1. Choi, Jinyoung Program in cognitive science
Chapter 2. A Constructive Approach To Models Self-Modifying Systems in Biology and Cognitive Science Ch.2.
Choi, Jinyoung
Program in cognitive science

2. Contents 2.7 The Concept of Information Set
2.8 Encoding of Observables into Variables
2.9 The Modelling Relation
2.10 Implications
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3. 2.7 The Concept of Information Set
Definition
Description of specific observations on specific observables in a given time interval
We use a notation I. I i to j means observation on specific observables between time step i to time step j
Look at the Figure 2.7. I1 means that we observed X1=2 and X2=3 at time step 1. I12 means that we observed X1=2 ,X2=3 at time step 1 and X1=7,X2=2 at time step 2
The definition of the information set is ‘Description of specific observations on specific observables in a given time interval.
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4. 2.7 The Concept of Information Set
Example
These are turing machines. They read tape with their heads. Think about the turing machine with one head reads tape length of n.
The machine will need n time steps. Therefore the tape will be described as I1n.
Let’s think about simple example.
Now consider the machine with n heads. It will only take 1 time step to read whole tape.
Thus, the tape will be described as I1
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5. 2.7 The Concept of Information Set
Complexity theorem and modelling
A model needs empirical data and observables.
Different models need different data or encoding operations.
Information sets directly contribute to the number of encoding operation steps.
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6. 2.8 Encodings of Observables into Variables
maps observables to variables
encoding has a role similar to that of the empirical information about the system.
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7. 2.8 Encodings of Observables into Variables
Cases of encoding
(1) Dynamic observables and dynamic variables
‘Dynamic’ means they have temporary and transitory nature. they are temporarily available and temporarily observable.
In this case, the encoding is simply a list of paired dynamic variables and dynamic observables. They always have a one-by-one correspondence.
There are three cases of encoding. The first case is encoding dynamic observables to dynamic variables.
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8. 2.8 Encodings of Observables into Variables
Cases of encoding
(2) Dynamic observables and Static variables
For example, we can encode the number of antigens in an organism to a time variable.
At different time, different antigens are present so there are great number of temporary observations. But we have one static variable that measures their total number.
The second case is encoding of dynamic observables to static variables.
This case is many-to-one encoding and it is closer to practical modelling.
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9. 2.8 Encodings of Observables into Variables
Cases of encoding
(3) Static observable and static variable
We can achieve this by defining various dynamic observables by states of a measuring device.
For example, we can use thermometer’s state to encode energy state of water.
The Third case is encoding of static observables to static variables.
This is probably the most familiar case. A measuring device can itself provide a method for labelling the dynamic observables.
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10. 2.8 Encodings of Observables into Variables
Encoding for modelling
The structure of the measuring device and the structure of the studied process must be kept unrelated. (otherwise, best measuring device will be dynamics itself)
Encodings must be done separately from dynamics
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11. 2.9 The Modelling Relation
Natural systems (N)
Domain of reality delimited by interaction
Cannot be defined by a description or a model
often being defined by natural entities.
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12. 2.9 The Modelling Relation
Abstraction
Subset of natural system
narrowing down interest from a totality of potentially measurable qualities to the subset which will be studied
Dynamic observables can be not available at the time when we form the abstraction. So the focus can only be defined as a phenomenal domain.
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13. 2.9 The Modelling Relation
Description Frame (d-frame)
unified notion to thefactors that influence model building.
Link between description D to a natural system N
abstraction, information set, encoding, postulates
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14. 2.9 The Modelling Relation
Overall scheme of the modelling relation
A model is not just a description. A model is a description plus a description frame together.
Figure is overall scheme of the modelling relation.
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15. 2.9 The Modelling Relation
Interpretation
First, we need to decode variables into observables.
And then, information set used by the description has to be identified.
Lastly, postulates such as time or causality need to be identified.
The correspondence of a description to a natural system is not a straightforward matter.
Models cannot be read out directly. They have to be interpreted.
Interpretation is an intricate process that may involve also formal elements. Figure shows elements of interpretation
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16. © 2015, SNU CSE Biointelligence Lab., http://bi.snu.ac.kr
2.10 Implications
Relevance of Models
Which model is better between equally valid descriptions?
adequacy : questions asked by the observer can be encoded into the description
interpretable : model is possible to assign an interpretation to it and the interpretation is acceptable.
Relevant : adequacy + interpretable -> good model
© 2015, SNU CSE Biointelligence Lab.,

17. © 2015, SNU CSE Biointelligence Lab., http://bi.snu.ac.kr
2.10 Implications
Relevance of Models
Which model is better between equally valid descriptions?
adequacy : questions asked by the observer can be encoded into the description
interpretable : model is possible to assign an interpretation to it and the interpretation is acceptable.
Relevant : adequacy + interpretable -> good model
© 2015, SNU CSE Biointelligence Lab.,

18. © 2015, SNU CSE Biointelligence Lab., http://bi.snu.ac.kr
2.10 Implications
Reduction and Equivalence
reduction : One model can be mapped to another
weak(mathematical) equivalence : mathematical descriptions are mathematically identical
strong equivalence : weak equivalence + equivalence of interpretations
strongly equivalent descriptions can replace one another
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19. Questions & Disussions
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