Page 226 - Artificial Intelligence for the Internet of Everything

Accessing Validity of Argumentation of Agents of the Internet of Everything 207

2. Let N be a nonroot vertex of the tree labeled <A n , h n > and Λ¼[<A 0 ,
h 0 >, <A 1 , h 1 >, …, <A n , h n >] (the sequence of labels of the path from
the root to N). Let [<B 0 , q 0 >, <B 1 , q 1 >, …, <B k , q k >] all attack
<A n , h n >.
For each attacker <B i , q i > with acceptable argumentation line [Λ,<B i ,
q i >], we have an arc between N and its child N i .
A labeling on the dialectical tree can be then performed as follows:
1. All leaves are to be labeled as U-nodes (undefeated nodes).
2. Any inner node is to be labeled as a U-node whenever all of its associated
children nodes are labeled as D-nodes.
3. Any inner node is to be labeled as a D-node whenever at least one of its
associated children nodes is labeled as U-node.
After performing this labeling, if the root node of the tree is labeled as a U-
node, the original argument at issue (and its conclusion) can be assumed as
justified or warranted.
In our DeLP example, the literal rent_receipt is supported by:
<A, rent_receipt> ¼ <{(rent_receipt -< rent_deposit_transaction),
(rent_deposit_transaction -< tenant_short_on_money)}, rent_receipt> and there
exist three defeaters for it with three respective argumentation lines:
<B 1 , ┐rent_deposit_transaction> ¼ <{(┐rent_deposit_transaction -<
tenant_short_on_money, three_days_notice_is_issued)}, rent_deposit_
transaction>.

<B 2 ,┐rent_deposit_transaction> ¼
<{( ┐ rent_deposit_transaction -<
tenant_short_on_money, repair_is_done), (repair_is_done -< rent_refused)},
rent_deposit_transaction>.
<B 3 , ┐rent_deposit_transaction> ¼ <{(┐rent_deposit_transaction -< ren-
t_is_overdue )}, rent_deposit_transaction>.
The first two are proper defeaters and the last one is a blocking defeater.
Observe that the first argument structure has the counter-argument,
<{rent_deposit_transaction -< tenant_short_on_money}, rent_deposit_transac-
tion), but it is not a defeater because the former is more specific. Thus no
defeaters exist and the argumentation line ends there.
B 3 above has a blocking defeater <{(rent_deposit_transaction -<
tenant_short_on_money)},
rent_deposit_transaction>, which is a disagreement sub-argument of <A,
rent_receipt> and it cannot be introduced since it gives rise to an unaccept-
able argumentation line. B 2 has two defeaters that can be introduced: <C 1 ,
┐repair_is_done >, where C 1 ¼ {(┐repair_is_done -< rent_refused,