A general account of argumentation with preferences

Sanjay Modgil, Henry Prakken
2013 Artificial Intelligence  
This paper builds on the recent ASPIC + formalism, to develop a general framework for argumentation with preferences. We motivate a revised definition of conflict free sets of arguments, adapt ASPIC + to accommodate a broader range of instantiating logics, and show that under some assumptions, the resulting framework satisfies key properties and rationality postulates. We then show that the generalised framework accommodates Tarskian logic instantiations extended with preferences, and then
more » ... instantiations of the framework by classical logic approaches to argumentation. We conclude by arguing that ASPIC + 's modelling of defeasible inference rules further testifies to the generality of the framework, and then examine and counter recent critiques of Dung's framework and its extensions to accommodate preferences. Proposition 30. Let (A, C, ) be defined by an AL argumentation theory, where is defined under the weakest or last link principles, based on the set comparison Eli . Then ∀A, B ∈ A, ∀A − ∈ A, if A ⊀ B then A − ⊀ B. Proof. Since all arguments are strict continuations of ordinary premises, the last and weakest link principles are evaluated in the same way. Suppose A ⊀ B. Then Prem(A) Eli Prem(B). That is to say, it is not the case that ∃X ∈ Prem(A) s.t. ∀Y ∈ Prem(B), X Y , i.e., ∀X ∈ Prem(A), ∃Y ∈ Prem(B) s.t. X Y . Since Prem(A − ) ⊆ Prem(A), it trivially follows that ∀X ∈ Prem(A − ), ∃Y ∈ Prem(B) s.t. X Y , i.e., A − ⊀ B. P Proposition 32. Let be the c-SAF based on (L , Cn) and (Σ, ). Then for any complete extension E of : S = {φ|φ ∈ Prem(A), A ∈ E} is AL-inconsistent iff S = Cl R s ({Conc(A)|A ∈ E}) is inconsistent. Proof. Left to right: if S is AL inconsistent then ϕ, −ϕ ∈ Cn(S) for any ϕ. By definition of R s , for some T , T ⊆ S there exist rules T → ϕ and T → −ϕ in R s . Since E is closed under sub-arguments and premises are sub-arguments, {Conc(A)|A ∈ E} includes T and T . Hence ϕ, −ϕ ∈ S . That is, S is inconsistent.
doi:10.1016/j.artint.2012.10.008 fatcat:wa65yv3rsndflelpno5felsygm