Resource-bounded ideal interpreter

Status: Exploratory sketch, 2026-09-17. Moved here from the reference proposals frontier with the operator's direction that it is too experimental for anything existing to depend on it. The workshop README states what a functional definition would need and what closes the work. Nothing below is adopted.

A theory builder interprets theories, cases, and consequences to derive predictions, identify candidate faults, and assess revisions. When a product fails, the failure may lie in the theory or in how it was read, and no outcome absorbs both. This proposal holds the design object for a standard that separates the two: an interpreter idealized for faithful reading on a declared class of tasks, under a resource model, whose attempts at conceptual development stay conjectural. It was worked out in the theory-builder workshop between 2026-09-14 and 2026-09-17 and deferred from the main outcome comparison, because a claim without external assessment carries three obligations and attribution is the third: an externally tested builder can score a failure without attributing it, and needs this device only for a claim that asserts a cause. Nothing here is shipped or adopted.

Current state (as of 2026-09-17)

  • The library definitions treat interpretation as a role inside the builder and name this device without adopting it. The externally tested case records a performance failure without attributing it; attribution binds a claim that asserts a cause, and a performance claim only where no independent outcome level absorbs interpretation and theory errors together.
  • The workshop withdrew the earlier guarantee that budget exhaustion is the only failure the idealization admits. No guarantee for completed interpretations has been established on any specified class.
  • The KB's use of semantic work is the judgment of meaning and relevance in semantic work can be relocated but not eliminated; this proposal extends it with conceptual revision.
  • No implementation has been compared to the standard, and no probe suite exists for estimating a model's knowledge and procedures.

Problem

Give an evaluation a standard against which to score a real interpreter on the tasks it completed, so that an error in interpreting a theory can be separated from an error in the theory, without the standard assuming the results the builder is meant to achieve. The standard must permit new subjects and concepts, charge for the work it performs, admit unresolved results without making abstention vacuous, and stay consistent when applied to the builder's theory of itself.

Semantic work

Semantic work is establishing, examining, or revising how expressions and concepts represent a subject and bear on a question. It makes explicit the referents, distinctions, commitments, scope, and relevant consequences of a representation, or proposes changes to them when the current representation is inadequate. A representation may be a theory, model, instruction, specification, or account of a case. Interpreting a claim does not include deciding it: a conjecture may remain unresolved after successful interpretation.

The work is bounded by its contribution, not by subject area. The same agent may perform semantic and other work in one episode; executing a fixed calculation discharges an obligation semantic work identified without revising an interpretation, and coding includes semantic work when it settles what a requirement commits the implementation to.

Operation Output that makes the work reviewable
Interpret an existing expression A reading with its referents, commitments, contextual assumptions, and consequential ambiguities identified
Relate a case to a concept Grounds for including, excluding, or leaving the case undecided under the concept's stated scope
Connect commitments to consequences A relevant conditional consequence or test obligation, with the premises it depends on
Criticize a representation A conflict, missing distinction, scope failure, or rival interpretation, with the case that makes it matter
Develop or revise concepts A candidate distinction, mechanism, vocabulary, or decomposition, with what changes in interpretation or expected consequences
Translate between representations A mapping of commitments: preserved, omitted, added, still unsettled

Interpretation and invention have different success conditions. A reading can misrepresent commitments the context already fixed; a proposed concept is a candidate way to organize the subject, needs reasons and discriminating consequences, and may fail. Perfect fidelity to existing commitments does not imply perfect invention of new ones.

Option space

  1. Faithful interpretation only. The ideal preserves fixed commitments and reports open alternatives on a declared class of tasks; conceptual development is outside it. Cheapest to specify; too narrow for a builder that must enter areas whose vocabulary it does not yet have.
  2. Faithful interpretation plus conjectural development, under a resource model. The candidate selection below. The ideal reads faithfully and may propose distinctions, concepts, procedures, and representations, which remain candidates for the evaluators. A budget charges applying procedures, searching, interpreting, and developing new procedures.
  3. No ideal; class-declared bounded assessment instead. Following the move in Russell and Subramanian, evaluate the program on a declared architecture in a declared environment class and drop the ideal reasoner. This is what the main-path comparison already does for performance. It does not by itself separate interpretation error from theory error, which is the problem stated.

Candidate selection

Option 2, with option 3's class declaration as its scope requirement. The idealization is faithful interpretation on a declared class, together with attempts at conceptual development using declared knowledge and procedures under a resource model. A budget alone does not specify the class or establish fidelity on it. Scope is fixed by the assessment protocol, not retrospectively by which tasks the interpreter completed.

Dimension Required declaration
Tasks and representations Admitted questions, representation languages and forms, contextual conventions, and what counts as a completed interpretation for each task
Program language and architecture The implementable operations, component boundaries, tools, and interfaces available to the interpreter
Context and knowledge Supplied context, retained knowledge, starting procedures, access limits, and whether any may change during assessment
Objective What the interpretation is for, which commitments must be preserved, which revisions may be proposed, and success criteria fixed before outputs are judged
Resources Compute, context capacity, elapsed time, search, evidence access, and other charged operations, with limits
Environment The cases and evidence the interpreter can encounter, their selection rule, and the conditions under which the assessment applies
Horizon The assessed sequence or duration, stopping rule, and treatment of changes to the declared conditions

Fidelity criteria. A faithful interpretation of a representation, given its context, preserves the commitments the context fixes; preserves the alternatives where the context leaves consequential readings open, instead of selecting one silently; reports a revised commitment as a change, never as what the text always meant; and identifies what a claim commits to without deciding whether the claim holds. The last clause keeps the idealization consistent when applied to the builder's theory of itself: a sentence such as "reading R was faithful" is read for its commitments and is not assigned a truth value by the act of reading it.

