Temporal logic: why continuous ingestion follows
Classical logic asks whether a sentence is true. It does not ask when. "Snow is white" is simply true, full stop, an eternal verdict independent of any clock. Temporal logic breaks that independence apart. It studies sentences whose truth changes with time, and it insists that truth is not a property of a sentence alone but a relation between a sentence and an index: a point in some ordered structure of instants. "The valve is open" is not true or false. It is true-at-t or false-at-t, for some t that must be specified before the question makes sense.
Once truth is indexed, tense stops being decoration and becomes structure. Temporal logic adds operators for it: G for "it will always be the case that", F for "it will at some point be the case that", their past-facing mirrors H and P, and the binary operators since and until, which relate two propositions across a stretch of time rather than at a single point. A sentence built from these operators has no truth value at all until an index is fixed. "It has rained since Tuesday" is not evaluable in the abstract. It is evaluable now, or at some other named moment, and at no moment at all if no moment is supplied.
This is a small formal move with large consequences, because it makes explicit something classical logic quietly hides: every present-tense claim anyone makes is a claim indexed to the moment of utterance, and every past-tense claim is a claim about the relation between that moment and an earlier one. Get the index wrong, or lose track of it, and the sentence does not become false. It becomes meaningless — a well-formed string with no assignment to check it against.
Origin
Arthur Prior worked this out in the 1950s, prompted by an odd mixture of theology and irritation. The theological question was foreknowledge: if God knows tomorrow's contingent truths today, is the future already fixed? The irritation was with logicians who treated time as just another domain for quantifiers, as if "always" were no different from "for all x". Prior thought tense was a feature of the logical connectives themselves, not of the things they ranged over, and built tense logic to make that precise.
Hans Kamp closed an important gap in 1968. He proved that, over Dedekind-complete linear orders — no gaps, no jumps, a genuine continuum of instants — the two operators since and until are expressively complete. Anything sayable with a richer set of temporal connectives is sayable with just those two. There is no hidden third temporal direction waiting to be discovered; the linear order exhausts what tense can express. Amir Pnueli then carried the apparatus into computing in 1977, arguing that concurrent programs are specified by ongoing behaviour — always eventually, never before — rather than by input-output pairs. Edmund Clarke, E. Allen Emerson and Joseph Sifakis turned that argument into model checking, automated verification against exactly these operators, work recognised by the 2007 Turing Award. A cache-coherence property like "every request is eventually granted" is written G(req → F grant) and checked against every state the system can reach. The property is meaningless without an index to evaluate at; the checker's entire function is to sweep across indices a human could not enumerate by hand.
The turn
Read the intake axis of the model lineage semantically, and it resolves into an axis of indices.
A Large Language Model is trained on a corpus frozen at some cutoff. It can produce tensed sentences fluently — it says "the treaty is in force" or "inflation has been falling" — but it has no index at which to evaluate them, because training does not preserve one. Its effective "now" is a constant baked into the weights at the moment of the last update, and every present-tense claim it makes silently means "was true, around then." The tense marker survives; the index does not.
A Large World Model recovers an index, at a cost. While a scene is present — a camera feed, a sensor array, a live simulation — there is a genuine moment of evaluation, and "the valve is open" becomes truth-apt in exactly the way temporal logic requires. But the index is not retained. When the scene ends, it is discarded, and nothing in the system supports "the valve has been open since 04:12", because since needs the traversed segment, not just the current point.
A Large Universe Model, on this reading, is the position where the index advances continuously and the traversed segment is kept, with provenance: what was believed, and when it was believed. That is what makes the full operator set evaluable. Since and until stop being aspirational and become computable, because both halves of the relation — an earlier index and the path from it to now — are on hand. Kamp's completeness result is the reason this is a ceiling rather than a stepping stone. Since and until are all the tense that a linear order supports; there is nothing further for a fourth generation to add on this particular axis.
What the misreading gets wrong
The common shorthand is that a frozen model "doesn't know what time it is," and that the fix is fresher training data. This is wrong in a way worth stating plainly, because it makes the defect sound cosmetic. A model retrained nightly still has exactly one index — just a nearer one — and still cannot evaluate since or represent a superseded belief alongside the record of having held it. Recency narrows the gap between the frozen index and the present moment; it does not change the fact that there is only one index, discarded and replaced rather than extended. The defect is structural. It is also worth conceding the opposite point, because it cuts the other way: a stale index is entirely adequate for atemporal claims. Arithmetic does not decay. The failure is specific to tensed content, not a general indictment of anything trained on a fixed corpus.
Three objections, taken seriously
Just put the date in the prompt. Attach retrieved documents. The index is a parameter of the query, not a property of the intake regime — and that dissolves the whole distinction.
This is correct as far as it goes, and it is how most present systems actually cope. But a timestamp supplies an index, not a valuation at that index. Temporal semantics needs a function from instants to states of the world; a date with no accompanying stream is an index pointing into an empty model. Retrieval fills that in for whatever happens to have been retrieved, and leaves it silently empty everywhere else. The distinction does not dissolve. It relocates, into the coverage and latency of retrieval — which is itself an intake property, just an unacknowledged one.
There is no single global present. Distributed systems have partial orders, clock skew, no fact of the matter about simultaneity. A linear index is an idealisation; claiming to maintain "the" present is claiming something incoherent.
This is genuinely right, and it narrows the claim. The standard response in the field is to weaken the order, not abandon the index: branching-time logics and partial-order structures such as Lamport and vector clocks evaluate at points in a causal structure rather than on a line. That changes what an index is. It does not remove the need for one, and reconstructing a partial order of events from a frozen corpus is harder than from a line, not easier. Weakening the temporal structure raises the intake requirement; it does not relax it.
Continuity is rhetorical excess. A system that samples hourly has a valid index at each waking, and sampling theory says a bounded-bandwidth signal is fully recoverable from discrete samples.
Conceded, for signals of known bandwidth — which is why hourly polling suffices for a thermostat and fails for an order book. But the claim was never that every stream needs infinite-rate reading. It is that there is no stopping point: no moment after which further observation becomes definitionally unnecessary. Sampling rate is a parameter chosen per stream, set as fine or coarse as the stream demands. A one-hour poll that runs indefinitely sits on the terminal position on this axis; a one-hour poll that ends in 2024 does not, because ending it is what reintroduces the frozen-corpus problem one layer up.
What this establishes, and what it does not
Bitemporal databases keep valid time and transaction time apart because provenance is itself temporal — a restated balance needs both "what was true" and "what we then believed." Aviation keeps METARs, TAFs and NOTAMs on explicit validity windows for the same reason: a nine-hour-old observation read as current is an index error, not a data error. Reserving, settlement disputes, pharmacovigilance signals, sanctions checks against ownership at the moment of loading — all of it is the same demand, that tensed claims be evaluated at the right index and revisable once a better one is known.
That is the limit of the argument. Satisfying the semantics of tense — a linear order, a live present, the traversed segment behind it — is necessary for tensed assertions to have truth values at all. It is not sufficient for good judgement, correct inference, or trustworthy belief revision once the index and the history are in hand. The lineage's third rung closes the intake requirement that temporal logic specifies. It does not close the much larger question of what to do with an index once you have one.