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

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

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

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

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!

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

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

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.

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.

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++

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

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: 2008-12-01T21:12:00 Besides providing a basic temporal ‘infrastructure’, this layer also enhances the semantics of the next layer

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.

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!!

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

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

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)

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)))

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)

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(http://www.w3.org/2001/XMLSchema#int))

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))))

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)

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))

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))

LBOs in tOWL – ABox Buyout firm Terra Firma mulls Boots bid Sun Mar 25, 2007 8:42am 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)

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.