The Relational Agent: How Symbolic Structure Shapes LLM Reasoning, Analysis, and Action: A Secretary Suite Project
DOI: [To be assigned]
John Swygert
August 25, 2026
Abstract
This paper extends relational symbolic analysis from static language-model outputs to agentic systems. An LLM agent does not merely answer a prompt: it receives layered instructions, maintains context, retrieves external material, chooses tools, decomposes tasks, evaluates intermediate results, and acts through interfaces. Each step introduces boundaries, scopes, precedence relations, state transitions, and possible routing errors. The paper proposes that many apparent failures of agent reasoning can be studied as relational failures rather than as undifferentiated 'intelligence' failures.
1. From Language Model to Agent
An isolated language-model completion can be represented as a conditional transformation from context to output. An agent adds persistence, tools, memory, planning, observation, and action. The relevant object is therefore not a single response but a trajectory through states.
Agent behavior can be represented schematically as Sₜ₊₁ = F(Sₜ, Iₜ, Cₜ, Mₜ, Tₜ, Oₜ), where I is instruction structure, C context, M memory or retrieved material, T available tools, and O observations returned by the environment.
The central claim is not that this equation is a complete agent model. It is a decomposition that makes relational dependencies explicit.
2. Instruction Hierarchy as Scope and Precedence
Agent systems commonly contain multiple instruction layers. System constraints, developer rules, user requests, retrieved text, tool outputs, and remembered context do not occupy equivalent authority. Confusion among those layers is structurally similar to precedence and scope errors in mathematics and programming.
A robust agent must distinguish content from instruction, quotation from command, data from authority, and local requests from higher-order constraints. These are boundary operations.
Instruction failure can therefore be analyzed as a precedence error, scope leak, boundary collapse, or source-attribution error rather than merely as a bad answer.
3. Analysis as Relational Decomposition
Complex requests can be decomposed into entities, constraints, dependencies, temporal relations, required evidence, transformations, and output conditions. This provides a relational lens for analysis before generation.
A useful analysis is not simply longer reasoning. It is better preservation of the relations that determine what counts as a correct result.
The proposed agent discipline is: identify components; identify relations; identify boundaries; identify precedence; identify state; select pathway; execute; compare outcome with target; inspect residual.
4. Tool Use as Routed Transformation
A tool call changes the system boundary. Information leaves the language model, enters another computational system, and returns as an observation. Tool selection is therefore a routing decision.
Errors may occur because the wrong tool was selected, the right tool received malformed arguments, returned data were mis-scoped, or the agent failed to incorporate the observation correctly.
Tool-use evaluation should record not only success or failure but the relational location of failure.
5. Memory and Retrieval
Retrieved information is not automatically relevant merely because it is semantically similar. It must be placed into the correct relational role.
Memory systems should preserve provenance, time, authority, subject, dependencies, and intended scope. Otherwise retrieval can create context contamination: accurate information inserted into the wrong relation.
A relational memory object is therefore richer than a text fragment. It is content plus metadata about how that content may legitimately connect to the current task.
6. Relational Sensitivity in Agents
The relational sensitivity vector introduced for symbolic analysis can be extended to agents. Candidate dimensions include instruction-order sensitivity, boundary sensitivity, retrieval sensitivity, tool-routing sensitivity, memory sensitivity, temporal sensitivity, and hierarchy sensitivity.
Repeated agent evaluations could produce a behavioral profile rather than a single benchmark score.
Such profiles may reveal why two models with similar aggregate accuracy behave differently in long-running workflows.
7. Reply Construction
Replies are downstream products of analysis. A relational agent should preserve the user's requested scope, distinguish facts from inference, maintain referents, avoid accidental contradiction, and organize output according to the task's dependency structure.
This framework therefore predicts that improved relational bookkeeping can change not only correctness but relevance, concision, continuity, and calibration.
8. Error Recovery and Residuals
An agent should compare observed output with target conditions and inspect the residual rather than restarting blindly.
R_A = Y_observed - Y_target can be treated as a diagnostic placeholder. The residual must be decomposed: missing information, wrong relation, wrong boundary, wrong route, wrong transformation, stale state, or execution failure.
Error recovery becomes a correction problem rather than a generic regeneration problem.
9. Experimental Program
Controlled agent experiments should vary one relational dimension at a time: instruction order, delimiter placement, retrieved-document position, memory inclusion, tool-result framing, or hierarchy conflict.
Outcome measures can include task success, tool selection, factual fidelity, constraint retention, recovery rate, latency, and number of corrective turns.
The important comparison is whether relational diagnostics predict failure better than undifferentiated prompt-length or model-size measures.
10. TSTOEAO Mapping
The agent domain maps naturally onto TSTOEAO because it contains gradients, boundaries, pathways, transformations, costs, corrections, targets, and residuals.
However, mappability is not validation. TSTOEAO gains scientific value only if its relational decomposition predicts failures, corrections, or efficiencies better than simpler competing descriptions.
Conclusion
The relational-agent perspective reframes agent intelligence as structured state transformation under layered constraints. The practical question is not merely whether an agent can reason, but whether it preserves the relations that make its reasoning valid while moving through tools, memory, context, and action.
If experimentally supported, relational profiles could become useful diagnostics for agent design, evaluation, and governance.
Methodological Guardrails
Do not confuse a useful relational description with proof of mechanism.
Operationalize variables before treating notation as measurement.
Compare relational diagnostics against simpler baselines.
Preserve provenance and distinguish observation from inference.
Use controlled perturbations and ablations wherever possible.
Treat residual disagreement and failed predictions as information.
References
Vaswani, A., et al. (2017). Attention Is All You Need. Advances in Neural Information Processing Systems, 30.
Shannon, C. E. (1948). A Mathematical Theory of Communication. Bell System Technical Journal, 27.
Grice, H. P. (1975). Logic and Conversation. In Syntax and Semantics, Vol. 3.
Pierce, B. C. (2002). Types and Programming Languages. MIT Press.
Jurafsky, D., & Martin, J. H. Speech and Language Processing. Stanford University.
Swygert, J. (2026). Punctuation as Linguistic Mathematics. Ivory Tower Publishing.
Swygert, J. (2026). Relational Symbolic Technologies across Language, Mathematics, and Code. Ivory Tower Publishing.
Swygert, J. (2026). TSTOEAO Empirical Core v1.0.0. Ivory Tower Publishing.
Swygert, J. (2026). 200 From Language to Computation: Linguistics, Punctuation, Mathematics, and Programming as a Unified Relational Architecture in Large Language Models. Ivory Tower Publishing.
No comments:
Post a Comment