Lecture 5 Emotion Logic Encounter

8/2/2019 Lecture 5 Emotion Logic Encounter

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A Machine Learning Approach to

the Stabilization of EmotionalDynamics in Emotion-Logic

Encounter

1Aruna Chakraborty, 2Amit Konar, 1Amit K. Siromoni

and3Atulya Nagar

1 St. Thomas College of Engg. & Tech.,2Jadavpur University

3LiverpoolHope University


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What is Emotion-Logic

Encounter?Example 1: A person is suffering from cancer,

and is at deaths door. Logic favors the patients

death to relieve him from pain, but emotionallypeople wish him to survive, so as not to misshim for ever.

Example 2: Suppose, a girl wants to marry her

lover, but friends and relatives for certain socialreasons ask her not to marry her beloved. Thegirl is in confrontation of emotion and logic.


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Pre-assumptions for Solving

Emotion-Logic Encounter ProblemPre-assumption 1: Emotional and Logical Reasoning

both share common information resources of the same

context.

Contextual Information

Resources

Reasoning

with

Emotion

Reasoningwithout

Emotion

(Classical)

Inferences guided by Emotion (Pure) Logical Inferences


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Pre-assumptions for Solving

Emotion-Logic Encounter ProblemPre-assumption 2: Changes in external/cognitive influences cause

state transition in one or more co-existing emotions.

Angert

Anxietyt

Happinesst

Sadnesst

Feart

Disgustt

[X]t=[X]0 [X]1 [X]2

Let [X]t= Emotional state at time t.

[X]3

External/cognitive influence atdifferent time

Emotion transition from state [X]0 through [X]3.


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Strategy Used for Solving

Emotion-Logic Encounter Problem

Strategies Used for Solving the Problem

1. Design a formal scheme to represent emotional and

logical reasoning dynamics (methodology).

2. Determine conditions for stability of these two dynamic

systems, and hence stabilize both the dynamics by realizing

the condition for stability.

3. Design strategies to control emotion using logic (or logic

using emotion), depending on personality and desire of the

subject.


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dxi

Representation of Emotional

State Transition by Dynamics

xj

-cki +bji

dt

dxi

dt

=aii (1- xi/k) + bji (xi xj)

j- cki (xi xk)

k

Let xi = i-th element of the emotional state vector X.

xi

xk

aii (1- xi/k)

xj


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An Example Illustrating Emotion

TransitionMother

Happy

Mother

Angry

Mother

Anxious

Mother

Sad

Child victim

of thalasamia

Child under treatment

Discovers wrong

treatment of doctor

Treatment successful

Treatment failure

Treatment failure

x1

x2x3

x4


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Stable, Unstable and Limit Cyclic

Response of Emotional Dynamics

Emotional

Dynamics of

two states x1

and x2

Initial

states:x1(0) and

x2(0)

States: x1(t) and

x2(t) at time t

Stable

Limit Cyclic

Unstable

x1

x2


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Xi

Steps of Stability Analysis of the

Emotional Dynamics Select a suitable Lyapunov

function for the dynamics.

Determine the condition for

stability of the dynamics

using Lyapunov function.

Realize the condition of

stability by selecting

suitable weights of the

transition graph.

dxi

dt

0< W< (aiik/2) (1- xi/k)2

=W,

say

Find aii

satisfying

above

condition.

Stable

Lyapunov:L(xi, xj, xk)= [-(aii k/2) xi(1- xi/k)2 + (bji xj - cki xk) xi dxi


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Representation of the Psychological State

Transition by Fuzzy Temporal Rules Resembling

Emotion Transition Dynamics

Given Dynamics of

Emotional state x1Corresponding Rule 1:

If x1(t) is LARGE

and x1(t) is SMALLER

than K, and the contact

between x1(t) and x2(t)

is SMALLThen X

x1(t+1) is LARGE

dxi

dt = ax1 (1-x1/k) b (x1 x2)p

x1, x2: Competitive emotional

states.

a: intrinsic growth rate;

k: largest value of x1 that keeps

growth rate in x1 positive

p: competition index


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Representation of the Psychological State

Transition by Fuzzy Temporal Rules Conveying

Emotion Transition (Contd.)

Given Dynamics of

Emotional state x2Corresponding Rule 2:

If x2(t) is LARGE

and contact between

x1(t) and x2(t) is SMALL

Then x2(t+1) is LARGE.

= -c (x1 x2)p + d x2

dx2

dt


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Fuzzy Dynamics

Corresponding to Rule 1Rule 1:If x1(t) is LARGE

and x1(t) is SMALLER

than K, and the contactbetween x1(t) and x2(t)

is SMALL Then X1(t+1)

is LARGE.

LARGE(x1, t+1)

=a. LARGE(x1, t).NEG(x1-k, t)

- b SMALL(x1, t). SMALL(x2, t).


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Results of Stability Analysis of

Fuzzy Temporal DynamicsLet V(L(x1, t+1), L(x2, t+1))

= (b L(x2, t+1) - c L(x1, t+1))2

= (-ac L(x1, t) NEG(x1-k, t) + ab L (x2, t))2

V= V(L(x1, t+1), L(x2, t+1))V(L(x1, t),

L(x2, t))< 0, if

L (x2, t)/L (x1, t) < c/b.


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Stabilization of Emotional

Dynamics

Condition of Stability: 0< dxi/dt < aii xi (2xi/k1).

Let

e= aii xi(2xi/k1) - dxi/dt

If e


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Stabilization of Emotional Dynamics

Emotional

Dynamics

D

aii xi(2xi/k -1)+

-

Error


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Controlling Emotional Response by

Fuzzy Temporal Logic

Stabilized

Emotional

Dynamics

Stabilized

Fuzzy

Temporal

System

G

ControllerEmotional

states at time 0

Emotional

states at time t


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Controlling Response of Fuzzy

Temporal Logic Using Emotion

Stabilized

FuzzyTemporal

System

Stabilized

Emotional

Dynamics

GController

Emotional

states at time 0

Emotional

states at time t


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Conclusions

1. The paper, to the best of the authors knowledge, is a firstsuccessful model to study emotion-logic encounter.

2. Conditions for stability for both emotional dynamics and

fuzzy temporal reasoning dynamics have been derived, and

the dynamics is stabilized by setting appropriate values of

the parameters, satisfying the conditions.

3. A scheme for controlling the response of emotional

dynamics by fuzzy temporal system (and vice-versa) is

presented.

4. The proposed system can be used to model emotional

response of intelligent agents in the next generation human-

computer interfaces.


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Thank you.

Lecture 5 Emotion Logic Encounter

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