Arguing over Goals for Negotiation: Adopting an Assumption-Based Argumentation Decision Support System - Efficient Decision Support Systems: Practice and Challenges from Current to Future - page 223

D 2

fast

r 31 ( d )

s ( d ) reply ( accept ) Price ( d , low )

f 43

s ( d ) reply ( accept )

Fig. 1. The argument D 2 concluding fast

Arguments are concurrent if their conclusions are identical or incompatible. In order to
compare the strength of concurrent arguments, various domain-independent principles of
commonsense reasoning can be applied. According to the specificity principle (Simari
& Loui, 1992), the most specific argument is stronger one. According to the weakest
link principle (Amgoud & Cayrol, 2002), an argument cannot be justified unless all of its
subarguments are justified. In accordance with the last link principle (Prakken & Sartor,
1997), the strength of our arguments comes from the preferences between the sentence of
the arguments. By contrast, the strength of our argument does not depend on the quality of
information used to build that argument but it is determinated by its conclusion.
Definition 12 (Strength relation) . Let DF = DL P I T P RV , sm , , , , be a decision framework

and A 1 , A 2

A 1 is stronger than A 2 (denoted

∈A ( DF ) be two structured which are concurrent.

A 1 A 2 ) iff conc ( A 1 A 2

P )= ∈G , conc ( )= ∈G P g 1 g 2 and g 1 g 2 .

P T P

Due to the definition of over , the relation is transitive, irreflexive and asymmetric over

A ( DF )

.
The attack relation and the strength relation can be combined. As in (Amgoud & Cayrol, 1998;
Bench-Capon, 2002), we distinguish between one argument attacking another, and that attack
succeeding due to the strength of arguments.

Definition 13 (Defeat relation) . Let DF = DL ,

P

sm ,

I

,

T

,

P

,

RV

be a decision framework and

¯ Aand B be two structured arguments. A defeats B iff:
1. A attacks B;
2. and it is not the case that B

A.

P