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Tools: Drucken

ASPARTIX for Claim-augmented Argumentation Frameworks

Here we provide systems to compute claim-based extensions of and reasoning with Claim-augmented Argumentation Frameworks (aka argument-conclusion structure). We provide two types of encodinges:


CAFs extend Dung AFs by associating a claim to each argument. Here a claim is abstract identifier, which allows to identify arguments with the same claim. So-called well-formed CAFs satisfy an additional constraint that arguments with the same claim attack the same arguments.

Input Format


CAFs are encoded by a sequence of statements that either encode an argument and its claim, or an attack from one argument to another.

arg(a,c). ... a is an argument with claim c att(a,b). ... argument a attacks argument b
Consider the following example
CAF Input File
Consider a CAF with
  • arguments alpha, beta, gamma1 and gamma2
  • such that the claim of alpha and beta is a
    and the claim of gamma1 and gamma2 is c.

arg(alpha,a). arg(beta,a). arg(gamma1,c). arg(gamma2,c). att(alpha,beta). att(alpha,gamma1). att(beta,alpha). att(beta,gamma2).

Well-formed CAFs

arg(a,c). ... a is an argument with claim c att(x,b). ... all arguments with claim x attack argument b
Notice that it is important to keep the argument and claim names disjoint.
Consider the following example
well-formed CAF Input File
Consider a well-formed CAF with
  • arguments alpha, beta, gamma1 and gamma2
  • such that the claim of alpha is a,
    the claim beta is b
    and the claim of gamma1 and gamma2 is c.

arg(alpha,a). arg(beta,b). arg(gamma1,c). arg(gamma2,c). att(a,beta). att(a,gamma1). att(b,alpha). att(b,gamma2).

AF-based Approach

This version is based on the encoding of AF-Semantics. Thus one needs the encoding for the semantics of interest from ASPARTIX for Dung AFs and additionally the file CAF.lp in order to compute the claim-based extensions.


arg(X) :- arg(X,C). claim(C) :- in(X), arg(X,C). att(Y,X):- arg(Y,C), att(C,X). #show claim/1.

Using clingo (see Potassco) the usage is as follows:

Stand-alone Approach

The encodings provided in this section are stand-alone in the sense that they do not require additional enodings for Dung semantics. We provide separate encodings for general CAFs and well-formed CAFs that are encoding in the specific input syntax given above.

Encodings for CAFs.

In the following we provide the encodings for different argumentation semantics.

Encodings for well-formed CAFs.

For well-formed CAFs we provide two classes of Encodings. Argument-driven encodings where non-deterministic guesses are on the arguments and claim-driven encodings where non-deterministic guesses are on the claims.

Semantics argument-driven claim-driven
complete CO.lp CO.lp
preferred PR.lp PR.lp
stable ST.lp ST.lp
semi-stable SST.lp SST.lp
stage STG.lp STG.lp

Again notice that the well-formed CAF must be encoded in the special syntax for well-formed CAFs in order to apply the above encodings. If not you can use the encodings for general CAFs.


Main References

[26] Argumentation Frameworks with Claims and Collective Attacks -- Complexity Results and Answer-Set Programming Encodings
Alexander Greßler.
Masters Thesis, Technische Universität Wien, 2019 [.pdf ]
more system-related references

References for CAFs

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