Appearance at FIS2010.

1. An emergence of formal logic
induced by an internal agent
Koji Sawa
The Senior High School, Japan Women’s University, Japan
Yukio-Pegio Gunji
Kobe University, Japan
FIS2010
Beijing, China, Aug 21-24, 2010

2. Proposal
• A dynamical model of formal logic
– It is autonomously transformed.
– It is composed of a system and its subsystem.
– It is represented as transformation of directed
graphs.

3. Motivations 1: Logic
• Where does logic come from?
• Our previous work:
Dialogue models as the origin of logic
(Sawa and Gunji, 2007, 2008)
– Each model is represented in the form of a
multi-agent model.

4. Motivations 2: Multi-agent model
• The behavior of a system is influenced by
agents and interactions between agents.
→ System is not autonomous.
• Agent
– autonomy, sociality, ...
→ Agent is external to system.

5. A connection with FIS
• Brenner (2010). Information in Reality. Logic and Metaphysics
“every real complex process is accompanied, logically and functionally, by its
opposite or contradiction (Principle of Dynamic Opposition), but only in the
sense that when one element is (predominantly) present or actualized, the other
is (predominantly) absent or potentialized, alternately and reciprocally, without
either ever going to zero”
→ We realize a concept touching on above by the invalidation of reflexive law.
• Hofkirchner (2010). Four ways of thinking in information
“Reductionism, Projectivism, Disjunctivism, and Integrativism”
→ In my opinion, Reductionism and Projectivism correspond to deduction and
induction, respectively. Just as Hofkirchner claims that Integrativism must be
needed, so we also consider that the third inference abduction must be needed
(cf. Sawa and Gunji, in press).
– Actually in this presentation, we do not treat these inferences directly, however these
inferences are in the scope of our study.

6. A connection with FIS
• Collier (2010). Kinds of Information in Scientific Use
“For each kind of substantive information used in the sciences there is a distinct
level formed by bifurcations that form cohesive structures at the next higher
level. This is reflected in the information at each level, which inherits the
properties of the lower level, but produces new asymmetries at its own level
through the formation of new cohesions peculiar to the level.”
→ We propose an idea of the way to raise a level presented above:
a representation by nonhierarchical, divisible, and incorporable objects.

7. Model

8. Multi-agent model
System
“Emergence” Restriction
Agent
Interaction
• Each agent is autonomous.
→ Agent is independent and external to
system.
→ System refers external.

9. Internal Agent Model
System
“Emergence” Restriction
Agent
Interaction
• Internal agent := A part of a system.
– Internal agent is sometimes abbreviated to agent.
• System never refers external.
– Internal measurement (Matsuno, 1989)
• S-IA interaction := Interaction between system and internal agent.

10. Formal logic represented
by a directed graph
Implicational relation
Arrow
Object Object
Directed Graph

11. Identity and obviousness
of object
• A implies A.
– A is A.
– There is no doubt about the obviousness of
object.
Assuming the
• Derivation of LK obviousness of object
A├ A B ├ B
A, A B ├ B C ├ C
A, A B , B C ├ C
A B, B C ├ A C

12. Soft object
• Soft object := a cycle of arrows
• Example

13. Soft object
• Identity: X → X
Soft Object
X
• If
X → Y, Y → Z, Z → X,
then X
X X
Y Y
Z Z.
(assuming transitive law) Y Z
Soft Object

14. Soft object
• Soft object := a cycle of arrows
• Example
Number of arrows
Soft Hard
(breakable) less （nonbreakable）
more

15. Identity and obviousness
of object
• Equivalence law:
(Condition that a set is treated as one unit)
– Reflexive law: A→A
– Symmetric law: A → B implies B → A
– Transitive law:
A → B and B → C implies A → C
• A soft object (except the hardest one (a
complete graph)) is an object in which the
equivalence law is partially invalidated.

16. Soft arrow
• Soft arrow :=
a bundle of arrows in the same direction.
• Example
Number of arrows
Soft Hard
(Breakable) Less More (Nonbreakable)

17. Summary of model
from a logical perspective
• Formal logic
– Represented by a directed graph.
– Consists of objects and arrows.
• Object
– Represented by a cycle of arrows.
– Soft object
• Arrow
– Represented by a bundle of arrows
– Soft arrow

18. Interaction between system and agent
in formal logic
× System
× Agent
• Agent influences system through pursuit of agent’s “purpose”.
• System influences agent through pursuit of system’s “purpose”.

19. Transitivity Rate (TR)
• Def. Given a directed graph G,
T R : |G | / |G | ,
where |G | : the number of arrows in G,
G : the graph transformed from G,
in which the transitive law holds
completely by adding requisite
arrows.

