Linking Big Data to Rich Process Descriptions

1. Introduction Motivation Math. Semantics Ontology Integration & Interoperability Software Verification Conclusion Linking Big Data to Rich Process Descriptions Christoph Lange1 1Project ‘‘Formal Mathematical Reasoning in Economics’’, School of Computer Science, University of Birmingham, UK http://cs.bham.ac.uk/~langec 2013-09-19 Lange Linking Big Data to Rich Process Descriptions 2013-09-19 1

2. Introduction Motivation Math. Semantics Ontology Integration & Interoperability Software Verification Conclusion “Hello, World!” 2011 Ph.D. (Jacobs Univ. Bremen, with Michael Kohlhase): Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration [Lan11] 2011–12 Postdoc (Univ. Bremen, with John Bateman, Till Mossakowski): Ontology Integration and Interoperability (OntoIOp) ↝ Distributed Ontology Language (DOL) OMG standard [13] 2012–13 Postdoc (Univ. Birmingham, with Manfred Kerber, Colin Rowat): Formal Mathematical Reasoning in Economics (ForMaRE) [KLR] Lange Linking Big Data to Rich Process Descriptions 2013-09-19 2

3. Introduction Motivation Math. Semantics Ontology Integration & Interoperability Software Verification Conclusion Linking Big Data to Rich Process Descriptions Linked data is one key to coping with big data. Big data are created or consumed by technical/business processes. Formal process descriptions are more complex than data. Why integrate process descriptions and data? How to integrate them? Lange Linking Big Data to Rich Process Descriptions 2013-09-19 3

4. Introduction Motivation Math. Semantics Ontology Integration & Interoperability Software Verification Conclusion Linked Data as a Key to Big Data Linked (Open) Data enables . . . decentralised, collaborative management of big datasets, low-overhead information retrieval, and scalable reasoning. Lange Linking Big Data to Rich Process Descriptions 2013-09-19 4

5. Introduction Motivation Math. Semantics Ontology Integration & Interoperability Software Verification Conclusion Sources of Big Data Big data = )︀⌉︀⌉︀⌉︀ ⌋︀ ⌉︀⌉︀⌉︀]︀ high volume, high velocity, high variety [︀⌉︀⌉︀⌉︀ ⌈︀ ⌉︀⌉︀⌉︀⌊︀ information [BL12] Where does it come from? Science 150 million sensors in the Large Hadron Collider Trade High-frequency trading (HFT) accounts for 50% of US equity trading. Web 100 hours of video uploaded to YouTube every minute Lange Linking Big Data to Rich Process Descriptions 2013-09-19 5

6. Introduction Motivation Math. Semantics Ontology Integration & Interoperability Software Verification Conclusion Big Data Result from Processes Science sensor measurements determined by experimental setup experiments inform hypotheses Trade trading strategies influenced by demand and supply Web YouTube does not just store uploads, but notifies subscribers, Facebook friends, Twitter followers. Lange Linking Big Data to Rich Process Descriptions 2013-09-19 6

7. Introduction Motivation Math. Semantics Ontology Integration & Interoperability Software Verification Conclusion Formal Process Descriptions Why describe processes formally? to check their compliance with quality standards to verify the software that controls them Science workflows modelled using: logic programming, computational tree logic, linear temporal logic. Trade Knight Capital HFT software repeatedly sold shares below purchase price, lost $440 million within 1 hour – could formal verification have helped? Web social networks modelled using epistemic modal logic, probabilistic soft logic Lange Linking Big Data to Rich Process Descriptions 2013-09-19 7

8. Introduction Motivation Math. Semantics Ontology Integration & Interoperability Software Verification Conclusion Linking Process Descriptions and Data Knowledge Mgmt. Under what experimental setup were these measurements taken? Reasoning Given the current variance of measurements, would it help to use a sensor with different specifications? Which trading strategy responds best to the current offers? Inform. Retrieval Which of my friends are actually interested in my latest video upload? Where can I buy the cheapest parts to feed into my manufacturing process? Lange Linking Big Data to Rich Process Descriptions 2013-09-19 8

9. Introduction Motivation Math. Semantics Ontology Integration & Interoperability Software Verification Conclusion Logic of Linked Open Data? RDF data and RDFS vocabularies do not suffice for modelling processes – so . . . ? Lange Linking Big Data to Rich Process Descriptions 2013-09-19 9

