A Net-based Formal Framework for Causal Loop Diagrams Guillermina - - PowerPoint PPT Presentation

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A Net-based Formal Framework for Causal Loop Diagrams Guillermina - - PowerPoint PPT Presentation

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A Net-based Formal Framework for Causal Loop Diagrams Guillermina Cledou 1 and Shin Nakajima 2 1 HASLab INESC TEC & University of Minho, Braga, Portugal 2 NaEonal InsEtute of InformaEcs, Tokyo, Japan CSD&M Asia 2018 Context Managing

slide-1
SLIDE 1

A Net-based Formal Framework for Causal Loop Diagrams

Guillermina Cledou1 and Shin Nakajima2

1 HASLab INESC TEC & University of Minho, Braga, Portugal 2 NaEonal InsEtute of InformaEcs, Tokyo, Japan

CSD&M Asia 2018

slide-2
SLIDE 2

Managing complex systems

Context

2

Calendar Time (CT) Due Date (DD) Time Remaining (TR) Assignment Rate (AR) Work Pressure (WP) Workweek (WW) Effort Devoted to Assignments (EDA) Assignment Backlog (AB) Productivity (PD) Work Completion Rate (WCR)

+ + + + + +

Structure Behaviour Dynamics

slide-3
SLIDE 3

Managing complex systems

Context

3

Calendar Time (CT) Due Date (DD) Time Remaining (TR) Assignment Rate (AR) Work Pressure (WP) Workweek (WW) Effort Devoted to Assignments (EDA) Assignment Backlog (AB) Productivity (PD) Work Completion Rate (WCR)

+ + + + + +

Structure Behaviour Dynamics Understand causal links between variables of the system

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SLIDE 4

Managing complex systems

Context

4

Calendar Time (CT) Due Date (DD) Time Remaining (TR) Assignment Rate (AR) Work Pressure (WP) Workweek (WW) Effort Devoted to Assignments (EDA) Assignment Backlog (AB) Productivity (PD) Work Completion Rate (WCR)

+ + + + + +

Structure Behaviour Dynamics Understand causal links between variables of the system

(QualitaEve approach)

Causal Loop Diagrams (CLD)

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SLIDE 5

Illustrates causal links between concepts Abstracts from quanHHes Describes system structure Brings out dynamic behaviour

Causal Loop Diagrams

5

Causes and Effects

+

Var1 Var2

  • Var2

Var1 Var1 Var2

+

  • +

Variables only Increase or Decrease Links’ polariHes: How the independent variable affects the dependent one?

(delay)

slide-6
SLIDE 6

Causal Loop Diagrams

6

Reinforcing Balancing Balancing with delay

[C.W. Kirkwood, System Dynamic Methods]

slide-7
SLIDE 7

Challenges

  • Complex interacEons
  • Informal semanEcs

Causal Loop Diagrams

7

New Vehicle Price Relative Marginal Utility

  • f Efficiency vs.

Performance

  • Present Vehicle

Population Used Vehicles for Sale Number of Scrapped Vehicles Used Vehicle Prices

  • Miles/Veh

Fuel Price Total Vehicle Miles Traveled + Cost/mile

  • +

Fuel Emissions Factors In-Use Emissions + + Unit Profit + Production Cost Producer Supply of New Vehicles +

  • LW Recycled

Material Stock Recyclability LW Virgin Material Stock Lightweight Material Price Total Lightweight Material Stock + +

  • LW Recycled

Matetial Production + + LW Virgin Exploration and Production + + + + Material Emissions Factors Vehicle Production Emission Factors Production Emissions + B2 B3 Scrappage Rate Fuel Demand + + B7 B4 Degree of Market Saturation R1 Fuel Demand Recycled Material Virgin Material Producer Profit Scrappage of Aging Vehicles Effect Used Vehicles Population + + +

  • +
  • +

+ + + + External Sources of Recycled Material +

  • New Vehicle

Demand + B8 Market Saturation

  • f Vehicles

Market Share of Fuel Efficient Vehicles

  • B6

Consumer Demand for Fuel Efficient Vehicles + + Producer Emphasis

  • n Efficiency

+ + B5 Producer-Consumer Interaction Effects Vehicle Fuel Efficiency + <Vehicle Fuel Efficiency>

  • +

Lightweight Material Demand + + <Producer Supply of New Vehicles> + + + Marginal Production Cost of Efficiency + New Vehicle Purchases + <New Vehicle Demand> + <LW Recycled Material Stock>

  • +

B1 Vehicle Price-Demand Effect + + <Vehicle Fuel Efficiency> + B9 <Vehicle Fuel Efficiency>

  • Market Retail

Price +

  • [M.D. Stepp et al., Greenhouse gas mitigation policies

and the transportation sector: The role of feedback effects on policy effectiveness]

slide-8
SLIDE 8

Challenges

  • Complex interacEons
  • Informal semanEcs

Causal Loop Diagrams

8

New Vehicle Price Relative Marginal Utility

  • f Efficiency vs.

