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ASPARTIX for Argumentation frameworks with recursive attacks

Here we provide an file that allows to compute extensions of Argumentation frameworks with recursive attacks as defined by Baroni et al. [1]. This is done by a reduction to Dung AFs and then using the encoding of the Dung semantics (see ASPARTIX for Dung AFs).


Input Format

Argumentation frameworks with recursive attacks (AFRas) extend Dung's argumentation frameworks (AFs) by incorporating to the argument-attack structure also attacks on attacks, and in a recursive fashion also attacks on attacks on attacks. AFRAs are encoded by a sequence of statements that either encode an arguments, an attack between arguments, or an attack on a attack.

afraA(a). ... a is an argument afraR(alpha,a,b). ... alpha is an attack from a towards b a needs to be an argument b can be either an argument or an attack

For instance consider the following argument graph (the Bob example from [1]).

EAF Input File
afraA(a). afraA(n). afraA(p). afraA(c). afraA(g). afraR(epsilon,a,n). afraR(delta,n,gamma). afraR(gamma,p,beta). afraR(beta,c,g). afraR(alpha,g,c).

Reduction from AFRAs to AFs

The following is an ASP implementation of the reduction from AFRAS to AFs introduced by Baroni et al. in [1]. It can be used for the following semantics: conflict-free, admissible, preferred, stable, complete, grounded, semi-stable and ideal [1, Proposition 12].

% arguments arg(X) :- afraA(X). arg(R) :- afraR(R,X,Y), afraA(X). % direct defeat att(V,W) :- afraR(V,X,W), arg(W), afraA(X). % indirect defeat att(V,A) :- att(V,W), afraR(A,W,X), afraA(W).


You need an ASP-solver (e.g. clingo, dlv), the encoding for the reduction from above, and the encoding for the semantics (see Encodings for Dung AFs) your are interested in.

Applying a Semantics

In order to enumerate all extensions of an AFRA (given in a file w.r.t. a semantics (encoded in the file semantics.dl) use one of he following commands (depending on your ASP-solver):

$ DLV afra.dl semantics.dl -filter=in
$ clingo afra.dl semantics.dl filter.lp 0

The filter.lp file filters out the predicates in(.) which denote the arguments and attacks contained in the extension.

Other reasoning modes work similar as in the case of Dung AFs, just add the afra.dl file for the reduction from AFRAs to AFs.

Performing the Reduction only

In order to apply the reduction to an AFRA (given in a file to obtain the corresponding Dung AF use one of he following commands (depending on your ASP-solver):

$ DLV afra.dl -filter=arg,att
$ clingo afra.dl filter_af.lp 0

The filter_af.lp file filters out the predicates arg(.),att(.,.) which denote the arguments and attacks of the Dung AF.


[1] AFRA: Argumentation framework with recursive attacks.
Pietro Baroni, Federico Cerutti, Massimiliano Giacomin, Giovanni Guida
Int. J. Approx. Reasoning 52(1): 19-37 (2011) [ doi: 10.1016/j.ijar.2010.05.004]

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