10.2, Argumentation, N-Person Games and Stable Marriage Problem

Notes taken from ‘On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games’, by Phan Minh Dung (1995)

2.1, Argumentation in N-Persons Games

Stable extensions do not capture the intuitive semantics of every meaningful argumentation system… As preferred extensions exist for every argumentation framework, we can introduce the preferred solutions to n-person games by defining them as the preferred extensions of the corresponding argumentation system… The new solutions satisfy both conditions of a rational standard behaviour: freeness from inner contradiction and the ability to withstand any attack from outside. This is clearly a contribution to the theory of n-person games.

2.2, Argumentation and the Stable Marriage Problem

Let P be a knowledge base represented either as a logic program, or as a non-monotonic theory or as an argumentation framework. Then there is not necessarily a “bug” in P if P has no stable semantics (as demonstrated by the stable marriage love triangle example).