1. Business Process Modeling in the tOWL Language
Viorel Milea, Flavius Frasincar, Uzay Kaymak
Erasmus University Rotterdam
the Netherlands

2. Outline Time and the Semantic Web The tOWL Language
Layered Approach
Concrete Domains
Fluents
Leveraged Buyouts in tOWL
11/22/2018

3. Time and the Semantic Web
For the current purpose, a clear definition of time is required.
We distinguish between:
Temporal ‘infrastructure’ (timepoints & intervals);
Change.
Providing support for the representation of these aspects of time in a Semantic Web context is the general goal of the TOWL language.
11/22/2018

4. Time and the Semantic Web
Temporal Infrastructure
Describes the quantitative aspect of time
Provides a basic texture for complex temporal representations
Common example: intervals + Allen’s relations
Very concrete
Requirements:
Rely on standards (we are extending a standard!)
Represent timepoints and intervals
Represent temporal dependencies
Level of granularity

5. Time and the Semantic Web
Change in general
Most entities change some of their traits in time
Think of:
Changing height of a person, from child- to adulthood
Changes in the price of a company’s share
Changes in variables (fundamental & technical indicators, etc.)
Representing change = enabling context-awareness
Context-awareness  better decision-making (though not invariably)
Think of reasoning over several versions of an OWL-DL ontology (snapshots). In the same time!

6. Time and the Semantic Web
Change as complex process
Many phenomena can be described as processes
Think of:
Obtaining a driver’s license
Drug trials
Leveraged Buy Outs
A process is described by its states (phases)
Each process has certain ‘transition rules’ (axioms)
A proper representation of processes and their associated axioms enables automated reasoning

7. Time and the Semantic Web
An Example of a Complex Process: LBOs

8. Summary
Until now...
Time is a relevant dimension of knowledge on the Semantic Web
Two state-of-the-art Semantic Web languages have currently been standardized: RDF & OWL
Although a (somewhat limited) temporal extension exists for RDF, none has been yet devised for OWL
We seek to:
Extend OWL-DL into a temporal dimension;
Enable the representation of quantitative time, as well as change.

9. The tOWL Language
Layered approach for the design of the TOWL language;
The extensions are built on top of the OWL-DL layer;
Concrete domains enable a meaningful time representation (intervals & Allen’s interval relations);
The timeslices & fluents approach employs the time representation for additional semantics.

10. The tOWL Language The OWL-DL Layer Based on Description Logics (DL)
OWL-DL offers the means to:
formalize a domain by defining classes and properties of those classes,
define individuals and assert properties about them, and
reason about these classes and individuals to the degree permitted by the formal semantics of the OWL language.
Tools & Reasoners: Protégé, Pellet, Racer, FaCT++

11. The tOWL Language The Concrete Domains Layer
OWL-DL has only limited support for concrete domains
We seek to:
Enable feature chains
Enable binary predicates on the concrete domain
Enable complex temporal restrictions based on the concrete domain
Temporal concrete domain = constraint system
Intervals and Allen’s 13 interval relations

12. The tOWL Language The Time Representation Layer
Constraint system based on intervals and Allen’s 13 interval relations
We define intervals in terms of their endpoints (start & end)
The endpoints are defined by relying on XML Schema dateTime
For example, December 1st 2008, at time 21:12:00, is represented as: T21:12:00
Besides providing a basic temporal ‘infrastructure’, this layer also enhances the semantics of the next layer

13. The tOWL Language
Example: In an LBO process, the early stage (may) be followed by the abort stage; in case this happens, the two stages follow each other immediately.

14. The tOWL Language The TimeSlices & Fluents Layer
Represent temporal aspects of entities other than timespan
This layer regards change and state transitions
TimeSlice = temporal part of an individual
Fluent = indicates the changing attribute value (in essence a special kind of property)
Up to some point, this layer can be seen as a vocabulary extension; but, semantics depend on underlying layers!!

