Post on 05-Apr-2018
transcript
8/2/2019 Lecture 5 Emotion Logic Encounter
1/20
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
8/2/2019 Lecture 5 Emotion Logic Encounter
2/20
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.
8/2/2019 Lecture 5 Emotion Logic Encounter
3/20
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
8/2/2019 Lecture 5 Emotion Logic Encounter
4/20
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.
8/2/2019 Lecture 5 Emotion Logic Encounter
5/20
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.
8/2/2019 Lecture 5 Emotion Logic Encounter
6/20
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
8/2/2019 Lecture 5 Emotion Logic Encounter
7/20
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
8/2/2019 Lecture 5 Emotion Logic Encounter
8/20
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
8/2/2019 Lecture 5 Emotion Logic Encounter
9/20
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
8/2/2019 Lecture 5 Emotion Logic Encounter
10/20
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
8/2/2019 Lecture 5 Emotion Logic Encounter
11/20
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
8/2/2019 Lecture 5 Emotion Logic Encounter
12/20
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).
8/2/2019 Lecture 5 Emotion Logic Encounter
13/20
8/2/2019 Lecture 5 Emotion Logic Encounter
14/20
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.
8/2/2019 Lecture 5 Emotion Logic Encounter
15/20
Stabilization of Emotional
Dynamics
Condition of Stability: 0< dxi/dt < aii xi (2xi/k1).
Let
e= aii xi(2xi/k1) - dxi/dt
If e
8/2/2019 Lecture 5 Emotion Logic Encounter
16/20
Stabilization of Emotional Dynamics
Emotional
Dynamics
D
aii xi(2xi/k -1)+
-
Error
8/2/2019 Lecture 5 Emotion Logic Encounter
17/20
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
8/2/2019 Lecture 5 Emotion Logic Encounter
18/20
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
8/2/2019 Lecture 5 Emotion Logic Encounter
19/20
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.
8/2/2019 Lecture 5 Emotion Logic Encounter
20/20
Thank you.