1. A Cognitive inspired algebra for
the Cognitive Heuristics Modeling
A. Guazzini
AWASS 2012
Edinburgh 10th-16th June

2. A Tri-Partite Model
of Cognitive Heuristics
Reaction time
Module I Flexibility
Unconscious knowledge
perceptive and attentive processes
Cognitive costs
Relevance Heuristic
Module II
Reasoning
Goal Heuristic
External Recognition Heuristic
Solve Heuristic
Data
Module III
Learning
Behavior
Evaluation Heuristic
The minimal structure of a Self Awareness
cognitive agent
AWASS 2012
Edinburgh 10th-16th June

3. A Tri-Partite Model
of Cognitive Heuristics
AWASS 2012
Edinburgh 10th-16th June

4. A Tri-Partite Model
of Cognitive Heuristics
Module I
Unconscious knowledge
perceptive and attentive processes Processes the external information and extract the context from it
Relevance Heuristic
Module II Estimates the objectives, Performs actions and Decides to stop (i.e.
Reasoning
physical and mental behaviors) as a consequence of a decision making
Goal Heuristic
Recognition Heuristic processing
Solve Heuristic
Module III
Learning Evaluates the achievements and gives feedbacks for the improvement
Evaluation Heuristic (evolution) of the system on different timescales.
Each module is composed by Schemes and Heuristics. Schemes deal with external data and
actions, while Heuristics control the working of schemes.
AWASS 2012
Edinburgh 10th-16th June

5. (I) Module A
Activation Pattern
(To be matched with k)
Input Vector
I Score
(Previous Experience)
Hard
I1 A Schemes
Confidence
Wired
Biological I2 A1 (To be matched with I and k)
Filtering
.
Delta K
. (Modification of K*)
Relevance
(N) . . Heuristic
In(I) .
1  I  n(I)
k1 An
n(I) 6= N
k2
1  k  n(k)
.
n(k) << N kn(k) Module
kA *: The activation of the A-Scheme implies a modification of the knowledge
B
Knowledge Vector Perceptive Vector (kA)
AWASS 2012
Edinburgh 10th-16th June

6. (I) Module A
“Input” Processing
The processing of the input information I is performed by schemes denoted A(i), characterized by:
- An activation pattern P(i), that is presented to the context K. If there is a sufficient strong match
(detailed below), the scheme is activated and can access the input I.
- A processing unit, W(i) that can be thought as a set of perceptrons, that takes input from I and K.
- The application of the processing unit to the input gives a proposed modification of the context
and a score.
˜(i)
k Knowledge modification
(i) Score of the Scheme
- The confidence that the scheme has about its capability of deal with the actual input I.
- Finally, schemes have a reputation S(i) (score) , that serves to estimate the success rate of the
scheme itself.
AWASS 2012
Edinburgh 10th-16th June

7. (I) Module A
Knowledge represention
K
Unconscious Working Memory
A (Knowledge)
K
Conscious Working Memory
(Knowledge)
KB
Pre- Since all schemes and Heuristics
⇥(A)
Activation
Thresholds communicate through the context K,
⇥(B) the vector K could be arranged in
Confidence
Thresholds
(A)
(B)
several sections
Goal
Section
G
Constraint
Time Section
Bandwidth
A crucial part of the context is devoted to goals and
Resources C constraints, and governed by the module II
Access AWASS 2012
....
Edinburgh 10th-16th June

8. (I) Module A
“Input” Processing A(i)
A Scheme
In order to introduce the model it
is possible to follow the processing
of the input information
I
The processing of the input
information I is performed by the
first building block of the model,
the A-Schemes, denoted A(1).
AWASS 2012
Input Edinburgh 10th-16th June

9. (I) Module A Activation
Pattern
(A scheme) A(i) Pi 2 ( 1, 1)
KnowledgeA A Scheme (A)
X (A)
Unwanted i = Pj K j
-1 Feature
Irrelevant j
0 (A)
K A
Pre-
1
Feature
Wanted i 2 (0, 1)
Activation ... Feature
(A)
Threshold
✓i 7⇥ (A)
⇥(A)
The first step of input information introduces some
cognitive pre-attentive elements, and is represented
by the computation of an Activation Pattern (Pi), that
is matched with the model-A context part (KA). If
there is a sufficient strong match the scheme is
activated and can access the input I.
In general the activation level can be
modeled as a perceptron
I X
= tanh( Pj K j )
j
Input AWASS 2012
Edinburgh 10th-16th June

