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ASPARTIX for Preference-based Argumentation Frameworks (PAFs)

Input Format

PAFs are encoded by a sequence of statements that either encode an argument, an attack, or a preference between arguments.

arg(a). ... a is an argument att(a,b). ... a attacks b pref(a,b). ... a preferred over b

For instance consider the encoding of an example from [Amgoud and Cayrol, AMAI 2002,].

arg(a). arg(b). arg(c). arg(d). arg(e). att(c,d). att(d,c). att(a,e). pref(c,d).


We use the following encoding to first compute the defeat relation based on the given attacks and preferences.

%% transitivity of pref pref(X,Y) :- pref(X,Z), pref(Z,Y). %% argument x defeats argument y, iff %% x attacks y, and y is not preferred to x defeat(X,Y) :- att(X,Y), not pref(Y,X).


You need an ASP-solver (e.g. clingo, dlv), the paf.dl encoding. and the encoding for the semantics (see below) your are interested in.

Applying a Semantics

In order to enumerate all extensions of a PAF (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 paf.dl semantics.dl -filter=in
$ clingo paf.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 paf.dl file.


Here we provide adjusted variants of the encoding for Dung semantics:

Most of the encodings can be used for both systems (dlv, clingo), but for some of them an adjustment, due to some differences in the syntax, is necessary. Those encodings are specially marked. In the following we provide the encoding.

DLV only Encodings

Clingo only Encodings


Main References

[8] Answer-Set Programming Encodings for Argumentation Frameworks.
Uwe Egly, Sarah Gaggl, and Stefan Woltran.
In Argument and Computation, 1(2): 147 - 177 (2010).[ bib |pdf]
[4] Solving Argumentation Frameworks using Answer Set Programming.
Sarah Gaggl.
Masters Thesis, Technische Universität Wien, 2009 [.pdf ]
more system-related references

Some References on Preference-based Argumentation Frameworks

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