It has been known for a long time that intuitionistically equivalent formulas have the same stable models. We extend this theorem to propositional formulas with infinitely long conjunctions and disjunctions and show how to apply this generalization to proving properties of aggregates in answer set programming.

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Theory and Practice of Logic Programming , Vol. 15, 1 (2015).

@article{harrison:lpnmr13, title={On Equivalence of Infinitary Formulas under the Stable Model Semantics}, author={Amelia Harrison and Vladimir Lifschitz and Miroslaw Truszczynski}, volume={15}, journal={Theory and Practice of Logic Programming }, number={1}, url="http://www.cs.utexas.edu/users/ai-lab?etinf", year={2015} }