Abstract argumentation and answer set programming: two faces of Nelson's logic
This work provides a theoretical foundation for researchers in logic and AI, but it is incremental as it builds on existing logical frameworks without introducing new practical applications.
The paper tackles the problem of unifying logic programming and abstract argumentation frameworks by interpreting both in terms of Nelson's constructive logic N4, formalizing principles like non-contradictory inference and strengthened closed world assumption to enable modular translations.
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 formalizing, in this logic, two principles that we call non-contradictory 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 non-contradictory inference principle. Attacks are then represented by combining this new implication with strong negation. Under consideration in Theory and Practice of Logic Programming (TPLP).