Introduction           Formalisation               Bridging the Gap: Representation & Services               Conclusion & ...
Introduction        Formalisation              Bridging the Gap: Representation & Services               Conclusion & Outl...
Introduction            Formalisation              Bridging the Gap: Representation & Services               Conclusion & ...
Introduction         Formalisation              Bridging the Gap: Representation & Services               Conclusion & Out...
Introduction              Formalisation              Bridging the Gap: Representation & Services                 Conclusio...
Introduction        Formalisation              Bridging the Gap: Representation & Services               Conclusion & Outl...
Introduction        Formalisation              Bridging the Gap: Representation & Services               Conclusion & Outl...
Introduction            Formalisation              Bridging the Gap: Representation & Services               Conclusion & ...
Introduction function f is analytic on an open subset R ⊂ C if f is complex the Gap: Representation & Services  Definition:...
Introduction        Formalisation              Bridging the Gap: Representation & Services               Conclusion & Outl...
Introduction        Formalisation              Bridging the Gap: Representation & Services               Conclusion & Outl...
Introduction        Formalisation              Bridging the Gap: Representation & Services               Conclusion & Outl...
Introduction        Formalisation              Bridging the Gap: Representation & Services               Conclusion & Outl...
Introduction        Formalisation              Bridging the Gap: Representation & Services               Conclusion & Outl...
Introduction        Formalisation              Bridging the Gap: Representation & Services               Conclusion & Outl...
Introduction        Formalisation              Bridging the Gap: Representation & Services               Conclusion & Outl...
Introduction                             Formalisation                                  Bridging the Gap: Representation &...
Introduction                             Formalisation                                        Bridging the Gap: Representa...
Introduction        Formalisation              Bridging the Gap: Representation & Services               Conclusion & Outl...
Introduction           Formalisation               Bridging the Gap: Representation & Services               Conclusion & ...
Introduction        Formalisation              Bridging the Gap: Representation & Services               Conclusion & Outl...
Introduction                                                   Formalisation                                              ...
Introduction        Formalisation              Bridging the Gap: Representation & Services               Conclusion & Outl...
Introduction        Formalisation              Bridging the Gap: Representation & Services               Conclusion & Outl...
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Bridging Domain Knowledge and its Formalisation – and Integrating Services on Top of That

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Presentation at the University of Birmingham, UK, 2011-12-19

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Bridging Domain Knowledge and its Formalisation – and Integrating Services on Top of That

  1. 1. Introduction Formalisation Bridging the Gap: Representation & Services Conclusion & Outlook Bridging Domain Knowledge and its Formalisation – and Integrating Services on Top of That Presentation 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
  2. 2. Introduction Formalisation Bridging the Gap: Representation & Services Conclusion & Outlook‘Hello, World!’ Ph.D. from Jacobs University Bremen (with Michael Kohlhase) Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration Postdoctoral researcher at the University of Bremen (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
  3. 3. Introduction Formalisation Bridging the Gap: Representation & Services Conclusion & OutlookWhy Formalise? Take advantage of machine support for domain-relevant tasks ⇒ teach the computer about your domain Machine support needed for verifying assumptions retrieving relevant information automating 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
