How to translate logical formulas into arrays and calculate?

Question

I want to translate logical formulas into arrays and calculate with them. First of all it should input the number of circumstances. Then the given name of the formula. Then the values of the formula, for example:

                        PQ  ~PQ   P~Q   ~P~Q
one circumstance:   p =  a   u     a      u
two circumstances: p&q=  A   N     N      N
...

I want that a given number of circumstances defines the arrays' shape like a binary tree, because the values in the formulas can be the same over every n^2 place of the formula, as you could see for p=au-au before.

I tried this, but I don't know how to define the arrays' values to 3 (or more) possible values ('a', 'u', 'n',...).

It also would be nice to iterate through the array to input the values and to set for example every second value of the formula the same (p=au-au). I didn't know how to do it and don't know if it's possible.

I also dont know, if this is the "right" way to do it at all. I am almost totally new to programming.

After this, the programm should calculate conclusions of given formulas. The algorithm is mechanical and easy. Yet, I don't know how to do it with arrays and to generalise the calculations. If you are interested, here is more information:

https://github.community/t/present-you-strict-logic-with-an-example-program-in-python-and-prolog/132220

Maybe my next aim is a homepage for calculations with these formulas and this way of calculations.

import numpy as np
import pdb; pdb.set_trace()

def array_zero_number_name_fn(number_circumstances_int):
    if number_circumstances_int == 1:
        a = np.zeros((2),np.dtype=({'names':['a','u','n'], 'formats':['S1',np.uint8]}))
        b = 1
        c = input('Name the logical formula!')
        input_gf_fn(a,b)
        return(a,b,c)
    elif number_circumstances_int == 2:
        a = np.zeros((2,2),np.dtype({'names':['a','u','n'], 'formats':['S1',np.uint8]}))
        b = 2
        c = input('Name the logical formula!')
        input_gf_fn(a,b)
        return(a,b,c)

def input_gf_fn(a,b,c):
    if b == 1:
        a[0] = input('Please type value of circumstance of logic formula!')
        a[1] = input('Please type value of complement-circumstance of logical formula!')
    elif b == 2:
        a[0,0] = input('Please type value 1 of logic formula!')
        a[0,1] = input('Please type value 2 of logic formula!')
        a[1,0] = input('Please type value 3 of logic formula!')
        a[1,1] = input('Please type value 4 of logic formula!')
    print(a)
    return(0)
    
number_circumstances_str = input('How many circumstances should your formula have?')
number_circumstances_int = int(number_circumstances_str)

array_zero_and_number = array_zero_number_name_fn(number_circumstances_int)
array_zero = array_zero_and_number[0]
name = array
print(array_zero)
number = array_zero_and_number[1]
input_gf = input_gf_fn(array_zero,number,name)
print(input_gf)
input('Exit with Enter!')
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