A Framework for Dynamic Model Construction and Its Implications for System Design
Abstract
Traditional accounts treat a theory as a set of propositions—axioms, equations, rules—that can be written down and transmitted. Peter Naur challenged this view by arguing that the real theory is the understanding held by the practitioner, not the document. This article accepts Naur’s starting point and goes further: we propose that a theory is neither a static body of knowledge nor merely an ineffable intuition, but a structured capability held by an agent to select, instantiate, and revise models appropriate to the current informational situation.
We resolve several tensions in existing accounts. First, we distinguish the content of a theory (concepts, mechanisms, negative knowledge, scope conditions) from its operation (model selection, contradiction detection, revision) and its identity (what persists through change). Second, we adopt a position of scoped realism: within a declared scope, truth claims are binding; across scopes, appropriateness replaces universal validity. Third, we argue that a theory is inherently agent-relative—it requires a mind or reasoning system to exist as a theory—while artifacts carry only traces that prompt reconstruction.
The framework is developed with a running example from systems engineering and concludes with design principles for artificial systems that aim to hold, apply, and revise theories rather than merely store information.
1. The Problem: Two Incomplete Pictures
1.1 The propositional view
Most scientific and engineering disciplines treat a theory as something that can be fully written down. A theory consists of facts, equations, definitions, algorithms, or logical rules. Knowledge is represented explicitly. Learning means acquiring these representations. Application means executing them.
This picture works well for closed formal systems—mathematics, type theory, hardware verification—where assumptions are fixed, every term has a precise meaning, and no external context intrudes.
It fails for everything else.
1.2 Naur’s correction
Peter Naur (1985) observed that a program can survive for decades while the understanding that produced it vanishes. Future maintainers may parse every line of syntax while lacking the reasons behind design decisions. They can modify the artifact only superficially because they do not possess the theory.
Naur’s conclusion: the theory is not the document. It is the understanding possessed by the person who built the system.
This redirects the question from What should be written down? to What constitutes the understanding that enables correct application and extension?
1.3 What Naur leaves open
Naur identifies the locus of theory (the agent’s mind) but does not characterize its structure. He tells us where theory lives, not what it is made of, how it operates, how it changes, or how it could be supported artificially.
The present article addresses these questions.
2. Definition
We propose the following:
A theory is an agent’s structured capability to select, instantiate, and revise the most appropriate model for a given informational situation.
This definition commits to four claims:
- Agent-relativity. A theory requires an agent—a human mind or an artificial reasoning system—to exist as a theory. Artifacts (documents, code, databases) carry traces that can prompt reconstruction, but they are not themselves theories. This is Naur’s insight made explicit.
- Structured capability, not stored content. A theory is not a list of facts. It is a disposition to act: to generate explanations, predictions, and decisions. However, this capability has structure—it draws on organized content (concepts, mechanisms, negative knowledge, scope conditions). The content is the substrate; the capability is what the theory is.
- Model selection as the primary operation. A mature theory does not apply one universal description. It selects among a family of models at different levels of abstraction, choosing the one appropriate to the information currently available and the task at hand.
- Revision as constitutive. A theory that cannot revise itself when confronted with contradictions is incomplete. The revision procedure is not external maintenance; it is part of the theory’s identity.
The remainder of this paper unpacks each of these claims.
3. Running Example: A Task Scheduler
To ground the abstraction, consider an engineer designing a task scheduler for an operating system.
A junior engineer might state the theory as: „Assign the highest-priority ready task to the CPU.“ This is a proposition. It can be written down. It can be transmitted.
An experienced engineer’s theory is richer and different in kind. It includes:
- The concept of priority, and the knowledge that priority inversion can make priority meaningless unless inheritance protocols are in place.
- The causal mechanism by which context switching introduces overhead, and the approximate threshold below which switching cost dominates useful work.
- The rejected alternative of pure round-robin scheduling, and the specific workload profiles under which it was tried and failed.
- The assumption that tasks are independent, and the knowledge that this breaks down with shared resources, requiring a different model.