10. (I) Module A Activation
Pattern
(A scheme) A(i) Pi 2 ( 1, 1)
KnowledgeA A Scheme (A)
X (A)
Unwanted i = Pj K j
-1 Feature
Irrelevant j
0 (A)
K A
Pre-
1
Feature
Wanted i 2 (0, 1)
Activation ... Feature
Threshold (A)
F ✓i 7⇥ (A)
Flag
⇥ (A) Memory
The activation state is accumulated
into an activation memory F, that
serves for the a-posteriori evaluation
I of the performances
AWASS 2012
Input Edinburgh 10th-16th June

11. (I) Module A Activation
Pattern
(A scheme) A(i) Pi 2 ( 1, 1)
A Scheme
KnowledgeA
A processing unit, W that is formed
A Flag Pi by arbitrary functions (can also be
K Memory a neural network), that takes input
F from I and K
Confidence
Function
Constraint (I)
Time Section
Bandwidth i
Resources
Access
C (T )
.... j
The Knowledge vector is
characterized also by a Constraint
Section, where the time and
resources limits are considered.
I Such section is integrated into the
Wi
Sub confidence function
Processing
Unit
AWASS 2012
Input Edinburgh 10th-16th June

12. (I) Module A Activation
Pattern
(A scheme) A(i) Pi 2 ( 1, 1)
A Scheme
KnowledgeA The first component of Wi0 gives the confidence
level. This quantity measures the confidence that the
scheme has about the actual input I, given the context
A Flag Pi (KA) and the constrains (T).
K Memory Confidence
F
Function i
W0 = i
(A)
X (I)
X (T )
Time
Constraint
Section
(I)
i = i Ii + j Tj
Bandwidth i
i j
Resources C
Access
....
(T )
j
(A)
2 (0, 1)
(A)
i 7 (A)
The confidence of the scheme is compared with a
threshold, also in the context. However, the
confidence is also processed in a competitive way
I with other active schemes, and this may bring to the
Wi modification of the confidence threshold.
Sub
Processing
(A)
7 (A)
Unit
Input
i

13. (I) Module A Activation
Pattern AWASS 2012
(A scheme) A(i) Pi 2 ( 1, 1) Edinburgh 10th-16th June
A Scheme
KnowledgeA
The application of the processing unit to the input
A Pi gives a proposed modification of the context.
Flag
K Memory Where the first term symbolizes that the relevant
activating pattern is removed (or decreased) from
F the context K(A)
Confidence
Function
Constraint (I)
Time Section This modification is accepted by the Relevance
Bandwidth i Heuristics if the confidence level is sufficiently hight,
Resources
Access
C (T ) and if there are no conflicting modifications
.... j K
Function
(A) X X
W1j
W2j Ki = f ( wij Ij ) + g( wij Kj )
Confidence ... i i
Threshold Wnj K (A)
= ˜ (A) + K (A)
P ˜
I ˜
K (A)
Wi K (B) ˜ (B)
=K
Sub
˜
K (B)
Processing
Unit Modifications
Input produced by the
Activated Scheme

14. (I) Module A Activation
Pattern AWASS 2012
(A scheme) A(i) Pi 2 ( 1, 1) Edinburgh 10th-16th June
A Scheme
KnowledgeA
A Pi
K
F
Flag Confidence
Memory Function
Constraint (I)
Time Section
Bandwidth i
Resources
Access
C (T )
.... j K
Function
(A)
W1j
W2j
Finally, Schemes have a “reputation” score S, that
Confidence ...
serves to keep memory of the success rate of the
Threshold Wnj
scheme itself. It is managed by the evaluation
I ˜
K (A) heuristics of module III.
Wi ˜
Sub K (B)
Processing
Unit Memory of Past
Reputation Performances
Input (Representativity)

