Stable Models for Infinitary Formulas with Extensional Atoms
This work provides a theoretical enhancement for answer set programming semantics, but it appears incremental as it builds on existing definitions and theorems.
The authors extended the definition of stable models for infinitary propositional formulas by distinguishing intensional and extensional atoms, and generalized the symmetric splitting theorem to infinitary formulas for reasoning about infinitary definitions.
The definition of stable models for propositional formulas with infinite conjunctions and disjunctions can be used to describe the semantics of answer set programming languages. In this note, we enhance that definition by introducing a distinction between intensional and extensional atoms. The symmetric splitting theorem for first-order formulas is then extended to infinitary formulas and used to reason about infinitary definitions. This note is under consideration for publication in Theory and Practice of Logic Programming.