An Alternative Theory of Stable Revision for Nondeterministic Approximation Fixpoint Theory and the Relationships

Abstract

Approximation fixpoint theory (AFT) is a robust and popular mathematical framework that characterizes many nonmonotonic semantics, where the construction of stable fixpoints, called stable revision, play a central role. Nondeterministic AFT is a recent development that redefines AFT for a nondeterministic setting to capture disjunctive semantics. This theory departs from traditional AFT by introducing distinct definitions, thus raising the question of whether deterministic AFT can be adopted directly to define nondeterministic stable revision. This work proposes such an alternate theory and creates a new way to study disjunctive semantics in terms of normal (non-disjunctive) knowledge bases. To demonstrate the viability of our framework, we show how to capture stable and partial stable models for disjunctive logic programs. We then study the relationships between this alternative theory and the state-of-the-art nondeterministic AFT.