10. Introduction Motivation Math. Semantics Ontology Integration & Interoperability Software Verification Conclusion Logic of Linked Open Data? RDF data and RDFS vocabularies do not suffice for modelling processes – so . . . ? ☀ make your stuff available on the Web (whatever format) under an open license ☀☀ make it available as structured data (e.g., Excel instead of image scan of a table) ☀☀☀ use non-proprietary formats (e.g., CSV instead of Excel) ☀☀☀☀ use URIs to denote things, so that people can point at your stuff ☀☀☀☀☀ link your data to other data to provide context [12] Who says it needs to be RDF? Lange Linking Big Data to Rich Process Descriptions 2013-09-19 9

11. Introduction Motivation Math. Semantics Ontology Integration & Interoperability Software Verification Conclusion Think URIs, not RDF! How to achieve an integration of . . . ? rich process descriptions (expressive logics) big data (scalability before expressivity) Ad hoc extensions of RDF exist (e.g. for CSPs in product range specification at Renault [BSP11]) My approach systematically base expressive logics beyond RDF and OWL on the URI foundation of LOD thus enable large-scale data/knowledge integration Lange Linking Big Data to Rich Process Descriptions 2013-09-19 10

12. Introduction Motivation Math. Semantics Ontology Integration & Interoperability Software Verification Conclusion Derived Values in Statistical Datasets Comparing unemployment rates in micronations: Principality of Sealand :pop_sealand2012 a qb:Observation ; sdmx-dim:refArea :PrincipalityOfSealand ; sdmx-dim:refPeriod :Year2012 ; :refAgeGroup :People18to65years ; sdmx-attr:unitMeasure :Count ; sdmx-meas:obsValue 7 . :unemployed_sealand2012 a qb:Observation ; sdmx-dim:refArea :PrincipalityOfSealand ; sdmx-dim:refPeriod :Year2012 ; :refAgeGroup :People18to65years ; sdmx-attr:unitMeasure :Count ; sdmx-meas:obsValue 2 . :unemp_rate_sealand2012 a qb:Observation ; sdmx-dim:refArea :PrincipalityOfSealand ; sdmx-dim:refPeriod :Year2012 ; sdmx-attr:unitMeasure :Ratio ; sdmx-meas:obsValue 0.286 . Lange Linking Big Data to Rich Process Descriptions 2013-09-19 11

13. Introduction Motivation Math. Semantics Ontology Integration & Interoperability Software Verification Conclusion Derived Values in Statistical Datasets Comparing unemployment rates in micronations: Principality of Sealand :pop_sealand2012 a qb:Observation ; sdmx-dim:refArea :PrincipalityOfSealand ; sdmx-dim:refPeriod :Year2012 ; :refAgeGroup :People18to65years ; sdmx-attr:unitMeasure :Count ; sdmx-meas:obsValue 7 . :unemployed_sealand2012 a qb:Observation ; sdmx-dim:refArea :PrincipalityOfSealand ; sdmx-dim:refPeriod :Year2012 ; :refAgeGroup :People18to65years ; sdmx-attr:unitMeasure :Count ; sdmx-meas:obsValue 2 . :unemp_rate_sealand2012 a qb:Observation ; sdmx-dim:refArea :PrincipalityOfSealand ; sdmx-dim:refPeriod :Year2012 ; sdmx-attr:unitMeasure :Ratio ; sdmx-meas:obsValue 0.286 . Republic of Kugelmugel :pop_kugelmugel2012 a qb:Observation ; sdmx-dim:refArea :KugelmugelRepublic ; sdmx-dim:refPeriod :Year2012 ; :refAgeGroup :People18to65years ; sdmx-attr:unitMeasure :Count ; sdmx-meas:obsValue 11 . :unemployed_kugelmugel2012 a qb:Observation ; sdmx-dim:refArea :KugelmugelRepublic ; sdmx-dim:refPeriod :Year2012 ; :refAgeGroup :People18to65years ; sdmx-attr:unitMeasure :Count ; sdmx-meas:obsValue 1 . :unemp_rate_kugelmugel2012 a qb:Observation ; sdmx-dim:refArea :KugelmugelRepublic ; sdmx-dim:refPeriod :Year2012 ; sdmx-attr:unitMeasure :Ratio ; sdmx-meas:obsValue 0.091 . Lange Linking Big Data to Rich Process Descriptions 2013-09-19 11

