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some are good for some types of problems and
not as god for other types of problems. Ours is not
an exception. Our choice is mainly based on our
previous experience in developing medium size
expert systems and other related simulations.
There are two more advantages in our ap-
proach: first, it can deal with multivalued logics
and, second, logical formulae can be written
without any restrictions: they do not have to be
Horn clauses (i.e., the symbol “or” can appear in
both the antecedents and the consequents of the
production rules).
A problem appears when the number of vari-
ables, in our case, those that refer to the musical
characteristics of an epoch, is larger than 75-80.
In these cases it is advisable to divide the sys-
tem in two or more subsystems. In our chapter
we have divided the whole system into three
subsystems.
The logical connective “∨” (or) is also
allowed, both in the antecedents and
in the consequents. The KB may also
contain other items named integrity
constraints, and any other additional
information included by the experts,
but these are not used here. Letters as
X1, X2, X3 and A1 are called “propo-
sitional variables”. Both the proposi-
tional variables and their negations are
called “literals”.
•
A set “F” of “potential facts”. We call
“potential facts” both the literals that
are in the antecedents but not in the
consequents of the production rules
and their “contraries”. For instance, if
our RB consists of only the production
rule written previously, the potential
facts would be:
X1, ¬X1, X2, ¬X2, X3, ¬X3
generalItIes aBout
rule-Based expert sYstems
In some cases the consequent of a rule
may be part of the antecedent of another
rule. These types of literals are called
“derived facts”.
Expert systems have three components:
1.
A knowledge base, “KB”, composed by:
•
2.
An “inference engine” (IE). It is said that a
rule can be “forward fired”, if all the literals
in the antecedent are, either potential facts
(naturally, no pair of contrary potential facts
are allowed in a same antecedent of any
production rule) or “derived facts”. Forward
firing corresponds to the formal logic rule
of “modus ponens”. The “inference engine”
performs such a forward firing. The IE is a
procedure that extracts automatically con-
sequences from the information contained
in the KB. Ours, to be described in section
“Construction of the IE using CoCoA”, is
based on a computer algebra theorem (Laita,
Roanes-Lozano, de Ledesma, & Alonso,
1999; Roanes-Lozano, Laita, & Roanes-
Macías, 1998), original to the team to which
the authors belong. This theorem uses Hsiang
A set “RB” (Rule Basis) of logic ex-
pressions, called “production rules”.
Production rules are, in this chapter,
implications between a conjunction of
literals (premises or antecedents), and a
literal or a disjunction or a conjunction
of literals (conclusions or consequents).
The definition of “literal” comes next. A
simple example of a production rule is:
X1 and not-X2 and X3 implies A1
that can be written in logical nota-
tion:
X1 ∧ ¬X2 ∧ X3 → A1
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