A presentation given at a workshop for PhD students working with agent-based simulation

1. Informatik
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Axiomatisation and Simulation
Klaus G. Troitzsch, Universität Koblenz-Landau,
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2. Informatik
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 Introduction
 Target system and simulation model in the light of
non-statement view of the structuralist metatheory
 A case leading to a general principle
 Overcoming gender segregation in German high
schools
 Estimating values of T-theoretical values from a
comparison between simulation model and
intended empirical aplication
 Conclusion
Overview

3. Informatik
ESSA @work, TUHH, 22/11/201813/11/201 3/ 2113/11/2018
The logic of simulation as a
method [Gilbert and Troitzsch 2005:17]
Empirical frequency
density distribution of the
proportion of female
teachers in secondary
schools
Simulated Data
Target
Model
Systematic
Data Gathering
Similarity
Abstraction
Simulation
Collected Data
Empirical frequency
density distribution of the
proportion of female
teachers in secondary
schools

4. Informatik
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Empirical Desk
Casual
Observation
Formalization
Inducti
on
Propositions of
the prior theory
{Mpp1, Mpp2, …}
Theoretical
explanation
{M1, M2, …}
Prior
Theory
Theoretical
Without
Simulation
With
Simulation
Full model
(M)
Theory-based
Simulation
Environment
Implemen
tation
Instanti
ation
Adding
Axioms
Operationaliza
tion
Virtual
Experiments,
Simulation
Parameter
Setting
Research
Potential
model
(Mp)
Empirical Data,
Collected Data
Mental Models
Short-cut
Propositions
(Mpp)
Simulated Data
Real World
Issue,
Target
Executable
Simulation
Model
Deduction
Systematic
Data
Gathering
Check
for
Similarity
Check
for
Simila
rity
Check for
Similarity
Abducti
on
Simulated Data
Abstraction
Theory building
blocks {Mp1, Mp2, …}
An extended logic of simulation
[Ihrig and Troitzsch 2013]
Simulated Data
Target
Model
Systematic
Data Gathering
Similarity
Abstraction
Simulation
Collected Data

5. Informatik
ESSA @work, TUHH, 22/11/201813/11/201 6/ 2113/11/2018
 introduced in the late 1960s and 1970s by
Sneed, Stegmüller, Balzer, Moulines and
others
 to overcome the problem of translation
between observational and theoretical terms
and languages (which goes back to Carnap
1958)
 and introducing terms non-theoretical and
theoretical with respect to a certain theory
The structuralist theory concept
Rudolf Carnap (1958) “Beobachtungssprache und theoretische
Sprache”, Dialectica, 12(3–4): 236–248
Definition 1 (θ-theoreticity)
The function n is theoretical with respect to θ if and only if there is no application i of θ in
which ni is θ-independent; n is non-theoretical with respect to θ if and only if there is at
least one application i of θ in which ni is θ-independent.
Joseph D. Sneed (1971) The Logical Structure of Mathematical
Physics, Dordrecht: Reidel, 33

6. Informatik
ESSA @work, TUHH, 22/11/201813/11/201 7/ 2113/11/2018
 Introduction
 Target system and simulation model in the light of
non-statement view of the structuralist metatheory
 A case leading to a general principle
 Overcoming gender segregation in German high
schools
 Estimating values of T-theoretical values from a
comparison between simulation model and
intended empirical aplication
 Conclusion
13/11/2018
Overview

7. Informatik
ESSA @work, TUHH, 22/11/201813/11/201 8/ 2113/11/2018
 Process by which gender segregation in
German gymnasia was overcome after World
War II.
 Based on research done in the 1990s, using
official statistics of numbers of teachers and
pupils by sex for the years 1950/51 till
1989/1990, for between 114 and 140 of these
schools in the federal state of Rhineland-
Palatinate.
Coeducation model: Target and collected
data
in Germany and some other Continental countries,
a school of the highest grade, preparing pupils for universities

8. Informatik
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 The original (“shortcut”) simulation model (in MIMOSE) was based on a few
simple assumptions:
 that all teachers leaving their jobs are replaced by men and women with
equal overall probability,
 that men stay in their jobs twice as long as women and that the duration is
normally distributed with µ=30 and 15, respectively, and σ=5,
 that new women are assigned to an individual school with probability
P(W|)=(t) δ exp(x), δ=1.0, according to the percentage x of women
among its teachers.
 In the current version (in NetLogo)
  and δ are varied between simulation runs to find out which combination of
 and δ yields the best approximation to the empirical distributions, and (t)
is such that for δ=1 at all times men and women have the same overall
probability of replacing retired teachers.
Coeducation model: Abstraction from prior
theory and casual observation