15. (I) Module A Activation
(A scheme) A(i)
Pattern
Pi 2 ( 1, 1) (A)
X (A)
KnowledgeA A Scheme i = Pj K j
Unwanted j
-1 Feature (A)
0 Irrelevant
i 2 (0, 1)
A Feature
K 1 Wanted
Pre- (A)
Activation ... Feature ✓i 7 ✓(A)
Threshold
F (A)
X (I)
X (T )
Flag Confidence i = i Ii + j Tj
⇥ (A) Memory Function
i j
Constraint (I)
Time
Bandwidth
Section
i (A)
2 (0, 1)
Resources
Access
C (T )
K (A)
.... j
Function i 7 (A)
(A) X X
W1j
W2j Ki = f ( wij Ij ) + g( wij Kj )
Confidence ... i i
Threshold Wnj K (A)
= ˜ (A) + K (A)
P ˜
I ˜
K (A)
˜ (B)
Wi ˜ K (B)
=K
Sub K (B)
Processing
Unit Memory of Past Modifications
Input
Reputation Performances S 2 (0, 1) produced by the
(Representativity) Activated Scheme

16. (I) Module A Activation
Pattern AWASS 2012
Relevance Heuristic A(i) Pi 2 ( 1, 1) Edinburgh 10th-16th June
A Scheme
KnowledgeA
Unwanted
-1 Feature
Priming and Salience
0 Irrelevant
A Feature
K 1 Wanted
Pre-
Activation ... Feature By means of the activation pattern we can
Threshold model the attentive and neglective
F mechanisms of processing input.
Flag
⇥ (A) Memory
In an attentive phase, the context promotes
the activation of schemes that “search” or
refine a search on the input.
All communication among schemes happens
via the context.
LUCKY STRIKE
I
Input

17. (I) Module A Activation
Pattern
Relevance Heuristic A(i) Pi 2 ( 1, 1)
KnowledgeA A Scheme Cognitive Blindness
Unwanted
-1 Feature On the other hand, the presence of a pattern
0 Irrelevant
Feature
in the input which is not recognized by any
A 1 active scheme is simply ignored.
K Pre- Wanted
Activation ... Feature
Threshold
F The Nine
⇥ (A)
Flag
Memory Invisible Dolphins
This has the effect of “neglecting”
the presence of “camouflaged”
objects but has the advantage of
reducing enormously the number
of activated schemes, therefore
I decreasing the response time.
Input

18. (I) Module A Activation
Pattern
Relevance Heuristic A(i) Pi 2 ( 1, 1)
KnowledgeA A Scheme Perceptive Affordance
Confidence The confidence level has the goal of
Function signaling to the relevance heuristics that the
A Flag Pi input I has been processed in a correct way,
K Memory since the scheme are activated according to
the context.
F
Constraint (I)
Time Section
Bandwidth i
Resources
Access
C (T )
.... j
Equality Failure
A Non Triangle
I
Wi
Sub It may happen that a context is equivocated, and the
Processing
Unit activated schemes are unable to identify the objects or
Input patterns in the input, and signal it using this level

19. (I) Module A Activation
Pattern
Relevance Heuristic A(i) Pi 2 ( 1, 1) Cognitive and Perceptive
A Scheme
KnowledgeA Bystability
Pi The modification of the context (frequently
A
Pre- K operated by the A-Schemes activation) may bring to
Activation the inactivation (actually a missing reactivation) of
Threshold the scheme that proposed the modification.
F
Flag Confidence
⇥(A) Memory Function
Constraint (I)
Time Section
Bandwidth i
Resources
Access
C (T )
.... j K
Function
(A)
W1j
W2j
Confidence ...
The normal chaining of schemes actually can be thought
Threshold Wnj
as a never ending process where: given a context a
I ˜
K (A) scheme is activated and it modifies the context so that
Wi another scheme is activated .. etc etc
Sub
˜
K (B)
Processing
Unit Memory of Past
Reputation Performances
Input (Representativity)

20. (I) Module A Activation
Pattern
Relevance Heuristic A(i) Pi 2 ( 1, 1)
KnowledgeA A Scheme Apperceptive Analisys
It may happen that no schemes have a sufficiently high
confidence level, in this case the Relevance Heuristics
A Pi has to play a role (for instance by deleting part of the
Pre- K context, consequently ignoring part of the input) or by
Activation
Threshold forcing a sub-score scheme.
Confidence
⇥(A)
Function
The Rorschach legacy
Constraint (I)
Time Section
Bandwidth i
Resources
Access
C (T )
.... j
(A)
W1j
W2j
Confidence ...
Threshold Wnj
I ˜
K (A) One of the most typical human behavior is: since I am
pressed I apply the first scheme that comes to my
Wi ˜
Sub K (B) mind, even if we are in a different context
Processing
Unit
Reputation
Input

