Modellierungstechniken II Univ. Prof. Wilfried Gossmann Research Group Knowledge Engineering University of Vienna Business Intelligence, Wintersemester 2012/2013

2  Wilfried Grossmann, WS2012/13, University of Vienna – Models Contents The following tools are the most important structures in Business process modelling: 4. Logical Models 5. Graphs 6. Functions 7. Probability and Statistics

3  Wilfried Grossmann, WS2012/13, University of Vienna – Models 4. Logical Models – Propositional Calculus  Syntax r A set of atomic propositions r Operators for building formulas with atomic propositions  Semantic defined by truth-values r This semantic is extended to all formulas according to the well known rules (truthtable)

4  Wilfried Grossmann, WS2012/13, University of Vienna – Models 4. Logical Models – Predicate Logic Syntax 1 r Individual constants (names) r Individual variables (placeholders) r Function symbols r Predicates r Quantors r Rules for defining expressions in three steps: Terms, atomic formulas, well formed formulas

5  Wilfried Grossmann, WS2012/13, University of Vienna – Models 4. Logical Models – Predicate Logic Syntax 2 r Terms are expressions defined either by individual constants, individual variables or functions m Examples (Higher education example): Constants: Exercise1, Student_Nr, ….. Variables: SomeExercise, AnyStudent Functions: MilestonePoints(AnyStudent), Enrolement(MilestonePoint(AnyStudent), Presentation(AnyStudent), Exercise(AnyStudent))

6  Wilfried Grossmann, WS2012/13, University of Vienna – Models 4. Logical Models – Predicate Logic Syntax 3 r An atomic formula is defined by a predicate symbol followed by a number of terms in brackets for which the predicate is applicable m Examples (Higher education example): Belongs_to_course(Student_xx) Has_achieved(Student_xx, MilestonePoints)

7  Wilfried Grossmann, WS2012/13, University of Vienna – Models 4. Logical Models – Predicate Logic Syntax 4 r Well formed formulas are defined by application of propositional calculus and quantification of atomic formulas m Examples (Higher education example): There exist students, who have solved all exercises All students have mastered the presentation points

8  Wilfried Grossmann, WS2012/13, University of Vienna – Models 4. Logical Models – Predicate Logic Semantic 1  Semantic in predicate logic is defined by an interpretation obtained in the following way: r Individual variables and constants can take only values in a certain domain r For each individual constant we define a fixed value in and call it the Interpretation r For each function symbol we assign an operation r Each unary predicate represents a property, and each n-ary predicate represents a relation 

9  Wilfried Grossmann, WS2012/13, University of Vienna – Models 4. Logical Models – Predicate Logic Semantic 2 r The unary predicates define a subset of the domain and the n-ary predicates define a subsets of tuples defined by the domain r We denote the interpretation defined above by r Now we assign truth values to atomic formulas containing no individual variables, so called facts

10  Wilfried Grossmann, WS2012/13, University of Vienna – Models 4. Logical Models – Predicate Logic Semantic 3 r Starting from this facts we obtain truth values for all well formed formulas if we assign each free individual variable any possible individual constant from the domain and apply the rules of propositional calculus r If the interpretation results in the truth value for all possible assignments of the free variables we call the interpretation a model

11  Wilfried Grossmann, WS2012/13, University of Vienna – Models 4. Logical Models – Predicate Logic Semantic 4 r The model is not a theoretical construct, but an interpretation corresponding the theory  A data modelling language realizes this modelling techniques  Main issues of the processing logic are questions about decidability if we define a certain set of axioms and constructors for well formed formulas

12  Wilfried Grossmann, WS2012/13, University of Vienna – Models 4. Logical Models – Description Logic  Description logic combines a domain logic with logic based semantics of predicate logic  The domain logic describes the domain of interest by concept descriptors built from r Atomic Concepts (unary predicates) r Atomic roles (binary predicates)

13  Wilfried Grossmann, WS2012/13, University of Vienna – Models 4. Logical Models – Description Logic r Concept descriptions are done by a so called T-Box (terminological box) corresponding to a data base scheme m Examples: A happy man is a man that is married to a doctor and all his children are doctors or professors Only humans can have human children

14  Wilfried Grossmann, WS2012/13, University of Vienna – Models 4. Logical Models – Description Logic r The assertional part, so called A-Box corresponds to the data in a data base and describes concrete situations m Example: Bob is a happy man, Mary is one of his children, and Mary is not a doctor From that we can infer that Mary is a professor

15  Wilfried Grossmann, WS2012/13, University of Vienna – Models 4. Logical Models – Ontologies Most important application is the formulation of ontologies, which may be useful for the task of Business process description  An ontology defines the concepts, relationships, and other distinctions that are relevant for modelling a domain  The specification takes the form of the definitions of a presentational vocabulary (classes, relations,…), which provide meaning for the vocabulary and formal constraints on its coherent use (T. Gruber)

