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have the property of being true or false, which is different with ordinary formulas.
The basic property of decision algorithm is consistent or inconsistent, so we
mainly consider the consistency of data. Computational methods are used to infer
rules from data.
In this chapter, the decision logic languages defined and discussed are
composed by atomic formulas. Formulas are described by a pair with the form
“attribute-data”. Using some classical methods, formulas can construct complex
formulas with propositional connectives: “and”, “or”, “not”, etc.
First, we define the basic representation of decision logic language as follows:
ţ
the set of attributes;
(2) V=∪
V
a
,
(1)
A
ţ
the set of attribute values;
(3) The set of propositional connectives {∼, ∨, ∧, →, ≡} representing negative,
disjunction, conjunctionimplication and equivalence respectively.
a
∈A,
V
Note, propositional connectives can be viewed as logic connectors: “not”,
“or”, “and”, “if ……, then ……”, “if and only if”.
Basic representations do not include variables, and it is composed by symbols
for attributes and attribute values, propositional connectives, assistant symbols
(for example, bracket), and etc.
The formula set of decision logic language is the minimal set satisfying the
following conditions:
(1) Formula (
) (or a
v
for short) is an elementary atomic formula, and it is a
formula of decision logic language for each
a, v
v
∈
V
a
;
(2) If θ and ψ are formulas of decision logic language, ∼θ, θ'∨ψ, θ∧ψ, θ→ψ,
θ≡ψ are also formulas of decision logic language.
a
∈
A
and
11.3.3
Semantics of Decision Logic Language
Formulas are used as the tools to describe the objects in universe. It can also be
applied into the description of the object sets satisfying some properties. For
example, in atomic formula, ordered pair (
a
,
v
) can be explained as the
expression of objects with value
.
To describe decision logic language explicitly, we can use the concepts of
models and satisfiability to define the Tarski semantics of decision logic
language, that is, use models to express knowledge representation system
v
on attribute
a
S
=(
U
,
A
). Model S describes the meaning of predication symbol (
a
,
v
) in universe
U
and