- The invariant that no task starves indefinitely, and the recognition that this invariant holds only under the fairness constraint, which itself has a scope.
- The unresolved anomaly that real-time deadlines interact pathologically with garbage collection pauses, for which no clean model yet exists.
The junior engineer has a rule. The senior engineer has a theory. The difference is not quantity of information. It is structure, scope awareness, negative knowledge, and the ability to select the right model when the situation changes.
We will return to this example throughout.
4. The Three Layers
Understanding operates on three distinct levels. Confusing them is a primary source of failed knowledge transfer.
4.1 Deep theory
The deep theory is the complete conceptual structure held by the agent. It contains:
- concepts and their relationships,
- causal mechanisms,
- assumptions and their justifications,
- applicability conditions and scope boundaries,
- invariants (hard and soft; see §7),
- defaults and their override conditions,
- negative knowledge: rejected alternatives, failed experiments, dangerous modifications,
- unresolved anomalies,
- revision history: what changed, why, and what was abandoned.
This layer is rarely communicated in full. It is built over years of interaction with the domain.
4.2 Operative theory
The operative theory is the model currently instantiated for the present situation. It is a projection of the deep theory onto the relevant subset of concepts and assumptions.
In the scheduler example: when debugging a latency spike in a single-core context, the operative theory may include only priority scheduling, context-switch cost, and the assumption of task independence. The deep theory’s knowledge of multiprocessor cache affinity, real-time deadline anomalies, and garbage-collection interactions is present but inactive.
As new information arrives—a second core is added, a shared mutex appears—the operative theory expands or switches. The deep theory supplies the next model; the operative theory is what is actually running.
4.3 Communicated theory
Human communication transmits a lossy compression of the deep theory. The sentence „Use priority scheduling with inheritance“ assumes the listener can reconstruct the scope conditions, the rejected alternatives, and the failure modes. If the listener cannot, the communication fails silently: the words are received, the theory is not.
This is Naur’s observation in structural terms. The document is a communicated theory. It is not the theory.
5. The Revision Loop
A theory is not a fixed object. It operates as a continuous loop:
- Interpret the current situation: identify available information, constraints, and task.
- Select the most appropriate model from the family (see §6).
- Instantiate the operative theory: activate relevant concepts, assumptions, mechanisms.
- Derive expectations: predictions, explanations, or decisions.
- Compare with observations or outcomes.
- Detect contradictions, anomalies, or scope violations.
- Revise: adjust scope, refine concepts, incorporate new negative knowledge, or switch to a different model in the family.
- Return to step 1.
The theory is not identical to its state at any single iteration. It is the structured disposition to execute this loop competently. The loop is the operation; the deep theory is the resource it draws on; the operative theory is its current output.
In the scheduler example: the engineer deploys priority scheduling (steps 1–4), observes starvation under a specific workload (step 5–6), and introduces aging as a fairness mechanism while recording the original failure as negative knowledge (step 7). The theory has changed. It is still the same theory—same domain, same agent, same conceptual lineage—but its content has been revised.
6. Families of Models and Scope
6.1 No single correct description
A mature theory does not consist of one universal statement. It consists of a family of models at different levels of abstraction, each valid within a declared scope.
„Birds fly“ is not a false statement. It is a coarse model whose scope is: given only the information that x is a bird, with no further data, the best default prediction is flight. When additional information arrives (penguin, injury, fledgling), a more specific model in the family replaces it.
The scheduler’s deep theory similarly contains: a coarse model for initial capacity planning (tasks are independent, priorities are fixed), a mid-level model for single-core debugging (context-switch overhead matters, priority inversion is possible), and a fine-grained model for multiprocessor real-time analysis (cache affinity, deadline monotonicity, GC pauses).
6.2 Selection, not accumulation
Understanding does not work by continuously appending exceptions to a universal rule. It works by selecting the model whose scope matches the current informational situation. This keeps the operative theory simple without making it simplistic.
6.3 Scoped realism
We adopt the following position on truth:
- Within a declared scope, truth claims are binding. If the scheduler’s model assumes task independence and the scope condition holds, then the model’s predictions are true or false in the ordinary sense.
