Minimal Objectification and Maximal Unnesting in PSOA RuleML

The paper introduces two connected advancements of Positional-Slotted, Object-Applicative RuleML: (1) a model-theoretic semantics, realized transformationally, that directly handles atoms (i.e., predicate applications) without object identifiers (e.g., relationships as in Prolog) and (2) a transformational semantics that handles nested atomic formulas (e.g., nested frames as in Flora-2/F-logic). For (1), the model theory is extended to atoms with optional OIDs, the transformation is developed from static to dynamic objectification, and the correctness of the realization is proved. For (2), the unnesting transformation is defined to decompose nested atomic formulas into equivalent conjunctions.