Dear Editors, Please consider our manuscript, "Expressiveness, execution, and lifted recurrent closure in neurosymbolic intervention logic,” for the special issue "Neurosymbolic AI: First-Order Logic and Beyond” in Neurosymbolic Artificial Intelligence. The manuscript develops a formal account of when logical abstractions can be reused recurrently in neurosymbolic systems that combine symbolic queries, interventions, and learned representations. Its central question is not only whether a representation answers the currently declared queries, but whether that representation remains sufficient after future interventions. This distinction leads to a hierarchy between query adequacy, recurrent closure, stabilization, and type-determinism. The main technical contributions are threefold. First, for anonymous interventions we formulate recurrent reuse as a bisimulation problem and characterize one-step closure through successor 1-types. Second, for finite residual cores we give an explicit hidden-layer update and show that closure can be compiled independently of the ambient domain size. Third, we separate closure, stabilization, and type-determinism, including a single-mechanism family witnessing closure without stabilization and a six-control positive-horizon witness whose minimality is verified exhaustively through five controls. We also relate multiplicity-sensitive graded closure to strong lumpability and counting modalities. The paper connects first-order expressiveness, modal transition structure, and causal intervention semantics within a common neurosymbolic setting. It therefore directly addresses the special issue's focus on first-order logic and its extensions, while making the expressiveness–computation tradeoff operational: richer logical distinctions can support recurrently valid abstraction, but at increased representational and computational cost. The theoretical development is accompanied by controlled neural experiments designed to distinguish query-answering performance from recurrent-state adequacy. In particular, matched handwritten-digit experiments compare a query-head recurrent interface, a bit-head recurrent interface, and exact/probabilistic automaton updates after the same learned perceptual stage. The results support the theoretical distinction between a representation that answers current queries and one that retains the information required for reliable sequential execution. The manuscript is intended as a self-contained contribution at the intersection of logical expressiveness, causal reasoning, abstraction, and neural-symbolic computation. We believe it is particularly well aligned with the aims of this special issue and with Neurosymbolic Artificial Intelligence more broadly. Thank you for considering the manuscript. Sincerely, Aliefya Mahalva Ayn