14. Introduction Motivation Math. Semantics Ontology Integration & Interoperability Software Verification Conclusion Derived Values in Statistical Datasets II :unemp_rate_sealand2012 a qb:Observation ; sdmx-dim:refArea :PrincipalityOfSealand ; sdmx-dim:refPeriod :Year2012 ; sdmx-attr:unitMeasure :Ratio ; sdmx-meas:obsValue 0.286 . :unemp_rate_kugelmugel2012 a qb:Observation ; sdmx-dim:refArea :KugelmugelRepublic ; sdmx-dim:refPeriod :Year2012 ; sdmx-attr:unitMeasure :Ratio ; sdmx-meas:obsValue 0.091 . How to validate the derived values? How to compute them for new data points? How to collect data points and their dependencies? Make the mathematical semantics explicit! unemp. rate = unemployed population ⇒ link to “division” (→ OpenMath Content Dictionaries) [Vra+10; Lan10] OpenMath CDs are LOD: decentrally extensible Future work: OpenMath SPARQL entailment regime Lange Linking Big Data to Rich Process Descriptions 2013-09-19 12

15. Introduction Motivation Math. Semantics Ontology Integration & Interoperability Software Verification Conclusion The Big Picture of Interoperability Ontology Ontology Language/Logic Knowledge Software Agents written in Concepts/Data/Individuals represented in terms of Service Description Service Descr. Language written in Service satisfies processes refers to Target (Device) accesses Service-Oriented Architecture Smart Environment Target Description conforms to Device Target Descr. Language written in Ontology Ontology Language/Logic Concepts/Data/Individuals Service Description Service Descr. Language Service Target (Device) Target Description Device Target Descr. Language Knowledge Infrastructure mappingsfor interoperability Hardware Data Models Metamodels For now we focus on the “content”/ “knowledge” column Lange Linking Big Data to Rich Process Descriptions 2013-09-19 13

16. Introduction Motivation Math. Semantics Ontology Integration & Interoperability Software Verification Conclusion Towards Device Interoperability Ambient Assisted Living Scenario Clara, a vegetarian, 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. Afterwards she goes to bed. Lange Linking Big Data to Rich Process Descriptions 2013-09-19 14

17. Introduction Motivation Math. Semantics Ontology Integration & Interoperability Software Verification Conclusion Towards Device Interoperability Ambient Assisted Living Scenario Clara, a vegetarian, 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. Afterwards she goes to bed. Existing ontologies (e.g. OpenAAL) cover core of that: Lange Linking Big Data to Rich Process Descriptions 2013-09-19 14

18. Introduction Motivation Math. Semantics Ontology Integration & Interoperability Software Verification Conclusion Towards Device Interoperability Ambient Assisted Living Scenario Clara, a vegetarian, 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. Afterwards she goes to bed. Existing ontologies (e.g. OpenAAL) cover core of that: . . . but not all required concepts (e.g. food ingredients ⇒ need other ontologies/modules; tap into the Web of (Product, Geo) Data) Lange Linking Big Data to Rich Process Descriptions 2013-09-19 14

19. Introduction Motivation Math. Semantics Ontology Integration & Interoperability Software Verification Conclusion Towards Device Interoperability Ambient Assisted Living Scenario Clara, a vegetarian, 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. Afterwards she goes to bed. Existing ontologies (e.g. OpenAAL) cover core of that: . . . but not all required concepts (e.g. food ingredients ⇒ need other ontologies/modules; tap into the Web of (Product, Geo) Data) . . . not necessarily at the required level of complexity (e.g. space/time ⇒ need other logics) Lange Linking Big Data to Rich Process Descriptions 2013-09-19 14

20. Introduction Motivation Math. Semantics Ontology Integration & Interoperability Software Verification Conclusion What do Devices Need to Know? Some of the devices involved: kitchen light switch freezer (aware of its contents) wheelchair (with navigation) Services and Devices need to understand different aspects of the world at different levels of complexity. Quote from the “Hitchhiker” “Suddenly [the door] slid open. ‘Thank you,’ it said, ‘for making a simple door very happy.’” Lange Linking Big Data to Rich Process Descriptions 2013-09-19 15

21. Introduction Motivation Math. Semantics Ontology Integration & Interoperability Software Verification Conclusion Different Devices and their Knowledge Light Switch “switched on if and only if someone is in and it’s dark outside” Freezer “all toppings of a vegetarian pizza are vegetarian” Wheelchair “two areas are either the same, or intersect, or border, or separate, or one is part of the other” Lange Linking Big Data to Rich Process Descriptions 2013-09-19 16

