3 research outputs found
Abstract Argumentation and Answer Set Programming: Two Faces of Nelson’s Logic
In this work, we show that both logic programming and abstract argumentation frameworks can be interpreted in terms of Nelson’s constructive logic N4. We do so by formalising, in this logic, two principles that we call noncontradictory inference and strengthened closed world assumption: the first states that no belief can be held based on contradictory evidence while the latter forces both unknown and contradictory evidence to be regarded as false. Using these principles, both logic programming and abstract argumentation frameworks are translated into constructive logic in a modular way and using the object language. Logic programming implication and abstract argumentation supports become, in the translation, a new implication connective following the noncontradictory inference principle. Attacks are then represented by combining this new implication with strong negation. Under consideration in Theory and Practice of Logic Programming (TPLP)
The Attack as Intuitionistic Negation
We translate the argumentation networks into a theory
of intuitionistic logic, retaining as the domain and using intuitionistic
negation to model the attack in : the attack is translated
to . The intuitionistic models of characterise the complete
extensions of .
The reduction of argumentation networks to intuitionistic logic yields, in
addition to a representation theorem, some additional benefits: it allows us to
give semantics to higher level attacks, where an attack "" can itself
attack another attack ""; one can make higher level meta-statements on
and such meta-statements can attack and be attacked in the domain.Comment: 34 pages, 18 figure