16  Wilfried Grossmann, WS2012/13, University of Vienna – Models 4. Logical Models – Ontologies Graphical representation of ontology tasks

17  Wilfried Grossmann, WS2012/13, University of Vienna – Models 4. Logical Models – Ontologies  Basic constituents of an ontology r Concepts (terms) r Types representing object types define by the concepts r Instances r Relations r Inheritance r Axioms  The simplest case of an ontology is a taxonomy  One can distinguish domain ontologies and upper ontologies

18  Wilfried Grossmann, WS2012/13, University of Vienna – Models 4. Logical Models – Ontologies Example of a simple domain ontology

19  Wilfried Grossmann, WS2012/13, University of Vienna – Models 4. Logical Models – Ontologies Example of a complex “upper” ontology

20  Wilfried Grossmann, WS2012/13, University of Vienna – Models 4. Logical Models – Ontologies  Advantage of ontologies r Ontologies organize information without taking into account cumbersome details of data base modelling r In principle ontologies support knowledge integration and exchange of software r Ontologies play an important role in building the Semantic Web

21  Wilfried Grossmann, WS2012/13, University of Vienna – Models 4. Logical Models – Ontologies  Most important representation language is OWL r A ontology formulated in OWL-DL correspond to the T-Box in Description Logic r OWL Constructors: intersectionOfminCardinality unionOfmaxCardinality complementOfinverseOf one of allValuesFrom hasValue

22  Wilfried Grossmann, WS2012/13, University of Vienna – Models 4. Logical Models – Ontologies  OWL Axioms

23  Wilfried Grossmann, WS2012/13, University of Vienna – Models 4. Logical Models – Ontologies  This Ontology is decideable  Tools for ontology formulation: Protégé  The Knowledge Based Temporal Abstraction Method (KBTA) can be formulated as an ontology

24  Wilfried Grossmann, WS2012/13, University of Vienna – Models 5. Graphs Graphs are a powerful tool in Business process modelling applied for many different purposes, often in combination with other modelling techniques Syntax for Graphs 1 r Vertices (nodes) r Edges (arcs)

25  Wilfried Grossmann, WS2012/13, University of Vienna – Models 5. Graphs Syntax for Graphs 2 r Nodes and arcs may be specified by attributes m Example: In-degree and Out-degree of vertices r Different types of graphs: m Directed graph, Trees, Forests, Complete Graph, layered network, connected graph, bipartite graphs

26  Wilfried Grossmann, WS2012/13, University of Vienna – Models 5. Graphs Syntax for Graphs 3 r Special sub-graphs: m Path, spanning tree, circle, ….

27  Wilfried Grossmann, WS2012/13, University of Vienna – Models 5. Graphs Semantic for graphs  Semantic for graphs is defined from mathematical standard interpretations r Interpretation of attributes of vertices or edges as capacities r Interpretation of attributes for edges as distance, cost r Dynamic interpretation m Vertices represent activities, edges represent priority structure (partial ordering), possible transition m Edges represent activities, vertices represent states before/after an activity

28  Wilfried Grossmann, WS2012/13, University of Vienna – Models 5. Graphs Processing logic for graphs: r Graph theoretical algorithms offer solutions for a number of questions which can be formulated as optimization problems in the standard interpretation m Examples: Shortest path, Minimum spanning tree, Maximum flow, Min-Cost Flow, Traveling salesman Problem, ….

29  Wilfried Grossmann, WS2012/13, University of Vienna – Models 5. Graphs – Specific Models Combination of the generic model techniques for graphs with a specific domain logic allows more detailed specification of models Processes as Transition systems r Vertices represent states of a system r Edges represent possible transitions r A path in the graph is an instance of the process

30  Wilfried Grossmann, WS2012/13, University of Vienna – Models 5. Graphs – Specific Models Business Processes models with BPMN r Vertices are typed according to different business workflow concepts m Activities m Splits: AND, OR, XOR m Joins: AND, OR, XOR m Start, end r Edges represent priorities r Rules for building the graph Compare with knowledge representation by ontologies

31  Wilfried Grossmann, WS2012/13, University of Vienna – Models 5. Graphs – Specific Models Petri-Nets as state machines 1 r Two disjoint types of vertices: Places and Transitions r Edges are defined as directed edges between places and transition or transitions and edges r A function marking the places and defining an initial state

32  Wilfried Grossmann, WS2012/13, University of Vienna – Models 5. Graphs – Specific Models Petri-Nets as state machines 2 r If all places which are predecessors of a transition are marked and all successors places of the transition are free then the network can fire (activates the transition) and switches the network new state by removing the marking from all predecessors places and puts it to the places which are the successors of the transition r This is the simplest case; more elaborated rules are possible for handling conflicts r Firing generates a specific process path instance

