Are you an EPFL student looking for a semester project?
Work with us on data science and visualisation projects, and deploy your project as an app on top of Graph Search.
Concept
Argumentation framework
Summary
In artificial intelligence and related fields, an argumentation framework is a way to deal with contentious information and draw conclusions from it using formalized arguments.
In an abstract argumentation framework, entry-level information is a set of abstract arguments that, for instance, represent data or a proposition. Conflicts between arguments are represented by a binary relation on the set of arguments. In concrete terms, you represent an argumentation framework with a directed graph such that the nodes are the arguments, and the arrows represent the attack relation.
There exist some extensions of the Dung's framework, like the logic-based argumentation frameworks or the value-based argumentation frameworks.
Abstract argumentation frameworks, also called argumentation frameworks à la Dung, are defined formally as a pair:
A set of abstract elements called arguments, denoted
A binary relation on , called attack relation, denoted
For instance, the argumentation system with and contains four arguments ( and ) and three attacks ( attacks , attacks and attacks ).
Dung defines some notions :
an argument is acceptable with respect to if and only if defends , that is such that such that ,
a set of arguments is conflict-free if there is no attack between its arguments, formally : ,
a set of arguments is admissible if and only if it is conflict-free and all its arguments are acceptable with respect to .
To decide if an argument can be accepted or not, or if several arguments can be accepted together, Dung defines several semantics of acceptance that allows, given an argumentation system, sets of arguments (called extensions) to be computed. For instance, given ,
is a complete extension of only if it is an admissible set and every acceptable argument with respect to belongs to ,
is a preferred extension of only if it is a maximal element (with respect to the set-theoretical inclusion) among the admissible sets with respect to ,
is a stable extension of only if it is a conflict-free set that attacks every argument that does not belong in (formally, such that ,
is the (unique) grounded extension of only if it is the smallest element (with respect to set inclusion) among the complete extensions of .
Official source
About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.