This was a work-in progress presentation given in Nov 2010 (uploaded here for historic records). It was part of the ACSI EU project for process mining over processes with multiple objects. The slides discuss an example of an order process over multiple objects and propose how to model this data in a graph (event relation graph) that is stored in a database and supported by a relational algebra over behavior (e.g. to join event traces of multiple objects into a case). The final part of the presentation discusses the synchronous proclet model ultimately formalized in https://doi.org/10.1007/978-3-030-21571-2_1
2. abstract model of a database
• with events
• a normal form
• the Event Relation Graph
What is a case?
• Some ideas
• a “case algebra”
Synchronous artifact model
Overview
PAGE 1
3. Database DB = { R1, R2, …, Rn}
• table is a relation Ri D1 … Dk
events: defined by “time-stamp” columns in DB, so:
Ri D1 … Dk Tk+1 … Tl
relations between different tables:
• key-foreign key relations defined in some DB schema
PAGE 2
Abstract model of a database
data in Ti time-stamps in Ri
4. given table Ri D1 … Dk Tk+1 … Tl
separate data Di from events Ti
assume each Ri with events defines a key D1 = Ki
Ri Ki D2 … Dk Tk+1 … Tl
data table event table
Ri Ki D2 … Dk Ei Ki Type Time
PAGE 3
Normal form
{k+1,…,l} distinguish events of the
different columns Tk+1 … Tl
5. DB in normal form {R1, R2, …, Rn , E1, E2, …, En}
Ri Ki D2 … Dk, Ki – key of table Ri
Ei Ki Type Time
key(e) := Ki iff e Ei
Event Relation Graph: G = (V, F)
V = E1 … En, F V V
F = { (e1,e2) | there is a key-foreign-key relation
from key(e1) to key(e2) or key(e1) = key(e2) }
PAGE 4
Event Relation Graph
12. Abstract model of database
• with events
• a normal form
• the event relation graph
What is a case?
• some ideas
• a “case algebra”
Synchronous artifact model
Overview
PAGE 11
13. describes which event relates by data to which
other events
directed:
• event relations that can be retrieved by following the key-
foreign key relations forward
• directions indicate which events should be considered
together for a “case”
suggests notion of a case: subgraph
• starting at a specific event (without predecessor?)
• containing all transitive predecessor
and/or successors (or only up to a certain point)
• “viewpoint” = set of all cases of a specific kind
PAGE 12
Properties of the Event Relation Graph
21. a case is a subgraph of the event relation graph
different notions of a case, cases can be combined,
e.g. complete order + complete delivery etc.
define a case algebra:
• basic cases
• composition of cases (union)
• composition wrt. case properties (only completed cases)
• joins, etc.
operations all should follow from relational algebra
of the underlying database
PAGE 20
Case Algebra for Artifact Models
25. Abstract model of database
• with events
• a normal form
• the event relation graph
What is case?
• Some ideas
• a “case algebra”
Synchronous artifact model
Overview
PAGE 24
26. Proposition: Synchronous communication
describes more precisely how a set of artifacts
relates to a database.
PAGE 25
Aim: relate Database to Artifact model
27. Artifact
B C
Artifact C
Artifact B
Artifact A
Artifact
B A
PAGE 26
A first idea…
Table A
Table C
Table B
date1, date2
date3, date4
date5, date6
d1 d2 d1 d2
d3 d4
d5 d6 d5 d6
d3 d4
Event Relation Graph
Database schema
28. Artifact
B C
Artifact C
Artifact B
PAGE 27
A first idea…
Table A
Table C
Table B
date1, date2
date3, date4
date5, date6
d1 d2 d1 d2
d3 d4
d5 d6 d5 d6
d3 d4
“Artifact-Centric Traces”
Database schema
Artifact A
Artifact
B A
d1 d2
d3 d4 d3 d4
d5 d6 d5 d6
d3 d4 d3 d4
d1 d2
29. Artifact
B C
Artifact C
Artifact B
PAGE 28
A first idea…
d1 d2 d1 d2
d3 d4
d5 d6 d5 d6
d3 d4
“Artifact-Centric Traces”
Artifact A
Artifact
B A
d1 d2
d3 d4 d3 d4
d5 d6 d5 d6
d3 d4 d3 d4
d1 d2
describes occurrences of
events wrt. Table A
describes occurrences of
events the relation from B to A
describes occurrences of
events wrt. Table B
30. PAGE 29
Corresponding Petri net model
d1 d2 d1 d2 Artifact A
Artifact
B A
d1 d2
d3 d4 d3 d4
d1 d2
d1
d2
d1
d2
d3
d4
d3
d4
Artifact B
d3 d4 d3 d4
A B A B
…
31. PAGE 30
Corresponding Artifact-Model
d1 d2 d1 d2 Artifact A
Artifact
B A
d1 d2
d3 d4 d3 d4
d1 d2
d1
d2
d1
d2
d3
d4
d3
d4
Artifact B
d3 d4 d3 d4
A B A B
1,1
1,1
1,*
1,*
1,*
1,*
1,*
1,*
32. PAGE 31
Semantics of Synchronous Ports?
d1
d2
d1
d2
d3
d4
d3
d4
A B A B
1,1
1,1
1,*
1,*
1,*
1,*
1,*
1,*
c,m c,m
X X
A B
multiplicity m: how often X occurs in
one instance of A
cardinality c: with how many
instances of B does an occurrence
of X in A synchronize?
33. PAGE 32
Semantics of Synchronous Ports?
d1
d2
d1
d2
A B
1,1
*,1
*,1
*,1
d1
d2
B1
d1
d2
A1
d1
d2
B2
d1
d2
A2
d1
d2
A3
N:M Proclet Model
Instances