33  Wilfried Grossmann, WS2012/13, University of Vienna – Models 5. Graphs – Specific Models Petri-Nets as state machines 3 r Example: Gasoline station (kroening-online.de)

34  Wilfried Grossmann, WS2012/13, University of Vienna – Models 6. Functions Functions as a generic model for defining a specific relation as mapping from a domain (input) into some range of values (output) are a main tool in all kinds of business process analysis The basic information logic defined by function algebra is usually enlarged by special classes of functions depending on the on specification of the domain an the range

35  Wilfried Grossmann, WS2012/13, University of Vienna – Models 6. Functions In case of discrete domains main application of functions is summarizing characteristics of instances r Counting : Mapping the occurrence of instances into the natural numbers m Advantage: Additivity, i.e. we can do it iteratively r Aggregation: defining new values of an attribute by using a hierarchical taxonomy for the value domain of the terms m Basic operation in connection with OLAP (roll up) r Note that disaggregation (drill down) needs usually additional considerations

36  Wilfried Grossmann, WS2012/13, University of Vienna – Models 6. Functions In case of continuous domains the following ideas are used in many applications  Modelling of unknown relationships by using function classes r Define a set of basic functions, e.g. power functions, trigonometric functions, spline functions, … r Define a model for the relationship by a linear combination of these basic functions (regression model)

37  Wilfried Grossmann, WS2012/13, University of Vienna – Models 6. Functions r This model can be applied also in case of modelling the output in dependence of many input variables (multiple regression) m In that case we use many times only linear functions m Sometimes also quadratic functions

38  Wilfried Grossmann, WS2012/13, University of Vienna – Models 6. Functions  Projections r Sometimes it is rather difficult to understand the behaviour of a business process depending on many different input variables r Hence we look for a more compressed description in a small number of dimensions r These dimensions are usually defined as linear combination of the observed dimensions

39  Wilfried Grossmann, WS2012/13, University of Vienna – Models 6. Functions  Projections r Many times we use a normalisation of the coefficients r A well known simple case is a score r A main analysis task is defining methods which result in transformations keeping as much information as possible in the data

40  Wilfried Grossmann, WS2012/13, University of Vienna – Models 6. Functions  Transformations r In order to obtain values with some desired behaviour, for example a linear relationship, it is sometimes useful to transform the values of a function m Power transformation m Logarithmic transformation: symmetrizes the values of a ratio of two positive values

41  Wilfried Grossmann, WS2012/13, University of Vienna – Models 7. Probability and Statistics – Probability models Models for variability of process instances 1  Frequently the values of the attributes can be described / predicted only by a probabilistic law r Examples: Income of a person, preferences with respect to certain brands, measurement of some physical parameter, duration of an activity,….  For describing the observations we use a probability distribution

42  Wilfried Grossmann, WS2012/13, University of Vienna – Models 7. Probability and Statistics – Probability models Models for variability of process instances 2 r We use the generic symbol for characterization of this probability m Interpretation: is the likelihood that value occurs m Only in case of discrete value domains we can talk about probability  If we have only two possible values (0, 1) for the attribute (dichotomous attributes) we use frequently instead of probability odds or log-odds

43  Wilfried Grossmann, WS2012/13, University of Vienna – Models 7. Probability and Statistics – Probability models Markov chains as model for process description 1 r A Markov chain can be interpreted as description of a business process as state transition system where the main attribute for the edges are the probabilities that switches between states occur

44  Wilfried Grossmann, WS2012/13, University of Vienna – Models 7. Probability and Statistics – Probability models Markov chains as model for process description 2 r The model allows answering a number of interesting structural analysis questions: m What states can be reached from an initial state? m Is it possible to return to some state? m Is there a stable distribution for being in some states? m Is such a stable state achieved in the long run? Important application is the behaviour of internet users

45  Wilfried Grossmann, WS2012/13, University of Vienna – Models 7. Probability and Statistics – Statistical Models Statistics as model for variability of process instances r In Business process classification and business process segmentation we usually start with a model of the following form

46  Wilfried Grossmann, WS2012/13, University of Vienna – Models 7. Probability and Statistics – Statistical Models 7. Probability and Statistics – Statistical Models Statistics as a tool for business process estimation 1 r Estimation of unknown parameters of a distribution m Many times a probabilistic model for the behaviour of an attribute is determined only up to a number of parameters (c.f. function classes as a model for relationships) m We can use statistics for finding the “best” values for the parameters according to available observation data

47  Wilfried Grossmann, WS2012/13, University of Vienna – Models 7. Probability and Statistics – Statistical Models Statistics as a tool for business process estimation 2 r Estimation of missing observations m In case of missing values in the observations we can improve data quality by using statistical techniques for finding plausible values for the missing observations r Estimation of duration of processes m We want to find the distribution of the duration of processes in case of partial observation (censored data) m Example Duration of contracts: Observations of ended contracts and observations of existing contracts m Find the distribution of the lifetime of contracts