20. Transitivity Rate (TR)
• Example
Assuming
transitive law
TR=3/4=0.75
• Transitivity rate (TR) is one of measures of
reliability of a directed graph as formal logic.
• Agent’s purpose := increase of TR.

21. S-IA interaction
Agent → System System → Agent
– Add an arrow satisfying below – Add an arrow satisfying below
conditions to system conditions to agent
• increases TR of agent; • increases TR of system;
• does not exist in system; • does not exist in agent;
• shares at least one node with • shares at least one node with
arrows of agent. arrows of agent.
System
S-IA interaction:
succession of applications
of transitive law to two parts:
system and agent.
Agent

22. Example of time transitions
t=k by S-IA Interaction
System
Agent
t=k+1

23. Trial 1
• What kind of graphs emerge by S-IA interaction?
S-IA Interaction
Random graph ?

24. Result of Trial 1
• Initial random graph (50 nodes)
– All arrows: System
– A subset of arrows: Agent
• Convergent graph
– There are soft objects and soft
arrows among soft objects.
– All soft objects and soft arrows are
hardest ones.
– Transitive law holds among soft
arrows.
• In sum, a graph representing
formal logic in which the transitive
law holds completely.
Compress Another result

25. Trial 2
• Trial 1
S-IA Interaction
Graph representing
Random graph
formal logic
• Trial 2
What happens if the obviousness of objects is
invalidated in the emergent graph representing
formal logic?
Invalidation of the obviousness of objects
= Invalidation of reflexive law (A → A)
= Elimination of arrows in soft objects

26. Initial random graph of Trial 2




0 1 0 0

0 0 1 0
0 0 0 1
0 0 0 0
0 0 0 0
• Invalidation of the obviousness of
objects
• Softening of arrows




0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

27. Hardest soft arrows
S-IA Interaction
System
Choose arrows
Rate: p
Agent
Choose arrows
Rate: q

28. Initial graph (p=1.0, q=0.75)
System (100 arrows) Agent (82 arrows)


 


 
0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
 
0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
 
0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
 
0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
 
0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
 
0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0
 
0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0
 
0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0
 
0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0
 
0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0
 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0
 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0
 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0
 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0
 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 0 0
 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1
 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1
 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1
 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1
 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1
 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

29. Result 1 (p=1.0, q=0.75)


 


 •
0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Soft objects and soft arrows
 
1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 
1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 
1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
emerge as the hardest ones.
 
1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 
0 0 0 0 0 0 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 
0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 
0 0 0 0 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
•
  Transitive law holds among
0 0 0 0 0 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 
0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1
 
0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 1 1 1 1 1 1 1 1
soft arrows.
 
0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1
 
0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1
 
0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 1 1 1 1 1 1 1 1
 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1
 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 1 1 1
•
 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 1 1 1 1
Convergent graph represents
 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 1 1 1 1
 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 1 1 1
 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
1
1
1
0
1
1
1
formal logic.
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0
1 6 11 16 21
2 7 12 17 22
3 8 13 18 23
4 9 14 19 24
5 10 15 20 25

30. Result 2 (p=0.5, q=0.5)


 


 
0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 
1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 
1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 
0 0 0 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 
0 0 0 0 0 1 0 0 0 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1
 
0 0 0 0 1 0 0 0 0 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1
 
0 0 0 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 
0 0 0 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 
1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 
0 0 0 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 1 1 1 1
 
0 0 0 0 1 1 0 0 0 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1
 
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 1 1 1 1 1 1
 
0 0 0 0 1 1 0 0 0 0 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1
 
0 0 0 0 1 1 0 0 0 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1
 
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 1 1 1 1 1
 
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 1 1 1 1 1
 
0 0 0 0 1 1 0 0 0 0 1 1 0 1 1 1 1 0 1 1 1 1 1 1 1
 
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 1 1 1 1 1
 
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 0 1 1 1 1 1
 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 0 1 1 0 1 1
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 0 1 1 1 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0
1 6 11 16 21
2 7 12 17 22
3 8 13 18 23
4 9 14 19 24
5 10 15 20 25

31. Summary of results of Trial 2
• Convergent graph represents formal logic.
– Soft objects and soft arrows emerge as the hardest ones.
– Transitive law holds among soft arrows.
• “Latent” objects expected from soft arrows become valid
objects.
– Emergence of definite (=valid=“hardest”) concept
– Furthermore, emergence in the different forms than expected
ones
• Internal Agent Model realizes dynamical formal logic,
– in which logical structure is roughly retained.