22. Introduction Motivation Math. Semantics Ontology Integration & Interoperability Software Verification Conclusion Different Devices = Different Logics Light Switch: propositional logic “switched on if and only if someone is in and it’s dark outside” light_on ≡ person_in_room ∧ dark_outside Freezer: description logic (Pizza ontology) “all toppings of a vegetarian pizza are vegetarian” VegetarianPizza ≡ Pizza ⊓ ∀hasTopping.Vegetarian Wheelchair: first order logic (RCC-style spatial calculus) “two areas are either the same, or intersect, or border, or separate, 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) Lange Linking Big Data to Rich Process Descriptions 2013-09-19 17

23. Introduction Motivation Math. Semantics Ontology Integration & Interoperability Software Verification Conclusion The OntoIOp Initiative OntoIOp (Ontology Integration and Interoperability) initiative started in 2011 with ISO now continued with OMG Request for Proposals to be issued this autumn proposals due Dec. 2014 50 experts participate, ∼ 15 have contributed Relevant communities represented: different ontology languages and logics conceptual and theoretical foundations technical foundations applications: manufacturing, business rules, model-driven software engineering Lange Linking Big Data to Rich Process Descriptions 2013-09-19 18

24. Introduction Motivation Math. Semantics Ontology Integration & Interoperability Software Verification Conclusion Distributed Ontology Language (DOL) “distributed” means . . . logically heterogeneous modular interlinked: interpretations, equivalences, alignments decentrally maintained (using URIs) DOL: a logic-agnostic meta-language for ontologies, modeling and specification [MKL12; Lan+12] supports ontologies in several relevant languages framework can be decentrally extended with new languages, logics, serializations, translations Tool support: Hets: syntax check, theorem proving, model finding Ontohub: web-based repository engine http://ontoiop.org Lange Linking Big Data to Rich Process Descriptions 2013-09-19 19

25. Introduction Motivation Math. Semantics Ontology Integration & Interoperability Software Verification Conclusion The OntoIOp Registry (Subset) Common Logic SROIQDL-LiteR CLIF XCL Manchester Syntax OWL 2 XML RDF / XML Turtle OWL 2 DL RDF RDFS Common Logic RDFS RDF OWL 2 QL OWL 2 RL OWL 2 EL DL-RL EL ++ Serializations Ontology Languages Logics supports serialization sublanguage of induced translation exact logical expressivity translatable to sublogic of Lange Linking Big Data to Rich Process Descriptions 2013-09-19 20

26. Introduction Motivation Math. Semantics Ontology Integration & Interoperability Software Verification Conclusion DOL AAL Example %prefix( : <http://dfki.de/example/ouraal/> openaal: <http://openaal.org/SAM/Ontology#> productdb: <http://productdb.org/ean/> pizza: <http://www.co-ode.org/ontologies/pizza/pizza.owl#> lang: <http://purl.net/dol/languages/> log: <http://purl.net/dol/logics/> trans: <http://purl.net/dol/translations/> ser: <http://purl.net/dol/serializations/> )% distributed-ontology AAL language lang:OWL2/DL ontology OpenAALAdapted = openaal: %(import_of_openaal)% with openaal:AP ↦ AssistedPerson then %(some_extensions)% syntax ser:OWL2/Manchester { Class: LightSwitch SubClassOf: openaal:Device Class: Freezer SubClassOf: openaal:Device %(freezer_sub_device)% Class: RoomWith1Person EquivalentTo: openaal:Room that inverse openaal:is-in-room min 1 AssistedPerson Class: RoomWithAllLightsOn EquivalentTo: openaal:Room that inverse openaal:is-in-room only (not (LightSwitch that openaal:has-power-state value openaal:Off)) } then logic log:Propositional syntax ser:Prop/CASLLike : { props light_on, person_in_room, dark_outside . light_on ⇔ person_in_room ∧ dark_outside } with translation trans:PropositionalToSROIQ person_in_room ↦ RoomWith1Person, light_on ↦ RoomWithAllLightsOn Lange Linking Big Data to Rich Process Descriptions 2013-09-19 21

