Revisiting Explicit Negation in Answer Set Programming

[Abstract] A common feature in Answer Set Programming is the use of a second negation, stronger than default negation and sometimes called explicit, strong or classical negation. This explicit negation is normally used in front of atoms, rather than allowing its use as a regular operator. In this paper we consider the arbitrary combination of explicit negation with nested expressions, as those defined by Lifschitz, Tang and Turner. We extend the concept of reduct for this new syntax and then prove that it can be captured by an extension of Equilibrium Logic with this second negation. We study some properties of this variant and compare to the already known combination of Equilibrium Logic with Nelson’s strong negation.Ministerio de Economía y Competitividad; TIC2017-84453-PXunta de Galicia; GPC ED431B 2019/03Xunta de Galicia; 2016-2019 ED431G/01, CITICCentre International de Math´ematiques et d’Informatique de Toulouse; ANR-11-LABEX-004

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)

Inference Rules in Nelson’s Logics, Admissibility and Weak Admissibility

© 2015, Springer Basel. Our paper aims to investigate inference rules for Nelson’s logics and to discuss possible ways to determine admissibility of inference rules in such logics. We will use the technique offered originally for intuitionistic logic and paraconsistent minimal Johannson’s logic. However, the adaptation is not an easy and evident task since Nelson’s logics do not enjoy replacement of equivalences rule. Therefore we consider and compare standard admissibility and weak admissibility. Our paper founds algorithms for recognizing weak admissibility and admissibility itself – for restricted cases, to show the problems arising in the course of study