Wang’s Program II

This page recreates the logic-based conjecturing process of Wang’s early AI system using txgraffiti’s symbolic logic layer.

Wang’s system generated thousands of logical formulas in propositional logic and checked whether they were tautologies. We simulate that below using Predicate and Conjecture.

import pandas as pd
from txgraffiti.logic.conjecture_logic import Predicate, Conjecture, TRUE, FALSE

# Step 1: Simulate a truth table over 3 variables: A, B, C
from itertools import product

rows = list(product([False, True], repeat=3))
df = pd.DataFrame(rows, columns=["A", "B", "C"])

# Step 2: Create symbolic predicates
A = Predicate("A", lambda df: df["A"])
B = Predicate("B", lambda df: df["B"])
C = Predicate("C", lambda df: df["C"])

# Step 3: Create and test some formulas
formulas = [
    A >> A,
    A >> B,
    A >> (A | B),
    (A & B) >> C,
    (A & ~A),
    (A | ~A),
    (A & B) >> (A | B),
    ((A >> B) & (B >> C)) >> (A >> C),  # hypothetical syllogism
]

# Step 4: Evaluate and print which are tautologies
for f in formulas:
    print(f"{f}  ::  Tautology?  {f.is_true(df)}")