Inductive Learning - Advanced Artificial Intelligence - page 263

Here H weak implicit F means that fact F is not a definitive conclusion H but

a reasonable or partial conclusion . With the concept of weak implication, this

pattern has possible and partial hypothesis which only needs to explain some
facts of all facts. However, we still focus on the hypothesis of tautological
implication facts.

H

Table 7.1 Basic symbols

Symbols Significance

￿ not

∧ conjunctionlogic product

∨ disjunctionlogic add

￿ implication

￿ logic equivalence

↔ item rewrite

￿ exclusive or

F fact set

H hypothesis

|

specialization

|

generalization

￿ reformalization

￿ v i existentially quantified variable vi

￿ I v i value existentially quantified variable v i

￿ v i universally quantified variable vi

D i concept description

K i judge predicate of name of an concept

:: >

Implication conjunct concept description and concept name

e i an eventdescription of a situation

E i predicate only if event is true for concept k i

X i attribute

LEF evaluation function

DOM(P) domain of descriptor P

With regard to any given facts set, innumerable hypothesis implicit these facts
could be generated. This needs background knowledge to provide constraints and
optimal principles, so that innumerable hypothesis could be decreased to one or
several optimal hypothesis.
In order to formalize logic foundation of conceptual inductive learning, basic
symbols are given in Table 7.1, and the explanations to the simple are appended.