSubstituteName WHERE {# for each document Alice is responsible for, get all of its parts,# i.e., transitively, any kind of semantic (sub)object in the document?document ver:responsible <.../employees#Alice> ;

oo:hasPart ?object .

# find other objects that are related to each ?object# 1. in that ?object refines them w.r.t. the software process{ ?object sp:refines ?relatedObject }UNION# 2. or in that they are other mathematical symbols defined in terms# of ?object (only applies if ?object itself is a symbol){ ?object oo:occursInDefinitionOf ?relatedObject }

# find the document that contains the related object and the person responsible for that document ...?otherDocument oo:hasPart ?relatedObject ;

dc:date ?date ;sp:responsible ?potentialSubstitute .

# (only considering documents that are sufficiently up to date)FILTER (?date > "2009-01-01"^^xsd:date)

# ... and the real name of that person?potentialSubstitute foaf:name ?potentialSubstituteName .

}




The ‘Active Document’ Machinery




Connecting Mathematics↔Economics DataHow to deal with derived values in datasets?

As of September 2010

MusicBrainz

(zitgist)

P20

YAGO

World Fact-book (FUB)

WordNet (W3C)

WordNet(VUA)

VIVO UFVIVO

Indiana

VIVO Cornell

VIAF

URIBurner

Sussex Reading

Lists

Plymouth Reading

Lists

UMBEL

UK Post-codes

legislation.gov.uk

Uberblic

UB Mann-heim

TWC LOGD

Twarql

transportdata.gov

.uk

totl.net

Tele-graphis

TCMGeneDIT

TaxonConcept

The Open Library (Talis)

t4gm

Surge Radio

STW

RAMEAU SH

statisticsdata.gov

.uk

St. Andrews Resource

Lists

ECS South-ampton EPrints

Semantic CrunchBase

semanticweb.org

SemanticXBRL

SWDog Food

rdfabout US SEC

Wiki

UN/LOCODE

Ulm

ECS (RKB

Explorer)

Roma

RISKS

RESEX

RAE2001

Pisa

OS

OAI

NSF

New-castle

LAAS

KISTIJISC

IRIT

IEEE

IBM

Eurécom

ERA

ePrints

dotAC

DEPLOY

DBLP (RKB

Explorer)

Course-ware

CORDIS

CiteSeer

Budapest

ACM

riese

Revyu

researchdata.gov

.uk

referencedata.gov

.uk

Recht-spraak.

nl

RDFohloh

Last.FM (rdfize)

RDF Book

Mashup

PSH

ProductDB

PBAC

Poké-pédia

Ord-nance Survey

Openly Local

The Open Library

OpenCyc

OpenCalais

OpenEI

New York

Times

NTU Resource

Lists

NDL subjects

MARC Codes List

Man-chesterReading

Lists

Lotico

The London Gazette

LOIUS

lobidResources

lobidOrgani-sations

LinkedMDB

LinkedLCCN

LinkedGeoData

LinkedCT

Linked Open

Numbers

lingvoj

LIBRIS

Lexvo

LCSH

DBLP (L3S)

Linked Sensor Data (Kno.e.sis)

Good-win

Family

Jamendo

iServe

NSZL Catalog

GovTrack

GESIS

GeoSpecies

GeoNames

GeoLinkedData(es)

GTAA

STITCHSIDER

Project Guten-berg (FUB)

MediCare

Euro-stat

(FUB)

DrugBank

Disea-some

DBLP (FU

Berlin)

DailyMed

Freebase

flickr wrappr

Fishes of Texas

FanHubz

Event-Media

EUTC Produc-

tions

Eurostat

EUNIS

ESD stan-dards

Popula-tion (En-AKTing)

NHS (EnAKTing)

Mortality (En-

AKTing)Energy

(En-AKTing)

CO2(En-

AKTing)

educationdata.gov

.uk

ECS South-ampton

Gem. Norm-datei

datadcs

MySpace(DBTune)

MusicBrainz

(DBTune)

Magna-tune

John Peel(DB

Tune)

classical(DB

Tune)

Audio-scrobbler (DBTune)

Last.fmArtists

(DBTune)

DBTropes

dbpedia lite

DBpedia

Pokedex

Airports

NASA (Data Incu-bator)

MusicBrainz(Data

Incubator)

Moseley Folk

Discogs(Data In-cubator)

Climbing

Linked Data for Intervals

Cornetto

Chronic-ling

America

Chem2Bio2RDF

biz.data.

gov.uk

UniSTS

UniRef

UniPath-way

UniParc

Taxo-nomy

UniProt

SGD

Reactome

PubMed

PubChem

PRO-SITE

ProDom

Pfam PDB

OMIM

OBO

MGI

KEGG Reaction

KEGG Pathway

KEGG Glycan

KEGG Enzyme

KEGG Drug

KEGG Cpd

InterPro

HomoloGene

HGNC

Gene Ontology

GeneID

GenBank

ChEBI

CAS

Affy-metrix

BibBaseBBC

Wildlife Finder

BBC Program

mesBBC

Music

rdfaboutUS Census




Connecting Mathematics↔Economics DataHow to deal with derived values in datasets?:pop_sealand2010scv:dimension :PrincipalityOfSealand ;scv:dimension :Year2010 ;scv:dimension :People18to65years ;rdf:value 7 .

:unemployed_sealand2010scv:dimension :PrincipalityOfSealand ;scv:dimension :Year2010 ;scv:dimension :People18to65years ;rdf:value 2 .

:unemp_rate_sealand2010scv:dimension :PrincipalityOfSealand ;scv:dimension :Year2010 ;rdf:value 0.286 .

:pop_kugelmugel2010scv:dimension :KugelmugelRepublic ;scv:dimension :Year2010 ;scv:dimension :People18to65years ;rdf:value 11 .

:unemployed_kugelmugel2010scv:dimension :KugelmugelRepublic ;scv:dimension :Year2010 ;scv:dimension :People18to65years ;rdf:value 1 .

:unemp_rate_kugelmugel2010scv:dimension :KugelmugelRepublic ;scv:dimension :Year2010 ;rdf:value 0.091 .

How to validate the derived values?How to compute them for new data points?unemp. rate = unemployed

population ⇒ link to ‘division’

Can also link to custom/non-standard functionsChristoph Lange Bridging Domain Knowledge and its Formalisation – and Integrating Services on Top of That 2011-12-19 18



Conclusion

Semiformal knowledge representation . . .makes formalisation comprehensible to domain experts

allows for linking mathematical formalisations to arbitraryapplication domains

enables useful services for experts and non-experts



bridging domain knowledge and its formalisation – and integrating services on top of that

Technology