  4. 4. Introduction Formalisation Bridging the Gap: Representation & Services Conclusion & OutlookMachine Support (1): Mathematics PublishingThe author(s): The reader(s): The reviewer(s): 0 original idea (in one’s ‘What does that 1 read paper (← ) mind) mean?’: missing 2 verify claims background, 1 formalise into used to different 3 point out problems structured document notation with the paper and 2 search existing its formal concepts ‘How does that knowledge to build work?’ on ‘What is that good 3 validate formal for?’ structure look up background 4 present in a information in cited comprehensible way publications 5 submit for review Christoph Lange Bridging Domain Knowledge and its Formalisation – and Integrating Services on Top of That 2011-12-19 4
  5. 5. Introduction Formalisation Bridging the Gap: Representation & Services Conclusion & OutlookLogical Formalisation (1): Math. Publishing dependsOn, MathKnowledgeItem hasPart, subClassOf verbalizes Type other properties Theory Statement homeTheory imports From e imports, NonConstitutive p hasTy Import metaTheory Statement Notation Constitutive Definition Statement Proof Example Assertion proves Symbol hasDefinition Axiom exemplifies Definition bol Sym ers rend Christoph Lange Bridging Domain Knowledge and its Formalisation – and Integrating Services on Top of That 2011-12-19 5
  6. 6. Introduction Formalisation Bridging the Gap: Representation & Services Conclusion & OutlookMachine Support (2): Ambient Assisted Living Scenario Clara instructs her wheelchair to get her to the kitchen (next door to the living room). For dinner, she would like to take a pizza from the 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
  7. 7. Introduction Formalisation Bridging the Gap: Representation & Services Conclusion & OutlookLogical Formalisation (2): AAL Light Switch: propositional logic ‘light is switched on if and only if someone is in the room and it is dark outside’ – light_on ≡ person_in_room ∧ dark_outside Freezer: description logic (Pizza ontology) ‘a vegetarian pizza is a pizza whose toppings are all vegetarian’ VegetarianPizza ≡ Pizza ∀hasTopping.Vegetarian Wheelchair: first order logic (RCC-style spatial calculus) ‘two areas in a house (e.g. a working area in a room) are either the same, or intersecting, or bordering, or separated, or one is part 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
  8. 8. Introduction Formalisation Bridging the Gap: Representation & Services Conclusion & OutlookWhat is Wrong with Formalisation? The machine understands it Logic experts understand it Domain experts don’t understand it Recall well-known software engineering disasters e.g. the 1998 Mars Polar Lander ($ 165 million) Loss: then money, soon human lives? ICD-11 being formalised into an ontology Domain 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
  9. 9. Introduction function f is analytic on an open subset R ⊂ C if f is complex the Gap: Representation & Services Definition: A Formalisation Bridging Conclusion & Outlook differentiable everywhere on R; f is entire if it is analytic on all of C.Semiformal Mathematical Knowledge2 Proof of the Fundamental Theorem via Liouville Theorem 2.1 (Liouville). If f (z) is analytic and bounded in the complex plane, then f (z) is constant.Informal We now prove Theorem 2.2 (Fundamental Theorem of Algebra). Let p(z) be a polynomial Formalised = Computerised with complex coefficients of degree n. Then p(z) has n roots. Proof. It is sufficient to show any p(z) has one root, for by division we can then write p(z) = (z − z0 )g(z), with g of lower degree. Note that if p(z) = an z n + an−1 z n−1 + · · · + a0 , (2) then as |z| → ∞, |p(z)| → ∞. This follows as an−1 a0 p(z) = z n · an + + ··· + n . (3) z z 1 Assume p(z) is non-zero everywhere. Then p(z) is bounded when |z| ≥ R. 1 1 Also, p(z) = 0, so p(z) is bounded for |z| ≤ R by continuity. Thus, p(z) is a bounded, entire function, which must be constant. Thus, p(z) is constant, a contradiction which implies p(z) must have a zero (our assumption). [Lev] Semiformal – a pragmatic and practical compromise 2 anything informal that is intended to or could in principle be formalised combinations of informal and formal for both human and machine audience Christoph Lange Bridging Domain Knowledge and its Formalisation – and Integrating Services on Top of That 2011-12-19 9
  10. 10. Introduction Formalisation Bridging the Gap: Representation & Services Conclusion & OutlookServices (1): Look up Background Knowledge Christoph Lange Bridging Domain Knowledge and its Formalisation – and Integrating Services on Top of That 2011-12-19 10