15. The tOWL Language The TimeSlices & Fluents Layer
Create static individuals
Create timeslices for each individual
Associate timeslices with the static individual they represent
Associate a time interval with each timeslice (!)
Connect the timeslices with a fluent
Fluents only relate timeslices that hold over the same interval

16. The tOWL Language The TimeSlices/Fluents Layer – an example
Classes of timeslices of stages of an LBO process
Company timeslice

17. LBOs in tOWL – TBox
At TBox level we represent conceptual information that is known about LBO processes in general. In this context, two types of companies that take part in an LBO are known:HedgeFund and Target:
Class(Company)
Class(HedgeFund partial Company)
Class(Target partial Company)
The different stages of an LBO process are represented as subclasses of the Stage class, such as for example in the case of the Bidding stage. In tOWL abstract syntax, this is represented as:
Class(Bidding partial Stage)

18. LBOs in tOWL – TBox All stages are pairwise disjoint:
DisjointClasses(EarlyStage; DueDiligence; Bidding; RaiseBid; Acquisition; Abort; Extension)
We define the class of all timeslices of an LBO Process as follows:
Class(LBOProcess_TS complete restriction(timeSliceOf(
allValuesFrom LBOProcess)))

19. LBOs in tOWL – TBox
In similar fashion, we define, for each stage, the class of all timeslices of that stage. For the EarlyStage this achieved as follows:
Class(EarlyStage_TS complete
restriction(timeSliceOf(
allValuesFrom EarlyStage)))
For each stage, we define a functional property that links a particular LBO process timeslice to the timeslice of the stage belonging to it:
ObjectProperty(earlyStage
domain(LBOProcess)
range(EarlyStage))
Func(earlyStage)

20. LBOs in tOWL – TBox
We define the inStage fluent, that for each timeslice of a company points to the stage in which the company finds itself, and the stageImpact fluent that indicates the impacts the different stages have on companies.
FluentObjectProperty(inStage
domain(restriction(timeSliceOf(someValuesFrom Company)))
range(restriction(timeSliceOf(someValuesFrom Stage)))
FluentDatatypeProperty(stageImpact
range(

21. LBOs in tOWL – TBox
Timeslices of an LBO process are defined by the sequence of stages that a company may follow in this process:
Class(LBOProcess_TS complete
restriction(dataSomeValuesFrom(
ConcreteFeatureChain(earlyStage time),
time, starts))))

22. LBOs in tOWL – TBox
Finally, we define at TBox level the definitions of the impact that each stage has on the company involved.
Class(Impact8 partial
restriction(stageImpact someValuesFrom(8)))
Class(HedgeFund_to_EarlyStage partial restriction(inStage(someValuesFrom(EarlyStage_TS)))
restriction(timeSliceOf(someValuesFrom(HedgeFund))))
SubClassOf(HedgeFund_to_EarlyStage Impact8)
Class(Target_to_EarlyStage partial
restriction(inStage(someValuesFrom(EarlyStage_TS)))
restriction(timeSliceOf(someValuesFrom(Target))))
SubClassOf(Target_to_EarlyStage Impact8)

23. LBOs in tOWL – ABox
At ABox level we represent particular information that is known about the specific LBO process we seek to represent.
We start off by instantiating the relevant individuals that are known to play a role in the LBO process. First, we represent the participating companies.
Individual(iAllianceBoots type(Target))
Individual(iKKR type(HedgeFund))
Individual(iTerraFirma type(HedgeFund))

24. LBOs in tOWL – ABox LBOProcess(iLBOProcess_1
For each of the hedgefunds involved, we instantiate a process and define its stages, such as in the case of the TerraFirma:
LBOProcess(iLBOProcess_1
value(earlyStage iEarlyStage1)
value(dueDiligence iDueDiligence1)
value(bidding iBidding1)
value(abort iAbort1))
Individual(iLBOProcess_TS1 type(LBOProcess_TS)
value(timeSliceOf iLBOProcess_1))

25. LBOs in tOWL – ABox Buyout firm Terra Firma mulls Boots bid
Sun Mar 25, :42am EDT
This news message signals the beginning of the LBO, mentioning that Terra Firma is considering a bid for Alliance Boots (EarlyStage)
For representing the information contained in the news message we create a timeslice for the hedgefund and the target, respectively, a time interval associated to the stage, and employ the inStage fluent to associate the companies to the stage.
Individual(t1 type(Interval))
Individual(iEarlyStage1 type(EarlyStage_TS))
Individual(iEarlyStage1_TS1 type(TimeSlice)
value(timeSliceOf iEarlyStage1)
value(time t1))
Individual(iAllianceBoots_TS1 type(TimeSlice)
value(timeSliceOf iAllianceBoots)
value(time t1)
value(inStage iEarlyStage1_TS1))
Individual(iTerraFirma_TS1 type(TimeSlice)
value(timeSliceOf iTerraFirma)

26. Conclusions
tOWL is a temporal web ontology language that, building upon OWL-DL, enables the representation of complex temporal aspects on the Semantic Web
The language also lends itself to the area of Business Process Modeling, and allows the representation of complex processes that involve a temporal aspect, such as LBOs.