Dear Editors-in-Chief, We are pleased to submit the manuscript titled "Mapping the Neuro-Symbolic Landscape: A Formal, Unified Framework for Design and Comparison" for consideration in Neurosymbolic Artificial Intelligence. The paper addresses a structural gap in the NeSy survey literature: despite the field's rapid growth, no prior work provides a shared, formal vocabulary that makes different systems directly comparable. Our paper fills this gap by introducing the NeSy design space, a unified framework that characterises any NeSy system along four well-established dimensions (syntax, semantics, inference, and integration), each grounded in a common mathematical language and related to the others explicitly. The central contribution is the design space itself. Prior surveys characterise NeSy systems along the four dimensions of syntax, semantics, inference, and integration, but do so informally, in mutual isolation, or with inconsistent terminology across the literature. Our framework addresses all three problems simultaneously: it grounds each dimension in a shared formal language, makes the dependencies between dimensions explicit, and provides a unified vocabulary that maps conflicting usages onto a common structure. Concretely, the syntax dimension formalises the symbolic interface of a NeSy system as a typed language that separates domain-agnostic logical vocabulary from domain-specific symbols, classifying systems along a spectrum from propositional to full first-order logic with temporal, spatial, and higher-order extensions. The semantics dimension grounds symbolic expressions in a Kleisli-categorical framework parameterised by a category, a monad, and a truth object, which subsumes Boolean, fuzzy, and probabilistic semantics as special cases of the same structure and models neural components as parameterised arrows within it. The inference dimension provides a three-axis taxonomy (type, method, and faithfulness) that applies uniformly across logical, probabilistic, and neural paradigms, resolving the cross-community terminology clash and making inference chains legible as sequences of well-defined operations. The integration dimension formalises three structural patterns (Nesting, Co-routine, and Compilation) as compositions of the same categorical arrows used for semantics, making explicit that the integration choice is constrained by the semantic choice and not independent of it. For each dimension, the paper includes a dedicated treatment of related work, positioning existing surveys within the formal vocabulary of that dimension and thereby making the framework directly relatable to the existing literature. We demonstrate the framework's generality by positioning representative systems (DeepProbLog, Scallop, Logic Tensor Networks, NS-CL, LOGIC-LM, ABL, and others) as instances of the same design space, showing that systems previously described in incompatible terms can be compared directly. We believe this manuscript is well-suited to Neurosymbolic Artificial Intelligence. The journal is the primary venue for foundational and cross-cutting NeSy research, and the framework presented here is directly aimed at the community it serves: it gives practitioners a principled basis for system design and comparison, and it gives the research community a formal language for making precise claims about the properties of NeSy architectures. We confirm that this manuscript has not been previously published and is not currently under review elsewhere. All authors have read and approved the submission. There are no conflicts of interest to declare. We note that Ole Fenske and Daniel Romero Schellhorn contributed equally and share first authorship. We thank the editors and reviewers for their time and look forward to their assessment. Sincerely, Ole Fenske and Daniel Romero Schellhorn (on behalf of all authors) University of Rostock / University of Osnabrück ole.fenske@uni-rostock.de