Premise Discharge Checklist¶
Checklist — instantiates Propositional Mode Governance
A checklist that ensures temporary premises or proof assumptions are either discharged, scoped, or explicitly carried into the conclusion.
A Premise Discharge Checklist walks a completed argument and guarantees that every temporary premise introduced along the way reaches an honest disposition: it is discharged (paid back by the proof), scoped (the result restricted to the case where it holds), or carried (the conclusion stated explicitly as conditional on it). Its distinguishing idea is a completeness guarantee over temporary loans: a premise borrowed mid-argument must not silently leak into an unconditional conclusion, and the checklist is the sweep that leaves nothing open. It governs propositions that are meant to be repaid — which is exactly what sets it apart from an axiom, a permanent primitive that is never discharged because the system stands on it.
Example¶
A mathematician is finishing a theorem, and the proof introduced several temporary assumptions on the way down — "assume n is prime," "suppose the sequence converges," and a lemma left as a placeholder (sorry, in a proof assistant, marking a step not yet proved). The discharge checklist forces a disposition for each. "Assume n is prime" is discharged by conditional proof: the final statement properly reads "if n is prime, then …," so the assumption is folded into the result rather than forgotten. The convergence supposition is scoped: the theorem is stated only for convergent sequences, and says so. And the placeholder lemma is an open obligation — until it is proved, the checklist blocks the author from calling the theorem proved, because a sorry left in place is a hole the conclusion is silently standing over. The checklist is what stops a proof from advertising an unconditional result while quietly resting on premises it never paid back.[n1]
How it works¶
The checklist runs in two passes. First it enumerates every premise or assumption introduced anywhere in the argument, turning each into a tracked item that must be closed. Then, for each, it requires one of three dispositions — discharged, scoped, or carried — and refuses to certify the argument complete while any item is open. For premises that are carried, it attaches the scope to the stated conclusion, so a result true only under a condition is written as conditional. In formal settings the discharge is bound to the proof's own structure: a conditional-proof step, an assumption-elimination, a resolved placeholder — the disposition is not a note in the margin but a move in the proof. Its whole discipline is that temporary premises are loans with a due date at the conclusion.
Tuning parameters¶
- Discharge strictness — whether every premise must be formally discharged, or "carried with explicit scope" is an acceptable close. Strict discharge yields clean unconditional results; permissive carrying keeps more results alive but conditional.
- Tracking granularity — whether every minor supposition is enumerated or only the load-bearing ones. Fine tracking catches subtle leaks; coarse tracking stays usable.
- Placeholder policy — whether unproved placeholders are tolerated during drafting but hard-blocked at publication, or forbidden throughout.
- Scope-propagation rigor — how forcefully a carried premise's condition is pushed into the final statement versus left as a footnote.
When it helps, and when it misleads¶
Its strength is that it closes the classic leak: a temporary premise in a proof, an analysis, or a legal brief that silently becomes part of an unconditional conclusion. By demanding a disposition for each, it makes conditional results announce their conditions instead of hiding them. Its failure mode is checklist theatre — items ticked as "discharged" without a real discharge behind them, so the form of completeness masks an actual hole. A subtler misuse carries a premise so quietly that the conclusion is still advertised as unconditional in the abstract while the condition hides in the body. And in informal analysis, over-scoping can hedge a result into vacuity. The guarding discipline is that a carried premise's scope must appear in the stated conclusion, not buried, and that any open placeholder blocks the claim of completeness outright. The checklist verifies that premises are discharged; it does not adjudicate whether a foundational primitive should have been adopted in the first place.
How it implements the components¶
obligation_register— each introduced premise becomes a tracked obligation that must reach a disposition before the argument may be certified complete.dependency_and_scope_trace— carried premises attach their scope to the conclusion, so a conditional result is never presented as unconditional.formal_proof_or_model_binding— in formal proofs the discharge is bound to the proof's own structure: a conditional-proof or assumption-elimination step, or a resolved placeholder, rather than a marginal note.
It does not record why a foundational primitive is adopted or declare a permanent system boundary (mode_assignment_basis) — that is Axiom Boundary Statement, its nearest twin: a premise is a temporary loan the argument must discharge or carry with its scope, whereas an axiom is a permanent primitive the system never discharges. Nor does it define which operations each mode licenses (licensed_operation_matrix), which is Mode-Operation Matrix.
Related¶
- Instantiates: Propositional Mode Governance — the checklist governs temporary premises, ensuring each is discharged, scoped, or carried before the conclusion stands.
- Sibling mechanisms: Assumption Expiry Timer · Axiom Boundary Statement · Claim Status Labeling Standard · Decision Memo Epistemic-Mode Section · Epistemic Mode Linter · Epistemic Status Ledger · Hypothesis Promotion Gate · Mode-Operation Matrix · Proposition Lifecycle Board
Editorial Notes¶
Form Classification¶
Form family: Assessment, Review & Assurance
Rationale: Premise Discharge Checklist operates as a bounded evaluation of existing evidence or work that produces a finding or disposition because it a checklist that ensures temporary premises or proof assumptions are either discharged, scoped, or explicitly carried into the conclusion.
Independent corroboration: The frozen evidence defines Premise Discharge Checklist as 'A checklist that ensures temporary premises or proof assumptions are either discharged, scoped, or explicitly carried into the conclusion', so its operative form is Assessment, Review & Assurance.
Review outcome: Independent reviewer agreement; high confidence.
Origin Attribution¶
Primary origin: Philosophy
Origin pattern: Convergent development
Present-day reach: Universal
Rationale: The discharge of temporary assumptions is a canonical practice of formal logic and philosophical proof theory.
Related originating lineages:
- Computer Science & Software Engineering — The computer_science tradition materially shaped Premise Discharge Checklist through its own practice of algorithms, data structures, formal interfaces, and software-system practice.
- Mathematics — Premise Discharge Checklist is most plausibly rooted in the mathematics tradition because its characteristic form depends on formal definition, proof, mapping, and quantitative structure. The assignment tracks that formative lineage, not the many settings in which the mechanism can now be applied.
Review resolution: Light authoritative-source research resolves the primary-origin disagreement in favor of philosophy. Stanford Encyclopedia of Philosophy: Natural Deduction Systems in Logic documents the defining practice, history, or theory described in the selected origin rationale. Other domains are retained only where the blind reviews identify material co-development or translation; broad later application is recorded separately as domain_reach=universal, while origin_mode=convergent describes the relationship among formative lineages.
Attribution caveat: The blind-review boundary with mathematics is substantive: those traditions materially developed, translated, or operationalized part of the mechanism. The cited provenance places its defining lineage in philosophy.
Encyclopedia synthesis: The exact catalogued form synthesizes established practice rather than reproducing a single standard historical label.
Review outcome: Researched adjudication after independent review; high confidence.
Sources consulted:
Notes¶
[n1] In natural-deduction systems, discharging an assumption is the formal move by which a temporary premise is closed — e.g. conditional proof, where assuming P and deriving Q lets you conclude "if P then Q" and cancel the assumption. The checklist generalizes that move: every borrowed premise must be discharged, scoped, or carried, never just abandoned. ↩