- Across scopes, the relevant question is not truth but appropriateness. A coarse model is not false when a fine-grained model exists; it is appropriate or inappropriate for the information at hand.
This avoids both naïve realism (one true description of the world) and pure instrumentalism (theories are merely useful fictions). Truth operates within scope. Appropriateness governs scope selection.
7. Invariants, Contradictions, and Negative Knowledge
7.1 Two kinds of invariants
Not all invariants are equal.
- Hard invariants are logical or structural constraints within a fixed scope. Example: within the scheduler’s fairness model, no task’s waiting time exceeds the aging threshold. Violation means the implementation is wrong.
- Soft invariants are empirical regularities that hold under typical conditions. Example: higher-priority tasks usually complete sooner. Violation does not mean the theory is wrong; it triggers scope investigation.
Confusing these two types is a common source of error. Formal verification treats all invariants as hard. Theory building requires distinguishing them.
7.2 Contradictions as diagnostic signals
When an apparent contradiction arises, the agent does not immediately discard the theory. Instead, the revision loop asks:
- Was the model applied outside its declared scope?
- Were hidden assumptions violated?
- Is a concept defined too broadly or too narrowly?
- Has new evidence genuinely falsified a claim within scope?
Only the last case requires substantive revision. The first three require scope correction or conceptual refinement. All four outcomes feed back into the deep theory as updated knowledge.
7.3 Negative knowledge
Finished artifacts encode only positive knowledge: what works. They omit the failed designs, rejected hypotheses, and dangerous modifications that shaped the final solution.
This omission is costly. Negative knowledge—knowing why an alternative fails—dramatically constrains the search space and prevents future agents from re-exploring dead ends.
In the scheduler example: the knowledge that „pure round-robin was tried in 2019 and caused unacceptable tail latency under bursty I/O workloads“ is not in the code. It is in the senior engineer’s deep theory. When that engineer leaves, the negative knowledge leaves. A new team may re-derive the failure at significant cost.
A mature theory therefore consists of positive knowledge and the structured record of why neighboring explanations were rejected.
8. Identity, Agents, and Transfer
8.1 What persists through revision
If a theory continuously revises its content, what makes it the same theory over time?
We propose three identity conditions:
- Domain continuity. The theory addresses the same phenomenon or problem space.
- Conceptual lineage. Revisions are traceable to prior states; concepts evolve rather than being replaced wholesale.
- Agent continuity. The same agent (or a successor that has reconstructed the theory) holds and maintains it.
A theory that revises its fairness mechanism while retaining its scheduling concepts, its scope structure, and its negative knowledge is the same theory, updated. A theory replaced by an entirely different framework (e.g., switching from priority-based to lottery scheduling with no conceptual overlap) is a new theory.
8.2 Agent-relativity
A theory exists only in an agent. A document, a codebase, a database—these are artifacts. They carry traces of a theory: compressed propositions, structural hints, negative knowledge in comments or commit messages. But they do not constitute a theory because they cannot execute the revision loop. They cannot select a model, detect a contradiction, or refine a scope.
This is not a mystical claim. It is a functional one. A theory is a capability. Capabilities require an agent.
8.3 Transfer
Naur’s central frustration is that theory does not transfer through documents. Our framework explains why and suggests what might help.
What transfers: communicated theory (lossy compression), structural hints, negative knowledge if explicitly recorded, scope declarations.
What does not transfer: the operative model-selection disposition, the felt sense of when a scope boundary is approaching, the implicit weighting of which anomalies matter.
Transfer therefore requires not better documentation but guided reconstruction: the receiving agent must build its own deep theory by interacting with the domain, using the artifact as a prompt rather than a source. Apprenticeship, pair programming, and interactive explanation work because they support reconstruction. Handing over a manual does not.
9. Implications for System Design
The framework has direct consequences for building artificial systems that aim to hold and apply theories rather than merely store information.