  11. 11. Introduction Formalisation Bridging the Gap: Representation & Services Conclusion & OutlookServices (1): Look up Background Knowledge Authored in S EX, output to XHTML+MathML T 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
  12. 12. Introduction Formalisation Bridging the Gap: Representation & Services Conclusion & OutlookServices (2): Adaptive Presentation Christoph Lange Bridging Domain Knowledge and its Formalisation – and Integrating Services on Top of That 2011-12-19 11
  13. 13. Introduction Formalisation Bridging the Gap: Representation & Services Conclusion & OutlookServices (2): Adaptive Presentation Authored in LTEX, output to XHTML+MathML A 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
  14. 14. Introduction Formalisation Bridging the Gap: Representation & Services Conclusion & OutlookServices (3): Ontology Documentation Christoph Lange Bridging Domain Knowledge and its Formalisation – and Integrating Services on Top of That 2011-12-19 12
  15. 15. Introduction Formalisation Bridging the Gap: Representation & Services Conclusion & OutlookServices (4): Localised Peer Review Christoph Lange Bridging Domain Knowledge and its Formalisation – and Integrating Services on Top of That 2011-12-19 13
  16. 16. Introduction Formalisation Bridging the Gap: Representation & Services Conclusion & OutlookServices (4): Localised Peer Review Christoph Lange Bridging Domain Knowledge and its Formalisation – and Integrating Services on Top of That 2011-12-19 13
  17. 17. Introduction Formalisation Bridging the Gap: Representation & Services Conclusion & OutlookServices (4): Localised Peer Review hasDiscussion ` forum1 definition (IkeWiki ontology) exemplifies post1: Issue (UnclearWh.Useful) example has_reply elaborates_on post2: Elaboration has_container agrees_with resolvesInto post3: Position proposes_ solution_for knowledge post4: Idea items (ProvideExample) (OMDoc ontology) supports on wiki pages decides post5: Evaluation agrees_with post6: Position post7: Decision supported_by argumentative physical structure structure (SIOC Core) discussion page (SIOC Arg.) Christoph Lange Bridging Domain Knowledge and its Formalisation – and Integrating Services on Top of That 2011-12-19 13
  18. 18. Introduction Formalisation Bridging the Gap: Representation & Services Conclusion & OutlookServices (4): Localised Peer Review Theorem …… Example hasDiscussion ` SIOC forum1 definition (IkeWiki ontology) argumentation Position subClassOf module (partly shown) agrees_with/ agrees_with/ exemplifies disagrees_with post1: Issue disagrees_with (UnclearWh.Useful) Domain-specific Math. Know- example has_reply elaborates_on argumentation supported_by ledge Item classes (partly shown) post2: Elaboration subClassOf has_container agrees_with OMDoc ontology Ontology resolvesInto Decision post3: Position Entity proposes_ solution_for knowledge decides decides post4: Idea items resolves_into (ProvideExample) (OMDoc ontology) supports on wiki pages decides Issue Idea post5: Evaluation proposes_solution_for subClassOf subClassOf agrees_with post6: Position Wrong Inappropriate Incomprehensible Provide Keep as Delete for Domain Example Bad Example post7: Decision supported_by argumentative physical structure structure (SIOC Core) discussion page (SIOC Arg.) Christoph Lange Bridging Domain Knowledge and its Formalisation – and Integrating Services on Top of That 2011-12-19 13
  19. 19. Introduction Formalisation Bridging the Gap: Representation & Services Conclusion & OutlookServices (5): Software Eng. Expert Finding The V-Model introduces relations between document fragments Formalise V-Model vocabulary: refines, implements, describesUse Mark up these secondary (non-logical) relations as metadata S EX supports flexibly extensible metadata in RDFa style T specify their semantics in vocabularies; once more in S EX T 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
  20. 20. Introduction Formalisation Bridging the Gap: Representation & Services Conclusion & OutlookServices (5): Software Eng. Expert Finding (2) # application-specific dimensions: PREFIX ver: <http://www.sams-projekt.de/ontologies/VersionManagement#> # versioning PREFIX 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
  21. 21. Introduction Formalisation Bridging the Gap: Representation & Services Conclusion & OutlookThe ‘Active Document’ Machinery Christoph Lange Bridging Domain Knowledge and its Formalisation – and Integrating Services on Top of That 2011-12-19 16
