TY  - GEN
A1  - Aguado, Felicidad
A1  - Cabalar, Pedro
A1  - Fandinno, Jorge
A1  - Pearce, David
A1  - Perez, Gilberto
A1  - Vidal, Concepcion
T1  - Revisiting explicit negation in answer set programming
T2  - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
N2  - 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.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1104 
KW  - Answer Set Programming
KW  - non-monotonic reasoning
KW  - Equilibrium logic
KW  - explicit negation
Y1  - 2021
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-469697
SN  - 1866-8372
IS  - 1104
SP  - 908
EP  - 924
ER  - 
TY  - JOUR
A1  - Cabalar, Pedro
A1  - Fandinno, Jorge
A1  - Schaub, Torsten H.
A1  - Schellhorn, Sebastian
T1  - Gelfond-Zhang aggregates as propositional formulas
JF  - Artificial intelligence
N2  - Answer Set Programming (ASP) has become a popular and widespread paradigm for practical Knowledge Representation thanks to its expressiveness and the available enhancements of its input language. One of such enhancements is the use of aggregates, for which different semantic proposals have been made. In this paper, we show that any ASP aggregate interpreted under Gelfond and Zhang's (GZ) semantics can be replaced (under strong equivalence) by a propositional formula. Restricted to the original GZ syntax, the resulting formula is reducible to a disjunction of conjunctions of literals but the formulation is still applicable even when the syntax is extended to allow for arbitrary formulas (including nested aggregates) in the condition. Once GZ-aggregates are represented as formulas, we establish a formal comparison (in terms of the logic of Here-and-There) to Ferraris' (F) aggregates, which are defined by a different formula translation involving nested implications. In particular, we prove that if we replace an F-aggregate by a GZ-aggregate in a rule head, we do not lose answer sets (although more can be gained). This extends the previously known result that the opposite happens in rule bodies, i.e., replacing a GZ-aggregate by an F-aggregate in the body may yield more answer sets. Finally, we characterize a class of aggregates for which GZ- and F-semantics coincide.
KW  - Aggregates
KW  - Answer Set Programming
Y1  - 2019
U6  - https://doi.org/10.1016/j.artint.2018.10.007
SN  - 0004-3702
SN  - 1872-7921
VL  - 274
SP  - 26
EP  - 43
PB  - Elsevier
CY  - Amsterdam
ER  -