9.1 What current systems lack
- Traditional knowledge bases store propositions. They have content but no revision loop, no scope selection, no negative knowledge. They are communicated theories frozen in a database.
- Machine learning models learn statistical regularities. They generalize within a training distribution but lack explicit scope declarations, cannot articulate why an alternative was rejected, and do not revise their conceptual structure in response to a single contradiction.
- Large language models occupy an intermediate position. They carry broad background knowledge and can reason about scope, but their „theory“ is not structured, not versioned, and not tied to a persistent revision history. Each interaction reconstructs an operative model from scratch, with no guaranteed continuity.
None of these systems, as currently designed, holds a theory in the sense defined here.
9.2 Design principles
A system that aspires to hold a theory should implement the following:
- Explicit scope declarations. Every model or rule carries a declaration of the conditions under which it is valid. The system checks scope before applying a model, not after a failure.
- A model family, not a single representation. The system maintains multiple models at different levels of abstraction for the same domain and selects among them based on available information and task requirements.
- Negative knowledge as a first-class object. Rejected alternatives, failed experiments, and known failure modes are stored with the same structural status as positive knowledge. They are indexed by the conditions under which they apply.
- A revision loop. The system detects contradictions between predictions and observations, classifies them (scope violation, assumption failure, conceptual error, genuine falsification), and triggers the appropriate revision. Revisions are logged and traceable.
- Identity tracking. The system maintains conceptual lineage: what changed, why, what was abandoned. This supports both the agent’s own coherence and the possibility of transfer to another agent.
- Layered representation. The deep theory (full structure), the operative theory (current model), and the communicated theory (output for humans or other systems) are distinct layers. The system does not confuse its current operative output with its full knowledge.
9.3 The role of LLMs
An LLM can serve as the reasoning engine within such a system: it interprets situations, selects models, generates explanations, and detects contradictions. But it cannot serve as the theory itself, because it lacks persistent structure, versioned revision history, and explicit scope management.
A productive architecture pairs:
- a persistent theory store (structured content: concepts, mechanisms, scope conditions, negative knowledge, revision log),
- an LLM or reasoning engine (capability: interpretation, model instantiation, explanation generation, contradiction detection),
- an interaction context (current situation, task, available information),
- a revision controller (classifies contradictions, triggers updates, maintains lineage).
The operative theory emerges from the interaction of all four. It is reconstructed each time it is needed, but it is reconstructed from structured, persistent resources, not from scratch. This preserves Naur’s insight—understanding is an active capability, not a static artifact—while adding the structure Naur did not specify.
10. Summary: What Makes a Theory
A theory is not a collection of propositions. It is not a document. It is not a statistical model. It is not a single universal description of reality.
A theory is an agent’s structured capability to select, instantiate, and revise the most appropriate model for a given informational situation.
Its structure comprises:
- concepts and causal mechanisms,
- assumptions and scope conditions,
- hard and soft invariants,
- defaults and their override conditions,
- negative knowledge and rejected alternatives,
- unresolved anomalies,
- and revision procedures.
Its operation is a continuous loop of interpretation, model selection, prediction, comparison, contradiction detection, and revision.
Its identity persists through revision via domain continuity, conceptual lineage, and agent continuity.
Its truth is scoped: binding within declared conditions, governed by appropriateness across conditions.
Its transfer requires guided reconstruction, not document delivery.
Understanding, in this framework, is not the possession of facts. It is the disciplined, continuous practice of building, applying, evaluating, and refining models in response to an ever-changing world.
References
- Naur, P. (1985). Programming as Theory Building. Microprocessing and Microprogramming, 15(5), 253–261.
- Kuhn, T. S. (1962). The Structure of Scientific Revolutions. University of Chicago Press.
- Lakatos, I. (1970). Falsification and the Methodology of Scientific Research Programmes. In Criticism and the Growth of Knowledge. Cambridge University Press.
- Peirce, C. S. (1878). How to Make Our Ideas Clear. Popular Science Monthly, 12, 286–302.
- van Fraassen, B. C. (1980). The Scientific Image. Oxford University Press.
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