Performance

  • Present Vehicle

Population Used Vehicles for Sale Number of Scrapped Vehicles Used Vehicle Prices

  • Miles/Veh

Fuel Price Total Vehicle Miles Traveled + Cost/mile

  • +

Fuel Emissions Factors In-Use Emissions + + Unit Profit + Production Cost Producer Supply of New Vehicles +

  • LW Recycled

Material Stock Recyclability LW Virgin Material Stock Lightweight Material Price Total Lightweight Material Stock + +

  • LW Recycled

Matetial Production + + LW Virgin Exploration and Production + + + + Material Emissions Factors Vehicle Production Emission Factors Production Emissions + B2 B3 Scrappage Rate Fuel Demand + + B7 B4 Degree of Market Saturation R1 Fuel Demand Recycled Material Virgin Material Producer Profit Scrappage of Aging Vehicles Effect Used Vehicles Population + + +

  • +
  • +

+ + + + External Sources of Recycled Material +

  • New Vehicle

Demand + B8 Market Saturation

  • f Vehicles

Market Share of Fuel Efficient Vehicles

  • B6

Consumer Demand for Fuel Efficient Vehicles + + Producer Emphasis

  • n Efficiency

+ + B5 Producer-Consumer Interaction Effects Vehicle Fuel Efficiency + <Vehicle Fuel Efficiency>

  • +

Lightweight Material Demand + + <Producer Supply of New Vehicles> + + + Marginal Production Cost of Efficiency + New Vehicle Purchases + <New Vehicle Demand> + <LW Recycled Material Stock>

  • +

B1 Vehicle Price-Demand Effect + + <Vehicle Fuel Efficiency> + B9 <Vehicle Fuel Efficiency>

  • Market Retail

Price +

  • [M.D. Stepp et al., Greenhouse gas mitigation policies

and the transportation sector: The role of feedback effects on policy effectiveness]

PaOern of behaviour?

?

Eme X

slide-9
SLIDE 9

Challenges

  • Complex interacEons
  • Informal semanEcs

Causal Loop Diagrams

9

New Vehicle Price Relative Marginal Utility

  • f Efficiency vs.

Performance

  • Present Vehicle

Population Used Vehicles for Sale Number of Scrapped Vehicles Used Vehicle Prices

  • Miles/Veh

Fuel Price Total Vehicle Miles Traveled + Cost/mile

  • +

Fuel Emissions Factors In-Use Emissions + + Unit Profit + Production Cost Producer Supply of New Vehicles +

  • LW Recycled

Material Stock Recyclability LW Virgin Material Stock Lightweight Material Price Total Lightweight Material Stock + +

  • LW Recycled

Matetial Production + + LW Virgin Exploration and Production + + + + Material Emissions Factors Vehicle Production Emission Factors Production Emissions + B2 B3 Scrappage Rate Fuel Demand + + B7 B4 Degree of Market Saturation R1 Fuel Demand Recycled Material Virgin Material Producer Profit Scrappage of Aging Vehicles Effect Used Vehicles Population + + +

  • +
  • +

+ + + + External Sources of Recycled Material +

  • New Vehicle

Demand + B8 Market Saturation

  • f Vehicles

Market Share of Fuel Efficient Vehicles

  • B6

Consumer Demand for Fuel Efficient Vehicles + + Producer Emphasis

  • n Efficiency

+ + B5 Producer-Consumer Interaction Effects Vehicle Fuel Efficiency + <Vehicle Fuel Efficiency>

  • +

Lightweight Material Demand + + <Producer Supply of New Vehicles> + + + Marginal Production Cost of Efficiency + New Vehicle Purchases + <New Vehicle Demand> + <LW Recycled Material Stock>

  • +

B1 Vehicle Price-Demand Effect + + <Vehicle Fuel Efficiency> + B9 <Vehicle Fuel Efficiency>

  • Market Retail

Price +

  • [M.D. Stepp et al., Greenhouse gas mitigation policies

and the transportation sector: The role of feedback effects on policy effectiveness]

PaOern of behaviour?

