Self-referential implication

implication.py

from math import exp
import numpy as np
import matplotlib.pyplot as plt


def sigmoid(x):
    return 1.0 / (1.0 + exp(-x))


def implication(a, b):
    if (-0.5 * a + 1.0 * b) > -0.5:
        return 1.0
    else:
        return 0.0

def soft_implication(a, b):
    return -0.5 * a + 1.0 * b + 0.5


def sigmoid_implication(a, b):
    return sigmoid(-0.5 * a + 1.0 * b - 0.5)


plt.figure()
for n in range(4):
    plt.subplot(2, 2, n+1)
    a = n // 2
    b = n % 2
    aa = [a]
    a0 = a
    for n in range(20):
        a = soft_implication(a, b)
        aa.append(a)
    plt.plot(aa, linewidth=3.0)
    plt.title('a = %d, b = %d' % (a0, b,))
    plt.ylim(0, 2.)

plt.show()