21. Module A
AWASS 2012
Edinburgh 10th-16th June

22. (II) Module B
Activation Pattern
(To be matched with k)
Goal
Input Vector
I Score Heuristic
(Previous Experience)
I1 B Schemes
Confidence Solve
Module I
Inputs I2 B1 (To be matched with I and k)
Heuristic
.
Delta K
. (Modification of K*)
. . Recognition
(KA) Heuristic
In(I) .
EXIT
k1 Bn
k2
Action
.
kn(k)
kB
Knowledge Vector
Module
I
*: The activation of the B-Scheme implies a modification of the knowledge Vector (kB)

23. (II) Module B B(i)
B Scheme X
(B scheme) (B) (B)
-1 Pi 2 ( 1, 1)
Activation i = Pj K j
KnowledgeB 0 Pattern
1 j
(B)
Pre-
...
i 2 (0, 1)
B Activation
Pre- K Threshold (B)
Activation ✓i 7 ⇥(B)
Threshold
⇥(B)
Activation Pattern
Schemes in module B are similar to
that of module A, except that they may
trigger the execution of actions.
Each scheme B(i) is characterized by an
Activation Pattern P, that is matched
with the model-B context part K(B). If
there is a sufficient strong match the
scheme is pre-activated.

24. (II) Module B B(i)
B Scheme X
(B scheme) (B) (B)
-1 Pi 2 ( 1, 1)
Activation i = Pj K j
KnowledgeB 0 Pattern
1 j
(B)
Pre-
...
i 2 (0, 1)
Activation Activation
Pre- K B
Threshold F Level (B)
Activation ✓i 7 ⇥(B)
Threshold
Flag
⇥(B)
Memory Activation State
The activation level, similar to A-schemes, is
compared with the Pre-Activation Threshold.This
gives the Activation State
The Pre-Activation Threshold is manipulated by
the Recognition Heuristics
Finally the activation state is accumulated into
an activation memory F

25. (II) Module B B(i)
B Scheme AWASS 2012
(B scheme)
Edinburgh 10th-16th June
KnowledgeB
Pi
Confidence
Function
Confidence Level
Pre- K B F
Activation
Threshold
(I)
(B)
X (I)
X (T )
i
i = i Ii + j Tj
⇥(B) i j
Constraint (T )
Time Section (B)
2 (0, 1)
j
Bandwidth
i
Resources
Access
C
(B)
....
i 7 (B)
(B)
The Confidence Level of the pre-activated
Confidence B-schemes is compared with the
Threshold
threshold by the Recognition Heuristics,
which implements a competition among
Wi B-schemes
Sub
Processing
Unit

26. (II) Module B B(i)
B Scheme
(B scheme)
The Context (K) Modification
KnowledgeB
Pi
Confidence The application of the processing unit (W) to
Function
the input gives a proposed modification of the
Pre- K B F context, that has a generic symbolic form.
Activation
Threshold
(I)
i ˜ (A) This quantity serves for activating other
K A-schemes for further (required) input processing.
⇥(B)
Constraint (T )
Time Section j
Bandwidth
Resources C ˜ (B)This quantity represents the modification of the B-
K
Access W1j context that activates other B-schemes
....
W2j
(B) K ...
Function This quantity represents the “advancements” of
Wnj G the goals (estimated by the Solve Heuristic).
Confidence
˜
K (A) X X
Threshold
˜
K (B)
Ki = f ( wij Ij ) + g( wij Kj )
i i
Wi
Sub K (B)
= P ˜ (B) + K (B)
˜
˜ (A)
Processing
Unit
K (A) =K K (G)
= G
Modifications produced by the Activated Scheme