?

Eme X

SimulaEon 
 (not exhausEve)

slide-10
SLIDE 10

Challenges

  • Complex interacEons
  • Informal semanEcs

Causal Loop Diagrams

10

New Vehicle Price Relative Marginal Utility

  • f Efficiency vs.

Performance

  • Present Vehicle

Population Used Vehicles for Sale Number of Scrapped Vehicles Used Vehicle Prices

  • Miles/Veh

Fuel Price Total Vehicle Miles Traveled + Cost/mile

  • +

Fuel Emissions Factors In-Use Emissions + + Unit Profit + Production Cost Producer Supply of New Vehicles +

  • LW Recycled

Material Stock Recyclability LW Virgin Material Stock Lightweight Material Price Total Lightweight Material Stock + +

  • LW Recycled

Matetial Production + + LW Virgin Exploration and Production + + + + Material Emissions Factors Vehicle Production Emission Factors Production Emissions + B2 B3 Scrappage Rate Fuel Demand + + B7 B4 Degree of Market Saturation R1 Fuel Demand Recycled Material Virgin Material Producer Profit Scrappage of Aging Vehicles Effect Used Vehicles Population + + +

  • +
  • +

+ + + + External Sources of Recycled Material +

  • New Vehicle

Demand + B8 Market Saturation

  • f Vehicles

Market Share of Fuel Efficient Vehicles

  • B6

Consumer Demand for Fuel Efficient Vehicles + + Producer Emphasis

  • n Efficiency

+ + B5 Producer-Consumer Interaction Effects Vehicle Fuel Efficiency + <Vehicle Fuel Efficiency>

  • +

Lightweight Material Demand + + <Producer Supply of New Vehicles> + + + Marginal Production Cost of Efficiency + New Vehicle Purchases + <New Vehicle Demand> + <LW Recycled Material Stock>

  • +

B1 Vehicle Price-Demand Effect + + <Vehicle Fuel Efficiency> + B9 <Vehicle Fuel Efficiency>

  • Market Retail

Price +

  • [M.D. Stepp et al., Greenhouse gas mitigation policies

and the transportation sector: The role of feedback effects on policy effectiveness]

PaOern of behaviour?

?

Eme X

SimulaEon 
 (not exhausEve) Formal Analysis 
 (exhausEve)

Formal semanHcs

slide-11
SLIDE 11

t0 t1 t2 t4 t3 p1 p2 p3

Petri Nets

11

Places TransiHons Flows Tokens

p0

IniHal Marking

M0 =(1,0,0,0)

True Concurrency

  • MulEple transiEons enabled
  • TransiEons fired one at a Eme
slide-12
SLIDE 12

Causal Loop Nets

12

Variables as places Links as transiHons with polarity

Causal Loop Nets

Direct correspondence

t1 t2 t4 t3 +

  • +

+

Public Transport Traffic 
 Volume Traveling Times

Traveling Times Public
 Transport Traffic Volume + + +

slide-13
SLIDE 13

Causal Loop Nets

13

  • QualitaHve values
  • Delays
  • Concurrency

QualitaHve AbstracHons

Variables increase or decrease Tokens are not limited resources Delays are qualitaEve Tokens can be delayed

t1 t2 t4 t3 +

  • +

+

Public Transport Traffic 
 Volume Traveling Times

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SLIDE 14

QualitaHve values and non-determinisHc delays

Variables increase or decrease Causal Loop Nets

14

Tokens = { ↑e , ↓e , _}

Tokens

Delay

QualitaHve AbstracHons

No change or no informaEon

e ∈ 𝒪0

t1 t2 t4 t3 + d

  • +

+

Public Transport Traffic 
 Volume Traveling Times

Markings

M : P → 2Tokens

Sets of Tokens

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SLIDE 15

True concurrency and AMAN strategy

  • All enabled transiEons must fire
  • As many tokens as needed

Causal Loop Nets

15

Enabled TransiHons

All transiEons with in their incoming places

QualitaHve AbstracHons

{ ↑0 , ↓0 }

t1 t2 t4 t3 +

  • +

+

Public Transport Traffic 
 Volume Traveling Times

slide-16
SLIDE 16

t1 t2 t4 t3 +

  • +

+

Public Transport Traffic 
 Volume Traveling Times

Causal Loop Nets

16

(1,0,0) (0,1,0) (1,0,1) (0,{1,-1},0) (?) M0

Marking Graph (SemanEcs)