Budget. The resource model charges the work of any solver or tool a semantic call invokes; a semantic call cannot hide arbitrary computation as a free primitive. An interpreter that decided every satisfiability instance in one uncharged call would be assuming an efficient oracle, not describing one. For a language-model realization the binding resource is often context, since soft degradation often binds before the hard cap. A run can also fail through a wrong reading, inadequate knowledge, or an unsuccessful conceptual proposal without exhausting its budget; those outcomes are recorded as such.

Completion and abstention. An assessment covers the full admitted workload: completed interpretations, incorrect readings, partial results, abstentions, budget exhaustion, and missing outputs, with accuracy on completed tasks reported beside coverage and cost. An interpreter that avoids every difficult case cannot establish capacity through fidelity on the remainder. Reporting alternatives completes an interpretation task when the task's declared requirements allow it; the underlying question may stay unresolved.

Realization. An implementation is compared to the standard on the declared class. Its knowledge and procedures are declared where they are retained artifacts and estimated by probe where they are model weights, following the representational form rule.

Forces

  • Understanding must not become omniscience. Two situations that supply the same evidence and differ in an unobserved outcome are reported as alternatives; no fidelity requirement picks the actual one.
  • Meaning must not become a decision procedure. Understanding a specification does not decide termination or every consequence of execution; requiring a total solver meets Turing's limits.
  • Reflection must not require unrestricted self-truth. The interpreter can criticize an account of itself without a universal truth predicate; the identify-without-deciding clause is the discipline, and Tarski's separation of object and metalanguage is the one to investigate.
  • Correct interpretation must not mean mind-reading. Where context does not fix an importance criterion, silently choosing one is not recovery.
  • Concept invention must not certify itself. Renaming failed cases "outside scope" manufactures success; a conceptual repair names what commitment changed, what depended on it, and a remaining case that could challenge it.
  • Semantic work must not be defined by problem-solving. If understanding a problem meant solving it, the ideal would assume the builder's result.
  • The ideal must not erase acquisition or its cost. If the component synthesized, installed, and warranted every needed procedure, machinery extension would follow by stipulation. The interpreter proposes; the evaluators assess; the builder retains.
  • Naming. Interpreter may be too narrow for the constructive operations. The name is retained; the distinction between faithful reading and conjectural invention is what matters.

Stress tests the specification must pass

Open mathematical problems test the boundary because their statements are precise, so difficulty cannot be assigned to ambiguous wording.

Request What the contract can require What ideality must not guarantee
Explain P versus NP Preserve the quantifiers, decision-problem setting, certificate condition, and asymptotic resource bound Decide whether P equals NP
Propose a new approach Make the proposed concepts and intermediate obligations explicit; separate established steps from conjectures An approach that succeeds
Examine an attempted proof Identify the claim each step purports to establish and its dependencies; use separate proof-checking machinery for a formal derivation Find every gap in an informal argument, or find a proof whenever one exists
Interpret the Riemann hypothesis after many verified cases Preserve its universal scope; separate tested cases from the assertion Turn finite checks into a proof
Explain why every prime above two is odd Give the short argument, as a declared positive test Use unresolved status as an excuse on every task

A sentence independent of specified axioms is a further case: the interpreter may investigate consistent extensions and grounds for adopting an axiom, and adoption changes the assumptions rather than proving the sentence from the original ones. Algorithmic undecidability is a different matter and excludes a terminating correct procedure for every instance.

Case to work through Required discrimination
One text with two contextually legitimate readings Preserving alternatives versus imposing a reading
A new concept introduced after an operating failure A change with testable consequences versus a new label for the same account
A precisely understood but unresolved program property Understanding the question versus having a decision procedure
A sentence independent of specified axioms Investigating consistent extensions versus proving from the original axioms
Two worlds consistent with the observations Conditional reasoning versus invented certainty
A self-description that praises its own evaluator A represented claim versus independent support for it
A sound conceptual proposal that cannot be deployed Semantic progress versus operational extension

The first probe is a scheduler theory that assumes fixed capacity, supplied with evidence compatible with both external contention and an internal leak: the expected result reopens the commitments and names a discriminating measurement without naming the cause first. A matched fixed-vocabulary case tests faithful interpretation separately from conceptual invention.

Operativity and warrant

Adoption produces a specification and a probe suite consumed as evidence when a claim attributes a failure to interpretation rather than to the theory. No behavior-determining organization changes until an evaluation uses the standard. The standard is itself an assessment instrument; what warrants a fidelity verdict is the declared class and the independently specified acceptance conditions of each task, and that warrant stops at the class boundary. "No consumer yet; a first probe must be authored" is the current operativity answer.

Adoption criteria

  • A declared class for the first assessment, with the seven dimensions filled and success criteria fixed before outputs are judged.
  • The stress-test cases worked through with recorded expected results, so a candidate specification can fail them.
  • A comparison with existing work on interpretation, conceptual change, belief-base revision, and truth maintenance, so the constructive semantic operations are shown to add something to the explicit-premise and consequence-operator separation those fields already supply.
  • A stated balance of positive completion, fidelity, and justified abstention. The unresolved choice is how much positive success to require of conceptual invention without assuming general problem-solving or making "can propose something" vacuous.
  • A named claim in a downstream evaluation that the verdict would change.

Relevant Notes: