Eﬃcient Construction of Structured Argumentation Systems

We address the problem of efficient generation of structured argumentation systems. We consider a simplified variant of an ASPIC argumentation system and provide a backward chaining mechanism for the generation of structured argumentation graphs. We empirically compare the efficiency of this new approach with existing approaches (based on forward chaining) and characterise the benefits of using backward chaining for argumentation-based query answering.


Introduction Backward Chaining for Argumentation Evaluation & Conclusion
Structured Argumentation with ASPIC Intuition The Underlying Language Let T = (S, D) be a defeasible theory such that S = {r 1 , r 2 , r 3 , r 4 } and D = {r 5 , r 6 , r 7 }.
There are 7 arguments.The ASPIC Framework There are 7 arguments.The ASPIC Framework We assume that we have a preference relation on arguments.

Definition (Defeat)
A defeats B iff B A and either : The ASPIC Framework We assume that we have a preference relation on arguments.

Introduction Backward Chaining for Argumentation Evaluation & Conclusion
Structured Argumentation with ASPIC Intuition The ASPIC Framework We assume that we have a preference relation on arguments.

Definition (Defeat)
A defeats B iff B A and either : (Rebutting) there exists The ASPIC Framework We assume that we have a preference relation on arguments.

Definition (Defeat)
A defeats B iff B A and either : (Rebutting) there exists We get an argumentation system (AS) AS T = (A, Def) The Idea Behind The Paper We instantiate ASPIC on defeasible theories to reason with conflicting pieces of information.
We make the following observations : Most approaches generate the whole argumentation graph → Can we generate only a part of the AS ?
We have a huge number of arguments !→ How can we reduce the number of arguments ?The Idea Behind The Paper We instantiate ASPIC on defeasible theories to reason with conflicting pieces of information.
We make the following observations : Most approaches generate the whole argumentation graph → Can we generate only a part of the AS ?
We have a huge number of arguments !→ How can we reduce the number of arguments ?
Contribution of the paper : The study of backward chaining mechanisms in ASPIC instantiations with an empirical evaluation demonstrating the impact of our approach.

Characterising Rules
Definition (Activated rule) A rule is activated iff there exists a support path to r in GRI T .

Definition (Connected rule)
n is connected to n iff there exists (n 1 , . . ., n k ) such that : for every 1 ≤ i ≤ k, n i ∈ N and n i is activated

Definition (Potentially necessary rule)
A rule r is potentially necessary for l iff ∃r ∈ S ∪ D s.t.Head (r ) = l and r is connected to r .

Introduction Backward Chaining for Argumentation Evaluation & Conclusion
The Graph of Rule Interaction AS for a literal Defeasible Theory Filtration Characterising Rules r 3 is not potentially necessary for b whereas r 1 , . . ., r 6 ared.

Theoretical Properties
The AS for l is useful to draw conclusions on l Conclusions on other literals have to be taken carefully.

Links between the GRI and ASs :
Sufficient condition to have less arguments in the AS for l Removing not activated rules will not change AS T Removing not potentially necessary rules for l will not change the AS for l (AS l T )

Introduction Backward Chaining for Argumentation Evaluation & Conclusion
The Graph of Rule Interaction AS for a literal Defeasible Theory Filtration

Defeasible Theory Filtration
We propose a framework inspired from the work of Yun et al. 3 : 1 Compute the GRI of T 2 Compute and remove rules that are not potentially necessary for the literal.
3 Instantiate the AS for l.Please note that : The GRI only has to be computed once, stored in memory and reused for multiple queries.
It can potentially reduce the time taken to answer a query.

Conclusion
We provide a workflow for efficiently constructing structured AS using ASPIC on propositional logic : We introduce the Graph of Rule Interaction to study the behaviour of defeasible rules.
We give theoretical properties for ASs for literals.
We introduce a framework for filtering DTs.
We empirically compare our new approaches and show promising results.

Introduction Backward Chaining for Argumentation
Evaluation & Conclusion

Empirical Evaluation Conclusion
The Defeasible Theories We consider the following DT from Maher et al. 4 : In tree(n,k), the rules form a k-branching tree of depth n where every literal occurs only once.
In level(n), there is a cascade of n disputed conclusions, i.e. there are rules ⇒ p i and p i+1 ⇒ ¬p i , for 0 ≤ i ≤ n.
In levels(n), for odd i, the latter rule has a superior strength when compared to even rules.
In teams(n), every literal is disputed with two rules for p i and two rules for ¬p i , and the rules for p i are superior to the rules for ¬p i .

Figure
Figure -A support path in the GRI

Figure
Figure -Potentially necessary rules for b and Sub(A 7 ) = {A 7 , A 4 }

Table -
Arguments in the AS for b 3. Toward a More Efficient Generation of Structured Argumentation Graphs.Bruno Yun, Srdjan Vesic and Madalina Croitoru.COMMA (2018)