↑

Concurrency

t1 t2|t3 t1|t4 t2|t3

slide-17
SLIDE 17

t1 t2 t4 t3 +

  • +

+

Public Transport Traffic 
 Volume Traveling Times

Causal Loop Nets

17

(1,0,0) (0,1,0) (1,0,1) (0,{1,-1},0) (?) M0

Marking Graph (SemanEcs)

↑

Concurrency

t1 t2|t3 t1|t4 t2|t3

slide-18
SLIDE 18

t1 t2 t4 t3 +

  • +

+

Public Transport Traffic 
 Volume Traveling Times

Causal Loop Nets

18

(1,0,0) (0,1,0) (1,0,1) (0,{1,-1},0) (?) M0

Marking Graph (SemanEcs)

↑ ↑

Concurrency

t1 t2|t3 t1|t4 t2|t3

slide-19
SLIDE 19

t1 t2 t4 t3 +

  • +

+

Public Transport Traffic 
 Volume Traveling Times

Causal Loop Nets

19

(1,0,0) (0,1,0) (1,0,1) (0,{1,-1},0) (?) M0

Marking Graph (SemanEcs)

↑↑

Concurrency

t1 t2|t3 t1|t4 t2|t3

slide-20
SLIDE 20

t1 t2 t4 t3 +

  • +

+

Public Transport Traffic 
 Volume Traveling Times

Causal Loop Nets

20

(1,0,0) (0,1,0) (1,0,1) M0

Marking Graph (SemanEcs)

↑↑

Normalize Marking Graph

Concurrency

(0,{1,-1},0) (?)

t1 t2|t3 t1|t4 t2|t3

slide-21
SLIDE 21

t1 t2 t4 t3 +

  • +

+

Public Transport Traffic 
 Volume Traveling Times

Causal Loop Nets

21

(1,0,0) (0,1,0) (1,0,1) (0,-1,0) M0

Marking Graph (SemanEcs)

↑↑

Normalize Marking Graph

Concurrency

t1 t2|t3 t1|t4 t1|t4

slide-22
SLIDE 22

t1 t2 t4 t3 +

  • +

+

Public Transport Traffic 
 Volume Traveling Times

Causal Loop Nets

22

(1,0,0) (0,1,0) (1,0,1) (0,-1,0) M0

Marking Graph (SemanEcs)

↑↑

Normalize Marking Graph

(-1,0,-1) (0,{1,-1},0) …

Concurrency

t1 t2|t3 t1|t4 t1|t4 t2|t3 t1|t4

slide-23
SLIDE 23

t1 t2 t4 t3 +

  • +

+

Public Transport Traffic 
 Volume Traveling Times

Causal Loop Nets

23

(1,0,0) (0,1,0) (1,0,1) (0,-1,0) M0

Marking Graph (SemanEcs)

↑↑

Normalize Marking Graph

(-1,0,-1)

Concurrency

t1 t2|t3 t1|t4 t1|t4 t2|t3 t1|t4 t1|t4

slide-24
SLIDE 24

t1 t2 t4 t3 + 1

  • +

+

Public Transport Traffic 
 Volume Traveling Times

Causal Loop Nets

24

(1,0,0) M0

Marking Graph (SemanEcs)

↑

(0,11,0) (0,1,0)

Each step is consider a Hck Delay tokens are decreased Different Marking Graphs for different delays

Delays

t1

slide-25
SLIDE 25

t1 t2 t4 t3 + 1

  • +

+

Public Transport Traffic 
 Volume Traveling Times

Causal Loop Nets

25

(1,0,0) M0

Marking Graph (SemanEcs)

↑1

(0,11,0) (0,1,0)

Each step is consider a Hck Delay tokens are decreased Different Marking Graphs for different delays

Delays

t1

slide-26
SLIDE 26

t1 t2 t4 t3 + 1

  • +

+

Public Transport Traffic 
 Volume Traveling Times

Causal Loop Nets

26

(1,0,0) M0

Marking Graph (SemanEcs)

↑1

(0,11,0) (0,1,0)

Each step is consider a Hck Delay tokens are decreased Different Marking Graphs for different delays

Delays

t1

τ (silent transiEon)

slide-27
SLIDE 27

t1 t2 t4 t3 + 1

  • +

+

Public Transport Traffic 
 Volume Traveling Times

Causal Loop Nets

27

(1,0,0) M0

Marking Graph (SemanEcs)

↑

(0,11,0) (0,1,0)

Each step is consider a Hck Delay tokens are decreased Different Marking Graphs for different delays

Delays

t1

τ (silent transiEon)

slide-28
SLIDE 28

Queries on traces

  • Does a CLN exhibits a given behaviour?
  • How X behaves when Y saEsfies some behaviour?

