Gelfond-Zhang Aggregates as Propositional Formulas

  • Pedro Cabalar
  • Jorge Fandinno
  • Torsten Schaub
  • Sebastian Schellhorn
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10377)

Abstract

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 characterise a class of aggregates for which GZ- and F-semantics coincide.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Pedro Cabalar
    • 1
  • Jorge Fandinno
    • 1
  • Torsten Schaub
    • 2
  • Sebastian Schellhorn
    • 2
  1. 1.University of CorunnaA CoruñaSpain
  2. 2.University of PotsdamPotsdamGermany

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