A Workable ReasonRank

[myklob]

Here's Python script where the PageRank algorithm is modified to reflect an "ArgumentRank" approach. This modification adds the scores of supporting arguments and evidence and subtracts the scores of weakening arguments and evidence:

import numpy as np

def argumentrank(M, num_iterations: int = 100, d: float = 0.85):
    """ArgumentRank algorithm with explicit number of iterations. Returns ranking of nodes (arguments) in the adjacency matrix.

    Parameters
    ----------
    M : numpy array
        adjacency matrix where M_i,j represents the link from 'j' to 'i', such that for all 'j'
        sum(i, M_i,j) != 0 (due to adding and subtracting)
    num_iterations : int, optional
        number of iterations, by default 100
    d : float, optional
        damping factor, by default 0.85

    Returns
    -------
    numpy array
        a vector of ranks such that v_i is the i-th rank,
        v sums may not equal 1 due to addition and subtraction of arguments

    """
    N = M.shape[1]
    v = np.ones(N) / N
    M_hat = d * M + (1 - d) / N
    for i in range(num_iterations):
        v = np.dot(M_hat, v)
        # Adjustments to ensure scores are not negative and sum to 1 after each iteration
        v = np.maximum(v, 0)
        v /= v.sum()
    return v

# Example adjacency matrix for argument links
M = np.array([[0, -0.5, 0, 0, 1],
              [0.5, 0, -0.5, 0, 0],
              [0.5, -0.5, 0, 0, 0],
              [0, 1, 0.5, 0, -1],
              [0, 0, 0.5, 1, 0]])

v = argumentrank(M, 100, 0.85)
print(v)

This edited script represents an "ArgumentRank" algorithm where the adjacency matrix M now accounts for both strengthening and weakening arguments. The matrix entries are adjusted to add scores for supporting arguments and subtract scores for weakening arguments. Additionally, after each iteration, the algorithm ensures that the scores are normalized (non-negative and sum to 1) to maintain a consistent ranking system.