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Applications of answer set programming motivated various extensions of the stable model semantics, for instance, to allow aggregates or to facilitate interface with external ontology descriptions. We present a uniform, reductive view on these extensions by viewing them as special cases of formulas with generalized quantifiers. This is done by extending the first-order stable model semantics by Ferraris, Lee and Lifschitz to account for generalized quantifiers and then by reducing the individual extensions to this formalism.

Action language C+, a formalism based on nonmonotonic causal logic, was designed for describing properties of actions. The definite fragment of C+ was implemented in system the Causal Calculator (CCalc), based on a reduction of nonmonotonic causal logic to propositional logic. On the other hand, in this paper, we represent the language of CCalc in answer set programming (ASP), by translating nonmonotonic causal logic into formulas under the stable model semantics. We design a standard library which describes the constructs of the input language of CCalc in terms of ASP, allowing a simple modular method to represent CCalc input programs in the language of ASP. Using the combination of system f2lp and answer set solvers, our prototype implementation of this approach, which we call Cplus2ASP, achieves functionality close to CCalc while taking advantage of answer set solvers to yield efficient computation that is orders of magnitude faster than CCalc on several benchmark examples.