The Piano Axioms in Prolog

 prolog

    
% Piano Axioms

% Axiom 1: Law of Excluded Gray
key_type(white).
key_type(black).

% Axiom 2: The C Postulate
key_color(c, white).

% Axiom 3: The Diatonic Scale
next_white_key(c, d).
next_white_key(d, e).
next_white_key(e, f).
next_white_key(f, g).
next_white_key(g, a).
next_white_key(a, b).
next_white_key(b, c).

% Axiom 4: The Semitone Anomaly
semitone_gap(e, f, 1).
semitone_gap(b, c, 1).
semitone_gap(X, Y, 2) :- 
    next_white_key(X, Y),
    X \= e,
    X \= b.

% Axiom 5: Black Key Entropy
has_black_key_between(X, Y) :-
    next_white_key(X, Y),
    semitone_gap(X, Y, 2).

% Axiom 6: The "8 is 12" Principle.
octave_size(12).

% Axiom 7: Out of Bounds Exception
total_keys(88).

% Theorem 1: Conservation of "Wrong Notes"
style(jazz) :-
    wrong_notes > 0,
    write('All wrong notes are now intentional').