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of common predicate logicdecision treegenerative rule, semantic network,
framework, multi value logic, modal logic.
On the basis of predicate logic
representative capability can be improved
through modifying and expanding, adding some extra form and new concept.
Michalski et al. proposed APC(Annotated Predicate Calculus), so that it is more
proper for reasoning. Main differences between APC and common predicate
calculus include: (1) every predicate, variable and function are endowed a label.
Label is the set of background knowledge related to learning problem of the
descriptor. Such as definition of concept descriptor represents, relation between
the label and other concepts, effective range of descriptor, etc. (2) except for
predicate, APC also includes compound predicate, whose arguments can be
compound items. A compound item is combined with several common items,
such as
∨
t
2
,
A
). (3) relation predicate among expressions are represented as
selective symbol relation, such as: =,
≠
, >,
≥
,
≤
, <. (4) except for universal
quantified and existential quantified, there is numeral quantified, which is used to
represent numeral information of an object satisfied a expression.
P
(
t
1
7.2.3
Background knowledge of problems
With regard to a given observation statement set, innumerable inductive assertion
implicate these statement could be constructed. Therefore, some additional
information, i.e. background knowledge of problems, should be used to restrain
possible range of inductive assertion, and decide one or some optimal inductive
assertions. For example, in learning approach Star, background knowledge
includes several parts: (1) descriptor information used in observation statement is
added in every descriptor label; (2) form hypothesis about observation and
inductive assertion; (3) select standard of attributes of list inductive assertion; (4)
various reasoning rules, heuristic rules, specific subprogram, general and
independent procedure, so that learning system generates logic conclusion and
new descriptor of given assertion. Since descriptor choice in observation
statement makes important influence on generating inductive assertion, descriptor
choice should be considered firstly.
Main content of learning system input is an observation statement set.
Descriptor in these statements is observable feature and useful test data. Deciding
these descriptors is a main issue of inductive learning. Learning approaches can
be depicted by initial descriptor and relation degree of learning problem. The
relations include: (1) related completely, that is, all descriptors in observation
statement set are directly related to learning task. Learning task is forming an