32. Summary of results of Trial 2
X Y
X = A∧B Y = A∨B
A
A∧B A∨B
B

33. Summary of results of Trial 2
q Agent
1 0
p1
(A) Number of soft objects consisting of multiple nodes Similar to
former logic
System
(B) Number of singletons (soft objects consisting of only one node)
(C) = (A) + (B)
(D) Number of soft objects which are composed of nodes of Dissimilar to
different latent objects former logic
0
q 1 .0 0 0 .7 5 0 .5 0 0 .2 5
p (A ) (B ) (C ) (D ) (D )/(C ) (A ) (B ) (C ) (D ) (D )/(C ) (A ) (B ) (C ) (D ) (D )/(C ) (A ) (B ) (C ) (D ) (D )/(C )
1 .0 0 (1 ) 9 0 9 1 0 .1 1 8 4 12 0 0 .0 0 9 7 16 2 0 .1 3 5 0 5 4 0 .8 0
(2 ) 8 1 9 2 0 .2 2 6 4 10 0 0 .0 0 6 0 6 3 0 .5 0 4 2 6 3 0 .5 0
(3 ) 8 0 8 0 0 .0 0 8 1 9 2 0 .2 2 6 1 7 3 0 .4 3 4 0 4 3 0 .7 5
A ve. 0 .1 1 0 .0 7 0 .3 5 0 .6 8
0 .7 5 (1 ) 7 0 7 2 0 .2 9 8 3 11 5 0 .4 5 6 2 8 3 0 .3 8 5 0 5 4 0 .8 0
(2 ) 9 3 12 3 0 .2 5 9 3 12 5 0 .4 2 6 0 6 4 0 .6 7 5 0 5 4 0 .8 0
(3 ) 8 2 10 4 0 .4 0 8 2 10 3 0 .3 0 2 0 2 1 0 .5 0 4 0 4 2 0 .5 0
A ve. 0 .3 1 0 .3 9 0 .5 1 0 .7 0
0 .5 0 (1 ) 11 1 12 4 0 .3 3 6 5 11 5 0 .4 5 10 3 13 5 0 .3 8 6 1 7 4 0 .5 7
(2 ) 7 9 16 1 0 .0 6 11 0 11 4 0 .3 6 5 2 7 4 0 .5 7 3 1 4 3 0 .7 5
(3 ) 9 2 11 5 0 .4 5 7 4 11 3 0 .2 7 6 5 11 4 0 .3 6 3 3 6 2 0 .3 3
A ve. 0 .2 8 0 .3 6 0 .4 4 0 .5 5
0 .2 5 (1 ) 9 5 14 4 0 .2 9 8 1 9 8 0 .8 9 5 3 8 4 0 .5 0 8 0 8 6 0 .7 5
(2 ) 8 4 12 7 0 .5 8 11 2 13 6 0 .4 6 9 2 11 6 0 .5 5 7 1 8 6 0 .7 5
(3 ) 10 1 11 7 0 .6 4 8 5 13 6 0 .4 6 9 5 14 9 0 .6 4 9 1 10 8 0 .8 0
A ve. 0 .5 0 0 .6 0 0 .5 6 0 .7 7

34. Discussions

35. Discussion 1:
From a logical perspective
• Premise
– Reflexive law (A → A) is invalidated.
• This corresponds to invalidation of the obviousness of the
object.
– Transitive law (A → B and B → C implies A → C) is treated
as S-IA interaction,
• which is succession of applications of transitive law to system
(whole) and agent (part).
• Result
– Emergence of objects (Trial 1),
• as the hardest ones.
• Arrows also emerge as hardest ones.
– Emergence of objects expected from arrows (Trial 2),
• in the different forms than expected ones.
• This emergence corresponds to revision of objects due to
relations (arrows) of objects.

36. Discussion 2: Object and agent
• In Internal Agent Model, both soft object and internal
agent are mere subgraphs of system.
• Soft object
– is an alternative to an ordinary object:
• nonhierarchical,
• divisible,
• incorporable.
– represents a concept.
– takes on a spatial extent.
• Internal agent
– is an object which has purpose.
• In Internal Agent Model, internal agent purposes the adequacy
of the system as formal logic.
– takes on a temporal extent.

37. Future studies
• Internal Agent Model
Agent (purpose) → Soft object (concept).
• We would like to treat
Soft object (concept) → Agent (purpose),
– by the argument of the positional relation or inclusive
relation among soft objects.
• Mediation of Object-Relation Model
(Sawa and Gunji, in press)
– represents expansion and contraction of objects and
relations among objects.
– This model implies two fundamental logical
inferences, deduction and induction in the form of
classification of C. S. Peirce. In addition, it also implies the
third inference of Peirce, abduction, which is usually
disregarded.

38. Thank you very much
for your attention.