9. Informatik
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 T time
 M the school system as a whole, the ministry
 κ tendency to allocate staff according to current gender ratio
 δ tendency to abide by equal opportunities
 S the set of secondary schools
 P the set of teaching persons
 β gender
 φ affiliation
Reconstruction: base sets and
constant attributes

10. Informatik
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 M the school system as a whole, the ministry
 τε statewide teachers to be replaced at the end of the current school year
 τεf statewide women to be replaced at the end of the current school year
 ν a parameter for the probability of selecting a woman
 f and F probability density function and cumulative distribution of the gender ratio
 S the set of secondary schools
 τ teachers currently affiliated with this school
 x gender ratio of this school
 λ history of the gender ratio of this school
 π = ν δ exp(κ x) probability that a retiring teachers is replaced by a woman
 nε teachers to be replaced at the end of the current school year
 nεf women to be replaced at the end of the current school year
 P the set of teaching persons
 α age
 ρ time until retirement
Reconstruction: base sets and functions

11. Informatik
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 Whatever can be described with these terms (base
sets, constants and functions) is the core K(GDS) of
a theory element GDS:
 GDS = <K, I>, I being the set of intended (empirical) applications of
GDS
 K(GDS) = <Mp(GDS), M(GDS), Mpp(GDS), GC(GDS), GL(GDS)>
with
 Mp(GDS) the set of potential models,
 M(GDS) the set of actual models fulfilling the axioms of GDS,
 Mpp(GDS) the set of partial potential models which can be described
with the GDS-non-theoretical terms,
 GC(GDS) the set of constraints (relations between distinct potential
models or intended applications),
 GL(GDS) the set of links to other theories, particular those which make
GDS-non-theroetical terms measurable
Reconstruction: theory element

12. Informatik
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Coeducation model: Implementation

13. Informatik
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 It was mainly δ whose effect on simulation
results and their similarity with the historical
data needed to be assessed.
 But a closer inspection of the results of a
larger number of simulation runs revealed
that there is some influence of κ, too, at least
in the early years of the observed period.
Validating the model

14. Informatik
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 The Kolmogorov-Smirnov distance between
the empirical and the best simulated
frequency distribution for varying δ, κ is
always so small that the hypothesis both
come from the same distribution cannot be
refuted.
 κ is more or less meaningless after 1969
 δ is always meaningful
δ, κ and the goodness of fit

15. Informatik
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 The 50 best fitting (out of 660) simulated
frequency distributions for varying δ, κ allow
for estimating the value of δ, κ for every year.
Measuring GDS-
theoretical terms
κ(t) current local gender
ratio
δ(t) equal
opportunities
θ(t) Kolmogorov-Smirnov
distance

16. Informatik
ESSA @work, TUHH, 22/11/201813/11/201 17/ 2113/11/2018
 Introduction
 Target system and simulation model in the light of
non-statement view of the structuralist metatheory
 A case leading to a general principle
 Overcoming gender segregation in German high
schools
 Estimating values of T-theoretical values from a
comparison between simulation model and
intended empirical aplication
 Conclusion
Overview

17. Informatik
ESSA @work, TUHH, 22/11/201813/11/201 18/ 2113/11/2018
 It can help in
 verification
 replication
 validation
 measuring unobservable terms
Conclusion: Why structuralist
reconstruction?

18. Informatik
ESSA @work, TUHH, 22/11/201813/11/201 19/ 2113/11/2018
 verification supported by a structuralist
reconstruction of a mental model or an
available simulation model
 replication supported by reconstructing an
existing model and converting it into a new
model, perhaps with entirely different tools,
on the grounds of the structuralist
axiomatisation
Conclusion: Why structuralist
reconstruction?

19. Informatik
ESSA @work, TUHH, 22/11/201813/11/201 20/ 2113/11/2018
 validation: structuralist reconstruction makes
clear
 which of the simulation model terms represent real-world
terms and hence can be observed without using the theory
whose potential and partial models are defined in this
reconstructions — here GDS-non-theoretical terms — and
 which of these terms can only be made measurable as
GDS-theoretical terms
Conclusion: Why structuralist
reconstruction?

20. Informatik
ESSA @work, TUHH, 22/11/201813/11/201 21/ 2113/11/2018
 measuring θ-theoretical terms with the help
of simulation output by finding out which
values of these terms lead to simulation runs
whose output fits measurements of θ-non-
theoretical terms best
Conclusion: Why structuralist
reconstruction?

21. Informatik
ESSA @work, TUHH, 22/11/201813/11/201 22/ 2113/11/2018
Thank you for your attention
The research leading to the results of the gender equal opportunities examples
received funding from Deutsche Forschungsgemeinschaft under grant KR 960/5-
1 and -2 (,,Einführung und Auswirkung der Koedukation. Eine Untersuchung an
ausgewählten Gymnasien des Landes Rheinland-Pfalz“)
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