Information Technology Reference
In-Depth Information
Ta b l e 4 .
Inference schemes
L
1
,...,
L
k
,∼
L
l
,...,∼
L
m
⇒
L
n
L
1
...
L
k
∼
L
l
... ∼
L
m
DMP
1
L
n
asm
(
∼
L
)
2
∼
L
L
asm
(
∼
L
)
is inapplicable
asm
(
∼
L
)
uc
3
4
sat
(
a
,
[
P
]
α
,
0
)
count
(
a
,
[
P
]
α
,
∅)
P
1
(
a
)
...
P
n
(
a
)
P
1
≈
α
...≈
α
P
n
I
α
(
P
1
)
...
I
α
(
P
n
)
count
(
a
,
[
P
1
]
α
,{
P
1
,...,
P
n
}
)
5
sat
(
a
,
[
P
1
]
α
,
n
)
P
1
(
a
)
...
P
n
(
a
)
P
1
≈
α
...≈
α
P
n
I
α
(
P
1
)
...
I
α
(
P
n
)
count
(
a
,
[
P
1
]
α
,
S
⊂{
P
1
,...,
P
n
}
)
is inapplicable
count
(
a
,
[
P
1
]
α
,
S
)
uc
6
sat
(
a
,
[
P
]
α
,
n
)
sat
(
b
,
[
P
]
α
,
m
)
P
≈
α
P
n
>
m
prefinf
(
a
,
b
,
[
P
]
α
)
7
pref
(
a
,
b
)
α
sat
(
a
,
[
Q
]
α
,
n
)
sat
(
b
,
[
Q
]
α
,
m
)
Q
≈
α
Q
α
Pn
<
m
prefinf
(
a
,
b
,
[
P
]
α
)
uc
8
prefinf
(
a
,
b
,
[
P
]
α
)
is inapplicable
sat
(
a
,
[
P
]
α
,
n
)
sat
(
b
,
[
P
]
α
,
m
)
P
≈
α
P
n
=
m
eqprefinf
(
a
,
b
,
[
P
]
α
)
9
eqpref
α
(
a
,
b
)
sat
(
a
,
[
Q
]
α
,
n
)
sat
(
b
,
[
Q
]
α
,
m
)
Q
≈
α
Q
n
=
m
eqprefinf
(
a
,
b
,
[
P
]
α
)
uc
10
eqprefinf
(
a
,
b
,
[
P
]
α
)
is inapplicable
Arguments.
Arguments are built from formulas of a logical language, that are chained
together using inference steps. Every inference step consists of premises and a con-
clusion. Inferences can be chained by using the conclusion of one inference step as a
premise in the following step. Thus a tree of chained inferences is created, which we
use as the formal definition of an argument (cf. e.g. [17]).
Definition 3. (Argument).
An
argument
is a tree, where the nodes are inferences, and
an inference can be connected to a parent node if its conclusion is a premise of that
node. Leaf nodes only have a conclusion (a formula from the knowledge base), and
no premises. A subtree of an argument is also called a
subargument
.
inf
returns the
last inference of an argument (the root node), and
conc
returns the conclusion of an
argument, which is the same as the conclusion of the last inference.
Definition 4. (Language) .
Let
P
be a set of predicate names with typical elements
P
,
Q
;
O
a set of outcome names with typical elements
a
,
b
;
α
an audience; and
n
a non-
negative integer. The
input language
L
KB
and full
language
L
are defined as follows.