32. Introduction Motivation Math. Semantics Ontology Integration & Interoperability Software Verification Conclusion DOL AAL Example II then language lang:OWL2/DL : pizza: then logic log:CommonLogic syntax ser:CommonLogic/CLIF : { (forall (area1 area2) (or (equal area1 area2) (overlapping area1 area2) %% skipping some cases ... %% (define mutual disjointness of these predicates) (forall (area1 area2) (if (or (equal area1 area2) %% ... (exists (door) (and (openaal:Door door) (openaal:is-in-room door area1) (openaal:is-in-room door area2)))) (openaal:is-connected-to-room area1 area2))) } ontology ConcreteScenario = OpenAALAdapted hide along trans:RDFtoSROIQ and productdb: then language lang:RDF syntax ser:RDF/Turtle : { productdb:4001724819806 pizza:hasTopping [ a pizza:TomatoTopping ], [ a pizza:MozzarellaTopping ] . } with translation trans:RDFtoOWL2DL then { pizza: then syntax ser:OWL2/Manchester : { Individual: productdb:4001724819806 Types: pizza:hasTopping exactly 2 } Lange Linking Big Data to Rich Process Descriptions 2013-09-19 22

38. Introduction Motivation Math. Semantics Ontology Integration & Interoperability Software Verification Conclusion Importance of Auctions Auctions: a mechanism to distribute resources Applications eBay, mobile spectrum, internet domains Significance $268.5 billion in 2008 in the US Given a set of bids on goods (proxying valuations) Goals give goods to those valuing them most determine prices maximise revenue attract participants incentive compatibility (no need for tactic over-/underbidding) Auctions are designed; properties are tested and proved. Lange Linking Big Data to Rich Process Descriptions 2013-09-19 23

39. Introduction Motivation Math. Semantics Ontology Integration & Interoperability Software Verification Conclusion Generating Verified Auction Software 2. Theorems 1. Definitions formal specification (written by Isabelle user, needs review by auction designer) Code (executable Scala) 3. Proof (4. checked by Isabelle) state soundness and other properties of known to implement (by proof and by trusting code generator) 5. code generation (Isabelle) proves Lange Linking Big Data to Rich Process Descriptions 2013-09-19 24

40. Introduction Motivation Math. Semantics Ontology Integration & Interoperability Software Verification Conclusion Combinatorial Auctions [CSS06] Lange Linking Big Data to Rich Process Descriptions 2013-09-19 25

41. Introduction Motivation Math. Semantics Ontology Integration & Interoperability Software Verification Conclusion Combinatorial Vickrey Auction Bids on any subset of the set of available goods X. Winning allocation: X∗ ∈ argmax X1,...,XN N ∑ n=1 bn (Xn) s.t. N ⋃ n=1 Xn ⊆ X0, n ≠ n′ iff Xn∩Xn′ = ∅ Prices: pn ≡ αn − ∑m≠n bm (X∗ m) where αn ≡ max Xm m=1,...,N,m≠n {∑ m≠n bm (Xm)⋁︀ ⋃ m≠n Xm ⊆ X0 (︀ Bidder n pays the maximum sum of bids if the auction had been run without n (= αn), minus the winning bids on the items n did not get [AM06; Cam+13]. Lange Linking Big Data to Rich Process Descriptions 2013-09-19 26

42. Introduction Motivation Math. Semantics Ontology Integration & Interoperability Software Verification Conclusion Generating Verified Software: Comb. Vickrey Auction [Cam+13] paper-like formalisation X∗ ∈ argmax∑... {R ⊆ P(N)×N ∃P ∈ parts(G). Dom(R) ⊆ P ∧...} {P ⋃P = A ∧∀x ∈ P....} depends on depends on executable formalisation argmax (x # xs) f = if f x > f (hd (argmax xs f)) then ... alloc G N = concat [ [ R . R ← inj_fun P (list N) ] . P ← parts (list G) ] parts (x # xs) = ⋃ inject x ‘ (parts xs) depends on depends on ! ≡ winner determination ! ≡ allocations ! ≡ set partitions papersource(auctiondesigner) verifiedcode(auctionsoftware) human formalisation code generation http://formare.github.io/auctions/ Lange Linking Big Data to Rich Process Descriptions 2013-09-19 27

43. Introduction Motivation Math. Semantics Ontology Integration & Interoperability Software Verification Conclusion Conclusion Formal descriptions help to understand, verify and improve processes in general. Process executions create or consume data. Integrating process descriptions and data improves knowledge management reasoning information retrieval A wider view on linked data (beyond RDF) helps to integrate . . . process descriptions (often ≥ first-order logic; expressive) big data created or consumed by processes (often RDF; scalable) Lange Linking Big Data to Rich Process Descriptions 2013-09-19 28