SimulaHon relaHons

  • One to one relaEon
  • Abstract similar behaviour

{ ↑ , ↓ }_ ∼ { ↑ , ↓ }

Analysis of Causal Loop Nets

28

↑ ↓ ≁ ↑ _ ↓ ↑ ↓ ∼ ↑ _ ↓

↑n ∼ ↑ ↓n ∼ ↓

φ0(i, r, v, f ) = ⋀

k−1 j=0 ∃sj+1 . (σi(sj . . sj+1) . v ∼ f(j))

φ1(v, f ) = ∃i, r : φ0(i, r, v, f )

φ3(φ1(vm, f ), vℓ, gℓ)

(Sequence of Markings)

Over a variable

slide-29
SLIDE 29

Queries on traces

  • Does a CLN exhibits a given behaviour?
  • How X behaves when Y saEsfies some behaviour?

SimulaHon relaHons

  • One to one relaEon
  • Abstract similar behaviour

Analysis of Causal Loop Nets

29

Detailed informaEon about X Describe informaEon

{ ↑ , ↓ }_ ∼ { ↑ , ↓ } ↑n ∼ ↑ ↓n ∼ ↓

slide-30
SLIDE 30

t1 t2 t4 t3 +

  • +

+

Public Transport Traffic 
 Volume Traveling Times

Analysis of Causal Loop Nets

30

Marking Graph (SemanEcs)

(0,1,0) (1,0,1) (0,-1,0) M0 (-1,0,-1) M1 M2 M3 M4 (1,0,0)

true

Tr1 = M0 M1 M2 M3 M4 Tr2 = M0 M1 M2 M1 M2 M3 M4 Tr3 = M0 M1 M2 M1 M2 M3 M4 M3 M4 …

t1 t2|t3 t1|t4 t1|t4 t2|t3 t1|t4 t1|t4

Can Traveling Times eventually Increase and then Decrease?

↑

φ1(TravelingTimes, ( ↑ ↓ ))

slide-31
SLIDE 31

Analysis of Causal Loop Nets

31

Marking Graph (SemanEcs)

(1,0,0) (0,1,0) (1,0,1) (0,-1,0) M0 (-1,0,-1)

true

M1 M2 M3 M4 Tr1 = M0 M1 M2 M3 M4 Tr2 = M0 M1 M2 M1 M2 M3 M4 Tr3 = M0 M1 M2 M1 M2 M3 M4 M3 M4 …

φ2(TravelingTimes, ( ↑ ↓ ), PublicTransport)

true

Tr1 = _,1,0,-1,0 Tr2 = _,1,0,1,0,-1,0 Tr3 = _,1,0,1,0,-1,0,-1,0

t1 t2|t3 t1|t4 t1|t4 t2|t3 t1|t4 t1|t4

How Public Transport behaves when Traveling Times Increases and then Decreases?

t1 t2 t4 t3 +

  • +

+

Public Transport Traffic 
 Volume Traveling Times

φ1(TravelingTimes, ( ↑ ↓ ))

Can Traveling Times eventually Increase and then Decrease?

↑

slide-32
SLIDE 32

Analysis of Causal Loop Nets

32

slide-33
SLIDE 33

Wrapping up

33

CLD

  • Informal semanEcs
  • Difficult to analyse behaviour in complex systems
  • SimulaEon is not exhausEve

CLN

  • Formal semanEcs
  • ExhausEve analysis

Marking Graph (SemanEcs)

(1,0,0) (0,1,0) (1,0,1) (0,-1,0) M0 (-1,0,-1)

Automatic generation

Traveling Times Public
 Transport Traffic Volume + + +

  • t1

t2 t4 t3 +

  • +

+

Public Transport Traffic 
 Volume Traveling Times

slide-34
SLIDE 34

Thank you!