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In-Depth Information
•
To organize the musical knowledge in any
way admissible by the IE
constructs that lead to powerful implementations
for automated proving.
The method, original of the team to which the
authors belong, has been applied to illnesses diag-
noses, railway traffic control, automated theorem
proving in geometry and so forth, as will be seen
in the subsequent section. These applications have
been considered quite original and different to
others' approaches by the artificial intelligence
and symbolic computation community. It seems
that using this approach in music studies could be
a new interesting approach to relate music topics
with artificial intelligence.
A possible contrast with other methods is that
ours is based on strong mathematical results,
implemented in universally accepted algorithms:
Gröbner Bases.
We give next some arguments to support the
use of Gröbner Bases as our automated proving
method.
In Clegg, Edmonds, and Impagliazzo (1996),
a propositional Gröbner proving system is dis-
cussed. It is shown that this system polynomially
simulates Horn clauses resolution and weakly ex-
ponentially simulates resolution. The authors say
that this suggests that the Gröbner Bases algorithm
might replace resolution as a basis for heuristics
for NP-complete problems (Kapur & Narendran,
1984) already stated that using a Gröbner Bases
approach subsumes resolution. Let us observe
that there is an important difference between
the average case and worst case complexities of
Gröbner Bases computations.
In Clegg, Edmonds, and Impagliazzo (1996)
there is also a comparison with other methods,
which result only slightly superior. Thus, from
the point of view of complexity, using a Gröbner
Bases approach seems reasonable.
This was also the opinion of the referee of
Laita, Roanes-Lozano, de Ledesma and Alonso
(1999), an expert in automated theorem proving,
who judged our approach as competitive, even
though not the best for all types of problems. It is
a fact that, among all known automated provers,
•
To adapt and implement the IE, based on
a powerful tool for effective polynomial
computations: Gröbner Bases
•
To implement the GUI that will visually
output the results of the system
The objectives outlined above will be devel-
oped in detail afterwards.
Background
The general background of this chapter is a
relatively new field of computer science named
“symbolic computation”. The authors have been
working in this field for more than ten years. For
instance, they have been the invited editors of a
special volume of the Journal of the Royal Acad-
emy of Sciences of Spain (RACSAM) devoted
to this topic, where many very good specialists
from all around the world (Bruno Buchberger,
Deepak Kapur, Jacques Calmet, John Campbell,
Jochen Pfalzgraf, etc.) have collaborated (Laita,
Roanes-Lozano & Alonso, 2004).
Inside symbolic computation, there is a sub-
field to which the topic of this chapter belongs:
automated proving. We shall describe in section
“Constructing the IE Using CoCoA” the particu-
lar theoretical background of our method. It is a
theorem that links logical consequences with an
algebraic result, and it is due to a team to which
the authors belong. Prior related works are also
detailed in that section.
maIn thrust of the chapter
The main thrust of the chapter is to consider a
system of music styles identification as an “ex-
pert system” based on symbolic computation.
Moreover, such a computation uses Buchberger's
Gröbner Bases and normal forms, theoretical
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