I am computer scientist, not a mathematician, I've been reading some papers on argumentation in AI that uses the term 'maximal' set without defining it. I think it's left undefined because it's a term used widely in mathematics? The paper at the end of this post. I hope this question isn't too simple for this forum and I hope set theory is ok as a tag?!


Many thanks.


@article{Dung2007642,
title = "Computing ideal sceptical argumentation",
journal = "Artificial Intelligence",
volume = "171",
number = "10-15",
pages = "642 - 674",
year = "2007",
note = "Argumentation in Artificial Intelligence",
doi = "DOI: 10.1016/j.artint.2007.05.003",
author = "P.M. Dung and P. Mancarella and F. Toni"
}



What is a maximal set in the context of argumentation in AI
Typically, the term maximal means that a set $A$ has a property but $A \cup \{x \}$ does not have this property for any $x \notin A$. (For example, a maximal matching is a set of edges which is a matching, but if any new edge is added it is no longer a matching.) This is weaker than a *maximum* set, which is the largest (in cardinality) set with the property.