  22. 22. Introduction Formalisation Bridging the Gap: Representation & Services Conclusion & OutlookConnecting Mathematics↔Economics Data How to deal with derived values in datasets? Sussex St. Reading Andrews NDL Audio- Lists Resource subjects t4gm MySpace scrobbler Lists Moseley (DBTune) (DBTune) RAMEAU Folk NTU SH lobid GTAA Plymouth Resource Lists Organi- Reading Lists sations Music The Open ECS Magna- Brainz Music DB tune Library LCSH South- (Data Brainz LIBRIS ampton Tropes lobid Ulm Incubator) (zitgist) Man- EPrints Resources chester Surge Reading biz. Music RISKS Radio Lists The Open ECS data. John Brainz Discogs Library PSH Gem. UB South- gov.uk Peel (DBTune) FanHubz (Data In- (Talis) Norm- Mann- ampton (DB cubator) Jamendo datei heim RESEX Tune) Popula- Poké- DEPLOY Last.fm tion (En- pédia Artists Last.FM Linked RDF AKTing) research EUTC (DBTune) (rdfize) LCCN VIAF Book Wiki data.gov Produc- Pisa Eurécom P20 Mashup semantic NHS .uk tions classical web.org (EnAKTing) Pokedex (DB Mortality Tune) PBAC ECS (En- AKTing) BBC MARC (RKB Budapest Program Codes Explorer) Energy education OpenEI BBC List Semantic Lotico Revyu OAI (En- CO2 data.gov mes Music Crunch SW AKTing) (En- .uk Chronic- Linked Dog NSZL Base AKTing) ling Event- MDB RDF Food IRIT America Media Catalog ohloh BBC DBLP ACM IBM Good- BibBase Ord- Wildlife (RKB Openly Recht- win nance Finder Explorer) Local spraak. Family DBLP legislation Survey Tele- New VIVO UF .gov.uk nl graphis York flickr (L3S) New- VIVO castle Times URI wrappr OpenCal Indiana RAE2001 UK Post- Burner ais DBLP codes statistics (FU VIVO CiteSeer Roma data.gov LOIUS Taxon iServe Berlin) IEEE .uk Cornell Concept Geo World data ESD Fact- OS dcs Names book dotAC stan- reference Project Linked Data NASA (FUB) Freebase dards data.gov Guten- .uk for Intervals (Data GESIS Course- transport DBpedia berg STW ePrints CORDIS Incu- ware data.gov bator) (FUB) Fishes ERA UN/ .uk of Texas Geo LOCODE Uberblic Euro- Species The stat dbpedia TCM SIDER Pub KISTI (FUB) lite Gene STITCH Chem JISC London Geo KEGG DIT LAAS Gazette TWC LOGD Linked Daily OBO Drug Eurostat Data UMBEL lingvoj Med (es) Disea- YAGO Medi some Care ChEBI KEGG NSF Linked KEGG KEGG Linked Drug Cpd GovTrack rdfabout Glycan Sensor Data CT Bank Pathway US SEC Open Reactome (Kno.e.sis) riese Uni Cyc Lexvo Path- totl.net way Pfam PDB Semantic HGNC XBRL WordNet KEGG KEGG Linked Taxo- CAS Reaction Twarql (VUA) UniProt Enzyme rdfabout EUNIS Open nomy US Census Numbers PRO- ProDom SITE Chem2 UniRef Bio2RDF Climbing WordNet SGD Homolo Linked (W3C) Affy- Gene Cornetto GeoData metrix PubMed Gene UniParc Ontology GeneID Airports Product DB UniSTS MGI Gen Bank OMIM InterPro As of September 2010 Christoph Lange Bridging Domain Knowledge and its Formalisation – and Integrating Services on Top of That 2011-12-19 17
  23. 23. Introduction Formalisation Bridging the Gap: Representation & Services Conclusion & OutlookConnecting Mathematics↔Economics Data How to deal with derived values in datasets?:pop_sealand2010 :pop_kugelmugel2010 scv:dimension :PrincipalityOfSealand ; scv:dimension :KugelmugelRepublic ; scv:dimension :Year2010 ; scv:dimension :Year2010 ; scv:dimension :People18to65years ; scv:dimension :People18to65years ; rdf:value 7 . rdf:value 11 .:unemployed_sealand2010 :unemployed_kugelmugel2010 scv:dimension :PrincipalityOfSealand ; scv:dimension :KugelmugelRepublic ; scv:dimension :Year2010 ; scv:dimension :Year2010 ; scv:dimension :People18to65years ; scv:dimension :People18to65years ; rdf:value 2 . rdf:value 1 .:unemp_rate_sealand2010 :unemp_rate_kugelmugel2010 scv:dimension :PrincipalityOfSealand ; scv:dimension :KugelmugelRepublic ; scv:dimension :Year2010 ; scv:dimension :Year2010 ; rdf:value 0.286 . rdf:value 0.091 . How to validate the derived values? How to compute them for new data points? unemp. rate = unemployed ⇒ link to ‘division’ population Can also link to custom/non-standard functions Christoph Lange Bridging Domain Knowledge and its Formalisation – and Integrating Services on Top of That 2011-12-19 18
  24. 24. Introduction Formalisation Bridging the Gap: Representation & Services Conclusion & OutlookConclusion Semiformal knowledge representation . . . makes formalisation comprehensible to domain experts allows for linking mathematical formalisations to arbitrary application 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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