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:

The first type of encodings builds on top of the core ASPARTIX system for Dung AFs
The second type of encodings are stand-alone in the sense that they are independent of the core ASPARTIX system. However they follow the same approach of encoding the CAD as input database and he semantics as fixed query.

CAFs

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

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.

CAF.lp:

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:

USAGE: clingo input.af CAF.lp semantics.dl -n 0
- input.af: The encoding of the CAF to be processed (Input format)
- semantics.dl: The ASPARTIX file implementing the semantics (ASPARTIX for Dung AFs)
Example: clingo example1.af CAF.dl stable.dl -n 0

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.

USAGE: clingo input.af semantics.dl -n 0
- input.af: The encoding of the (well-formed) CAF to be processed (Input format)
- semantics.dl: The encoding of the corresponding semantics
Example: clingo example1.af ST.lp -n 0

Encodings for CAFs.

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

complete: CO.lp
preferred: PR.lp
stable: ST.lp
semi-stable: SST.lp
stage: STG.lp

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.

References

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

Wolfgang Dvořák, Stefan Woltran. Complexity of Abstract Argumentation Under a Claim-centric View, AAAI 2019.

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