27. (II) Module B B(i)
B Scheme AWASS 2012
(B scheme) Pi 2 ( 1, 1) Edinburgh 10th-16th June
Activation
KnowledgeB
Pi Pattern
Reputation (Score)
Pre- Confidence
Activation Function
Pre- K B
Threshold F
Activation Also B-schemes have a “reputation” score S,
Threshold
Flag
(I) that is considered by the Recognition
i
Memory Heuristics in the activation process.
⇥(B)
Constraint (T ) (also cited as Availability Heuristics)
Time Section j
Bandwidth
Memory of past
Resources
Access
C W1j performances S(i)
....
W2j S 2 (0, 1)
(B)
K ...
Function
Wnj
˜
K (A)
Confidence
Threshold
Actions
˜
K (B)
The B-schemes produce Action (i.e. Behavior),
Wi Reputation
Sub which can be physical or mental behavior.
Processing
Unit Action
Physical or Mental Action produced
if the B-Scheme is activated

28. (II) Module B B(i)
B Scheme AWASS 2012
(B scheme) Pi 2 ( 1, 1) Edinburgh 10th-16th June
Activation
KnowledgeB
Pi Pattern
Pre- Confidence
Activation Function
Pre- K B
Threshold F
Activation
Threshold
(I)
Flag
⇥(B)
Memory
i
Goal
Constraint (T )
Time Section j
Bandwidth The knowledge vector K(B) contains also a
Resources
Access
C W1j representation of the Goal furnished by the
....
W2j Goal Heuristics (i.e. a “specific” list of B-
(B) K ... schemes which have to be partially or
Function Wnj completely revealed into the K(B) and associated
Confidence
˜
K (A) with the reward - Pavlov). Such part of the
Threshold
˜ vector is used later by the Solve Heuristics in
K (B)
G order to stop the mental processing
Wi Reputation (Reasoning)
Sub
Processing
Unit Action
Goal
Managed by Solve
Heuristics

29. (II) Module B B(i)
B Scheme X
(B scheme) (B) (B)
Pi 2 ( 1, 1)
Activation i = Pj K j
KnowledgeB
Pi Pattern
j
(B)
Pre- Confidence i 2 (0, 1)
Activation Function
Pre- K B
Threshold F (B)
Activation 7 ⇥(B)
✓i
Threshold
Flag
(I)
(B)
X (I) X (T )
Memory
i
i = i Ii + j Tj
⇥(B) i j
Constraint (T )
Time Section K (B)
2 (0, 1)
j
Bandwidth Function
i
Resources
Access
C W1j
(B)
....
W2j i 7 (B)
(B) ... X X
Wnj Ki = f ( wij Ij ) + g( wij Kj )
Confidence
˜
K (A) i i
Threshold
˜ K (B)
= P˜ (B) + K (B)
˜
K (B)
G K (A) ˜ (A)
=K K (G) = G
Wi Reputation
Sub Modifications produced by the Activated Scheme
Processing
Unit Action
Goal Physical or Mental Action produced
Managed by Solve
Heuristics
if the B-Scheme is activated

30. Pi 2 ( 1, 1)
(II) Module B B(i)
B Scheme Activation
Pattern AWASS 2012
Recognition Heuristics
Edinburgh 10th-16th June
Confidence
KnowledgeB Pi Function
Recognition Phase
✓(B)
Pre-
Activation
Pre- K B
Threshold F
Activation
Threshold
Flag (I)
Recognition
Memory i Heuristic
⇥(B)
Constraint (T )
Time
Bandwidth
Section j Activated
Resources
Access
C W1j
....
W2j
Confident
(B) ...
K Wnj Competition
Confidence
Function ˜
K (A)
Threshold
˜
K (B)
G
Wi Reputation
The Recognition Heuristics is similar to the
Sub
Processing
Unit Action Relevance, and triggers the activation of the
Goal B-schemes
Managed by Solve
Heuristics

31. Pi 2 ( 1, 1)
(II) Module B B(i)
B Scheme Activation
Pattern AWASS 2012
Recognition Heuristics
Edinburgh 10th-16th June
Confidence
KnowledgeB
Pi Function
Goal Phase
Pre- Memory
B Activation
F M
Pre- K Threshold
Activation
Threshold Goal
Flag (I)
Memory i Heuristics
⇥(B)
Constraint (T )
Time j
Section
Bandwidth
Resources
Access
C W1j Evaluate Progress
....
W2j
(B) ...
Wnj
Confidence
˜
K (A) K
Function
Threshold
˜
K (B)
G The Goal Heuristics is devoted to the
Wi Reputation
establishment of goals and constraints, and
Sub
Processing
Unit Action it make use of a conventional memory M,
Goal where past experiences are recorded
Managed by Solve
Heuristics

