nucleation

CLAIM-306: Under a deadline, search can establish presence by finding one item but absence only by exhausting the collection, so "If I can't find it, it isn't there" acts on an unfinished search as negation as failure acts on a finished one: a default stronger than either the closed-world assumption or negation as failure, safe only when the arrangement makes the full search finish within the deadline

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Properties9
StatusSuperseded — by CLAIM-312 — "If I can't find it, it isn't there" asserts operational unavailability, that the item will not be put to use before the deadline, not absence: a search that fails by the deadline establishes unavailability outright, and licenses absence only with a certificate that the unsearched remainder cannot hold the item, from exhaustion, from an invariant of the arrangement, or from a closed-world default
Rolethesis
Warrantdemonstrated
Tagslogic, databases, cognition
Linedistributed-agency
GroundsCASE-085 — The medication in the ambulance: a drug the EMT knew was stocked could not be found during a resuscitation, the paramedic changed the request, and afterwards said "If I can't find it, it isn't there", CASE-094 — The LEGO bin: a brick owned in one copy and buried among hundreds of similar ones may as well not be owned, a black brick among white ones needs no bin of its own, and every brick can be found by going through the whole collection, THEORY-341 — Inferring not-P from failure to prove P is a deduction only under two separate conditions: Clark shows that when every branch of the search for a proof of P ends in failure, not-P is a theorem of the completed database, and a search that does not finish licenses nothing; Reiter's closed-world assumption, adding the negation of every ground atom the database does not entail, keeps a consistent Horn database consistent and can make a disjunctive one inconsistent
Objected byCLAIM-311 — A search cut off before an exhaustive pass can establish absence when the arrangement certifies that the unsearched remainder cannot hold the item: a sorted table answers non-membership in a logarithmic number of probes, and the Threshold Algorithm stops early with its answer proved, so absence needs a certificate about the remainder, not exhaustion; similarity search in high dimension is where no such certificate exists
ComplementsCLAIM-296 — What a system has, what it knows it has, and what it can deploy within a task's deadline are different, and the last is a relation among the resource, the agent, its environment, the task, the deadline and the cue, not a property of any one of them
UsesTERM-055 — operational availability, of a resource for an action: the chance that an agent–environment system, given the cue it actually has, deploys the resource for the task before the deadline

Graph View

Superseded 2026-10-15 by CLAIM-312. CLAIM-311 showed absence established without exhausting a collection, which meets this claim’s defeat condition. The restatement reads the rule as operational unavailability and keeps the analysis below as the account of its literal reading.

The claim

The asymmetry. “Present” is shown by one find. “Absent” is shown only by a pass that rules out every place it could be. The owner, in CASE-094: “every brick in my collection is detectable if I have the time to go through my entire collection, one at a time, checking every single brick.” With a deadline τ shorter than that pass, absence is never shown. The lab form is Treisman and Gelade’s target-absent trials (LIT-1082, read in NOTE-897). In serial search they took about twice the per-item time of target-present trials, 67.1 against 28.7 ms per item, and even when a present target popped out, absent responses grew with display size (25.1 against 3.1 ms per item).

Two assumptions, which the rule makes together. Reiter’s closed-world assumption (LIT-1088, read in NOTE-899, from his 1977 workshop report) adds the negation of every ground atom the database does not entail. The convention “presumes total knowledge about the domain being represented”. His own illustration is close to the medic’s: “If I fail to find an entry indicating that Air Canada flight 103 connects Vancouver with Toulouse I will conclude that it does not.” Clark’s negation as failure (LIT-1087, read in NOTE-894, from the author’s posted scan) takes not-P as a lemma only after “the exhaustive but unsuccessful search for a proof of P”. His soundness theorem makes that a consequence of the completed database: every branch must end in failure, and a branch that never ends licenses nothing. So there are two assumptions:

  1. The world is closed. What is there would be in the database. Reiter’s.
  2. The search finished. Every place has been tried and failed. Clark’s, required outright, not assumed.

A search cut off by a deadline satisfies neither. “If I can’t find it, it isn’t there” acts on an unfinished search as negation as failure acts on a finished one. It assumes both a closed world and that the part not searched would have failed too. It is therefore stronger than either inference, not one of them on a time bound, as first filed.

When it is safe. Let π be the prior that the item is present and h the chance a search finds a present item within τ. Then, by Bayes,

P(present | not found by τ) = π(1 − h) / (π(1 − h) + 1 − π).

As h → 1 this goes to 0. An arrangement in which the full search finishes within the deadline turns the second assumption from a gamble into a fact, and the rule becomes Clark’s: a labelled compartment, a bin of one’s own, or CLAIM-307’s carve. That is the time-bounded counterpart of Clark’s conditions under which evaluation terminates.

Where it is not an inference at all. In CASE-085 the unit had been checked: the EMT knew the drug was stocked, somewhere among the compartments. That is a disjunction, and Reiter’s Example 5.1 shows the closed-world assumption made inconsistent by one (from Pa ∨ Pb it adds both ¬Pa and ¬Pb). With that knowledge in the database, a proof of presence succeeds and negation as failure refuses “it isn’t there”. So in CASE-085, with π near 1 and h low, the rule was a decision to stop searching and change the request, not a conclusion about the drug.

Why it is Active

The asymmetry and the formula are elementary. The two sources are read, and the reading of the rule against them is now theirs: Reiter’s definition and his Example 5.1, and Clark’s soundness theorem and its finite-failure condition. That the medic’s rule is a decision under a deadline, not an inference, is CLAIM-296’s reading, which this claim complements.

What it does not say

  • That the medic was wrong to move on. Under a deadline, stopping is part of using a resource (CLAIM-296; A17 §4 in CASE-085).
  • That absence can never be established. A complete arrangement, or an exhaustive pass in time, establishes it.
  • That Reiter or Clark considered deadlines. Neither did. For Reiter, whether the database entails an atom does not depend on time, and the extension to search under a deadline is the record’s.

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