44. References References I 5 star Open Data. Apr. 3, 2012. url: http://5stardata.info/ (visited on 2013-09-18). OntoIOp (Ontology Integration and Interoperability) Standard Development Initiative. 2013. url: http://ontoiop.org (visited on 2013-09-18). L. M. Ausubel and P. Milgrom. “The Lovely but Lonely Vickrey Auction”. In: Combinatorial auctions. Ed. by P. Cramton, Y. Shoham, and R. Steinberg. MIT Press, 2006. Chap. 1, pp. 17–40. M. A. Beyer and D. Laney. The Importance of ‘Big Data’: A Definition. June 21, 2012. url: http://www.gartner.com/resId=2057415. Lange Linking Big Data to Rich Process Descriptions 2013-09-19 29

45. References References II F. Badra, F.-P. Servant, and A. Passant. “A Semantic Web Representation of a Product Range Specification based on Constraint Satisfaction Problem in the Automotive Industry”. In: Proceedings of the 1st Workshop on Ontology and Semantic Web for Manufacturing, Extended Semantic Web Conference. (Hersonissos, Crete, Greece, May 29, 2011). Ed. by A. García Castro, C. Toro, L. Ramos, and L. Schröder. CEUR Workshop Proceedings 748. Aachen, 2011, pp. 37–50. url: http://ceur-ws.org/Vol-748/. M. B. Caminati, M. Kerber, C. Lange, and C. Rowat. Proving soundness of combinatorial Vickrey auctions and generating verified executable code. 2013. arXiv: 1308.1779 [cs.GT]. Lange Linking Big Data to Rich Process Descriptions 2013-09-19 30

46. References References III P. Cramton, Y. Shoham, and R. Steinberg, eds. Combinatorial auctions. MIT Press, 2006. M. Kerber, C. Lange, and C. Rowat. ForMaRE. Formal Mathematical Reasoning in Economics. url: http:// cs.bham.ac.uk/research/projects/formare/ (visited on 2013-02-10). Lange Linking Big Data to Rich Process Descriptions 2013-09-19 31

47. References References IV C. Lange, T. Mossakowski, O. Kutz, C. Galinski, M. Grüninger, and D. Couto Vale. “The Distributed Ontology Language (DOL): Use Cases, Syntax, and Extensibility”. In: Terminology and Knowledge Engineering Conference (TKE). (Madrid, Spain, June 20–21, 2012). Ed. by G. Aguado de Cea, M. C. Suárez-Figueroa, R. García-Castro, and E. Montiel-Ponsoda. 2012, pp. 33–48. arXiv: 1208.0293 [cs.AI]. url: http://oeg- lia3.dia.fi.upm.es/tke2012/proceedings. Lange Linking Big Data to Rich Process Descriptions 2013-09-19 32

48. References References V C. Lange. “Towards OpenMath Content Dictionaries as Linked Data”. In: 23rd OpenMath Workshop. Ed. by M. Kohlhase and C. Lange. July 2010. arXiv: 1006.4057v1 [cs.DL]. url: http://cicm2010.cnam.fr/om/. C. Lange. “Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration”. PhD thesis. Jacobs University Bremen, 2011. Lange Linking Big Data to Rich Process Descriptions 2013-09-19 33

49. References References VI T. Mossakowski, O. Kutz, and C. Lange. “Three Semantics for the Core of the Distributed Ontology Language”. In: Formal Ontology in Information Systems. 7th International Conference (FOIS 2012). (Graz, Austria, July 24–27, 2012). Ed. by M. Donnelly and G. Guizzardi. Frontiers in Artificial Intelligence and Applications 239. (The paper has won the best paper award. Also published at IJCAI 2013 track on Best Papers in Sister Conferences.) Amsterdam: IOS Press, 2012, pp. 337–352. url: http://interop.cim3.net/file/pub/ OntoIOp/Publications/FOIS_2012/paper.pdf. Lange Linking Big Data to Rich Process Descriptions 2013-09-19 34

50. References References VII D. Vrandečić, C. Lange, M. Hausenblas, J. Bao, and L. Ding. “Semantics of Governmental Statistics Data”. In: Proceedings of WebSci’10: Extending the Frontiers of Society On-Line. Web Science Trust, 2010. url: http://journal.webscience.org/400/. Lange Linking Big Data to Rich Process Descriptions 2013-09-19 35

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