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Presentation at the University of Birmingham, UK, 2011-12-19
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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
Introduction Formalisation Bridging the Gap: Representation & Services Conclusion & Outlook
‘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
Christoph Lange Bridging Domain Knowledge and its Formalisation – and Integrating Services on Top of That 2011-12-19 2
Introduction Formalisation Bridging the Gap: Representation & Services Conclusion & Outlook
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!
Christoph Lange Bridging Domain Knowledge and its Formalisation – and Integrating Services on Top of That 2011-12-19 3
Introduction Formalisation Bridging the Gap: Representation & Services Conclusion & Outlook
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
Christoph Lange Bridging Domain Knowledge and its Formalisation – and Integrating Services on Top of That 2011-12-19 4
Introduction Formalisation Bridging the Gap: Representation & Services Conclusion & Outlook
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
Christoph Lange Bridging Domain Knowledge and its Formalisation – and Integrating Services on Top of That 2011-12-19 5
Introduction Formalisation Bridging the Gap: Representation & Services Conclusion & Outlook
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)
Christoph Lange Bridging Domain Knowledge and its Formalisation – and Integrating Services on Top of That 2011-12-19 6
Introduction Formalisation Bridging the Gap: Representation & Services Conclusion & Outlook
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)
Christoph Lange Bridging Domain Knowledge and its Formalisation – and Integrating Services on Top of That 2011-12-19 7
Introduction Formalisation Bridging the Gap: Representation & Services Conclusion & Outlook
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!
Christoph Lange Bridging Domain Knowledge and its Formalisation – and Integrating Services on Top of That 2011-12-19 8
Introduction Formalisation Bridging the Gap: Representation & Services Conclusion & Outlook
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
Christoph Lange Bridging Domain Knowledge and its Formalisation – and Integrating Services on Top of That 2011-12-19 9
Introduction Formalisation Bridging the Gap: Representation & Services Conclusion & Outlook
Services (1): Look up Background Knowledge
Authored in STEX, output to XHTML+MathML
\begin{definition}[for=subSet]...
\end{definition}...\subSet{R}{\cartProd{A,B}}
Christoph Lange Bridging Domain Knowledge and its Formalisation – and Integrating Services on Top of That 2011-12-19 10
Introduction Formalisation Bridging the Gap: Representation & Services Conclusion & Outlook
Services (1): Look up Background Knowledge
Authored in STEX, output to XHTML+MathML
\begin{definition}[for=subSet]...
\end{definition}...\subSet{R}{\cartProd{A,B}}
Christoph Lange Bridging Domain Knowledge and its Formalisation – and Integrating Services on Top of That 2011-12-19 10
Introduction Formalisation Bridging the Gap: Representation & Services Conclusion & Outlook
Services (2): Adaptive Presentation
Authored in LATEX, output to XHTML+MathML
\usepackage{siunitx}\DeclareSIUnit \foot { ft }...\SI{9144}{\feet}
Christoph Lange Bridging Domain Knowledge and its Formalisation – and Integrating Services on Top of That 2011-12-19 11
Introduction Formalisation Bridging the Gap: Representation & Services Conclusion & Outlook
Services (2): Adaptive Presentation
Authored in LATEX, output to XHTML+MathML
\usepackage{siunitx}\DeclareSIUnit \foot { ft }...\SI{9144}{\feet}
Christoph Lange Bridging Domain Knowledge and its Formalisation – and Integrating Services on Top of That 2011-12-19 11
Introduction Formalisation Bridging the Gap: Representation & Services Conclusion & Outlook
Services (3): Ontology Documentation
Christoph Lange Bridging Domain Knowledge and its Formalisation – and Integrating Services on Top of That 2011-12-19 12
Introduction Formalisation Bridging the Gap: Representation & Services Conclusion & Outlook
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
……
Christoph Lange Bridging Domain Knowledge and its Formalisation – and Integrating Services on Top of That 2011-12-19 13
Introduction Formalisation Bridging the Gap: Representation & Services Conclusion & Outlook
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
……
Christoph Lange Bridging Domain Knowledge and its Formalisation – and Integrating Services on Top of That 2011-12-19 13
Introduction Formalisation Bridging the Gap: Representation & Services Conclusion & Outlook
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
……
Christoph Lange Bridging Domain Knowledge and its Formalisation – and Integrating Services on Top of That 2011-12-19 13
Introduction Formalisation Bridging the Gap: Representation & Services Conclusion & Outlook
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
……
Christoph Lange Bridging Domain Knowledge and its Formalisation – and Integrating Services on Top of That 2011-12-19 13
Introduction Formalisation Bridging the Gap: Representation & Services Conclusion & Outlook
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]
Christoph Lange Bridging Domain Knowledge and its Formalisation – and Integrating Services on Top of That 2011-12-19 14
Introduction Formalisation Bridging the Gap: Representation & Services Conclusion & Outlook
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 .
}
Christoph Lange Bridging Domain Knowledge and its Formalisation – and Integrating Services on Top of That 2011-12-19 15
Introduction Formalisation Bridging the Gap: Representation & Services Conclusion & Outlook
The ‘Active Document’ Machinery
Christoph Lange Bridging Domain Knowledge and its Formalisation – and Integrating Services on Top of That 2011-12-19 16
Introduction Formalisation Bridging the Gap: Representation & Services Conclusion & Outlook
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
Christoph Lange Bridging Domain Knowledge and its Formalisation – and Integrating Services on Top of That 2011-12-19 17
Introduction Formalisation Bridging the Gap: Representation & Services Conclusion & Outlook
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
Introduction Formalisation Bridging the Gap: Representation & Services Conclusion & Outlook
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
Christoph Lange Bridging Domain Knowledge and its Formalisation – and Integrating Services on Top of That 2011-12-19 19
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