An Expert System Devoted to Automated Music Identification and Recognition - Intelligent Music Information Systems: Tools and Methodologies - page 95

Figure 3. Selection corresponding to a Baroque composition

X19 ^ ¬X20 ^ ¬X21 → H3
¬X19 ^ ¬X20 ^ X21 → H2

Ideal of production rules: the following ideal
J corresponds to the RB. Recall that the theorem
defines this ideal as the one generated by the poly-
nomials that translate the negations of production
rules (this is the reason of introducing “NEG”
before the letters “R” denoting production rules).
The same will be required later for the potential
facts F1,…, F23,F1N,…, F23N:

are introduced as follows

R39:=NF(IMP(AND1(AND1(x[19],NEG(x[20])),NEG(x[21
])),h[3]),I);

R40:=NF(IMP(AND1(AND1(NEG(x[19],NEG(x[20])),x[21
]),h[2]),I); J:=Ideal(NEG(R1),NEG(R2),NEG(R3),NEG(R4),NEG(R5)

,NEG(R6),NEG(R7),NEG(R8),NEG(R9),NEG(R10),
NEG(R11),NEG(R12),NEG(R13),NEG(R14),NEG(R1
5),NEG(R16),NEG(R17),NEG(R18),...,NEG(R292)
,NEG(R293),NEG(R294),...,NEG(R370));

Definition of potential facts: all the 23 pairs
of potential facts and their negations should be
declared. For the sake of space we only write
down the first two and he last two pairs. “Fi” (i =
1,…,23) means “fact corresponding to literal Xi”
and “FiN” (i = 1,..,23) means “fact corresponding
to literal negation of XI”.

examples

We suppose that a History of Music teacher pro-
poses to the students the next four scores for style
identification. The argument in the four examples
is similar. The identifiers of Table 1 appear in
Spanish in the four screenshots of the GUI that
follow, but the English translations are in most
cases expressed by very similar words.

F1:=x[1]; F1N:=NEG(x[1]);

F2:=x[2]; F2N:=NEG(x[2]);

... ...

F23:=x[23]; F23N:=NEG(x[23]);