32. Pi 2 ( 1, 1)
(II) Module B B(i)
B Scheme Activation
Recognition Heuristics Pattern
Confidence
Solve Phase
KnowledgeB Pi Function
Memory
✓(B) M
Pre-
Activation
Pre- K B
Threshold F Solve
Activation
Threshold
Flag (I) Heuristics
Memory i
⇥(B)
Constraint (T )
Solved
Time
Bandwidth
Section j Abort
Resources
Access
C W1j Escape
....
W2j
(B) ...
K Wnj
Confidence
Function ˜
K (A) EXIT
Threshold
˜
K (B)
G The Solve Heuristics has the task of checking if the
Wi Reputation
Sub task has finished, it it should be aborted (say, for loss
Processing
Unit Action of time) or restarted if a dead-end is detected. It
Goal stores this information in the memory M
Managed by Solve
Heuristics

33. (II) Module B
AWASS 2012
Edinburgh 10th-16th June

34. (III) Module C Evaluation Heuristics
K
Mirror
Knowledge
Vector Hebbian Schemes
Learning
n(KA) k1
Module I
Inputs k2 Activated/Flagged
A Schemes
. Imitation
n(KB)
Emulation A1 . An
Module II
.
Inputs
.
.
B1 . Bn
. Trial & Error Activated/Flagged
B Schemes
kn(k)
Simulation
Abstract
Module C has the task of Reasoning
making the system learn. Module
I & II

35. (III) Module C
Evaluation Heuristics
K Hebbian Learning
Unconscious Working Memory
(Knowledge)
K A Goals Accomplished ?
Conscious Working Memory
(Knowledge)
KB Reinforce
Confidence Pre-Activation
Thresholds Thresholds
⇥(A)
⇥(B)
Goal
Section (A) The Hebbian Learning is done using an
(B) appropriate “Hebbian Scheme”, rising the score
of schemes that were activated in a successful
Constraint elaboration and lowering those active in an
Section G unsuccessful one.
Time
Bandwidth
Resources
Access
C S(i) P(i) W(i) F(i) AWASS 2012
.... Edinburgh 10th-16th June
Scheme(i)

36. (III) Module C
Evaluation Heuristics
K Imitation
Unconscious Working Memory
(Knowledge)
K A Score ?
Conscious Working Memory
(Knowledge)
Pre-Activation
KB Thresholds Import from Outside
Confidence
Thresholds
⇥(A) Imitation may serve to duplicate (with or without mutations) successful schemes
⇥(B) replacing unsuccessful ones, or to import new schemes from outside. The
Goal Imitation strategy works in synergy with particular B schemes that we call Mirror
Section (A)
(B) Schemes (MS).
An MS is able to “invert” the normal flux of information. Given a particular
Constraint
pattern in K(A), recognized through K(B) as an action Z, a mirror scheme Bm set
Section G the pattern in K(B) that activates the scheme BZ that will cause the action Z itself.
Time
Bandwidth
Other Agents/Databases
Resources
Access
C S(i) P(i) W(i) F(i)
MIRROR SCHEMES
.... Scheme(i)

37. (III) Module C
Evaluation Heuristics
Trial and Error/Abstract Reasoning
K
Unconscious Working Memory
(Knowledge)
K A Cost?
Conscious Working Memory
(Knowledge)
KB Variate and Simulate
Confidence Pre-Activation
Thresholds Thresholds
⇥(A) The Trial and Error strategy aims at
⇥(B)
Goal
(A)
optimizing the system. By retrieving
Section
(B) pattern from memory and repeating
the elaboration with variations, the
Constraint
G abstract reasoning is able to speed-up
Section
the response time and use less
Time resources (Mental Simulation)
Bandwidth
Resources
Access
C S(i) P(i) W(i) F(i)
AWASS 2012
.... Scheme(i) Edinburgh 10th-16th June

38. (III) Module C
AWASS 2012
Edinburgh 10th-16th June

39. A Cognitive
Time Diagram
Time
AWASS 2012
Edinburgh 10th-16th June

40. AWASS 2012
Edinburgh 10th-16th June
... and thank you for the attention!