ASPARTIX for Value-based Argumentation Frameworks (VAFs)

Input Format

VAFs are encoded by a sequence of statements that either encode an argument, an attack, the value of an argument, or prefences between values.

arg(a). ... a is an argument att(a,b). ... a attacks b val(a,v). ... argument a has value v valpref(v,w). ... value v is preferred over value w

For instance consider the encoding of an example from [Bench-Capon, J.Log.Comput.13 2003,].

arg(a). arg(b). arg(c). arg(d). arg(e). arg(f). arg(g). arg(h). att(a,e). att(b,a). att(c,b). att(c,f). att(d,c). att(e,d). att(f,a). att(g,f). att(g,h). att(h,g). val(a,life). val(b,property). val(c,property). val(d,life). val(e,property). val(f,life). val(g,fact). val(h,fact). %valpref(fact,life). %valpref(life,property). valpref(fact,property). valpref(property,life).

Encoding

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

vaf.dl

%% valpref preference relation; transitiv valpref(X,Y) :- valpref(X,Z), valpref(Z,Y). %% pref computes preference of arguments depending on %% the preference relation valpref pref(X,Y) :- valpref(U,V), val(X,U), val(Y,V). %% 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).

Usage

You need an ASP-solver (e.g. clingo, dlv), the vaf.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 VAF (given in a file input.af) w.r.t. a semantics (encoded in the file semantics.dl) use one of he following commands (depending on your ASP-solver):

DLV:

$ DLV input.af vaf.dl semantics.dl -filter=in

Clingo:

$ clingo input.af vaf.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.

Semantics

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.

admissible: adm.dl
stable: stable.dl
complete: comp.dl
grounded: ground.dl
cf2: cf2.dl
resolution-based grounded: res_ground.dl

DLV only Encodings

preferred (DLV): prefexDLV.dl
semi-stable (DLV): semi_stableDLV.dl
stage (DLV): stageDLV.dl
stage2 (DLV): stage2.dl
ideal (DLV): ideal.dl *

Clingo only Encodings

preferred (clingo): prefex_gringo.lp
semi-stable (gringo/claspD): semi_stable_gringo.lp
stage (gringo/claspD): stage_gringo.lp
stage2 (gringo/claspD): stage2_gringo.lp

References

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 Value-based Argumentation Frameworks

T.J.M. Bench-Capon, Persuasion in Practical Argument Using Value Based Argumentation Frameworks, J. Log. Comput. 13(3): 429-448 (2003).

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