Part 9 of Foundations: what happens at the boundaries between the literatures, and why those boundaries are the interesting part.
The previous eight parts each pointed at a real research area. Certain answers came from database theory. Event semantics came from philosophy of language. Bitemporality came from temporal databases. Provenance came from a specific line of work on annotated relations. Modality came from formal semantics. Document geometry came from document engineering, which barely talks to any of the others.
Read them one at a time and each is convincing. Read them together and you notice something less comfortable. They were developed independently, for different purposes, by people who were not trying to be compatible with one another. Several of them describe the same phenomenon in terms that do not line up. Those mismatches are not footnotes. They are most of the work.
This part is about the seams, because showing where the literatures disagree is the honest way to convey how much is left over after you have read all the papers. Everything you need to check the disagreements is public, and the disagreements are the more interesting half anyway. How our implementation settles each one stays inside the product boundary.
Seam one: two different things called "unknown"#
Part 3 covered certain answers: a claim holds if it holds in every admissible completion of incomplete data. Part 5 covered modality: a speaker who says "might" has committed to less than a speaker who says "is."
These look like the same idea wearing different clothes. Both involve possibility. Both involve refusing to overcommit. The formal machinery even rhymes, because both lean on possible-world semantics, the technique of evaluating a claim against every way things could consistently be.
They are not the same idea, and treating them as one is a genuine mistake. Certain-answer uncertainty is a property of your records: you do not know whether the invoice was paid because your data is incomplete. Modal uncertainty is a property of the utterance: the speaker told you it might happen, and you recorded that faithfully. The first is your problem, and more data fixes it. The second is not your problem, and more data does not fix it, because there is nothing missing. Someone said "might" and meant it.
A system that collapses the two will do one of two bad things. It will treat a faithfully recorded hedge as a gap to go fill, or it will treat a genuine gap as though the source had deliberately hedged. Keeping the two kinds of "unknown" apart is a representational commitment you have to make early, and neither literature tells you how, because neither literature was looking at the other.
Seam two: two different things called "time"#
Part 4 put time inside the event. In the treatment Donald Davidson gave sentences like these, "Maria sold the bakery to Tom in 2023" has a selling event, and 2023 attaches to that event the same way Tom does, as one participant among several. Time is a role.
Part 6 put time around the record. In the bitemporal tradition, valid time is an interval during which a stored claim applies, and transaction time is a second interval describing when the database held that version. Time is a stamp.
Now read one sentence with both lenses. "Maria sold the bakery to Tom in 2023, according to a filing we received in 2024, correcting an earlier filing that said 2022." There is a time inside the event, a time the claim applies, a time we learned it, and a time we previously believed something else. The event literature gives you a clean account of the first and is largely silent on the rest. The temporal-database literature gives you a rigorous account of the last three and has no notion of a semantic role at all.
Neither field is wrong. They were solving different problems. But you cannot implement a memory that answers both "when did the sale happen?" and "when did we stop believing 2022?" by picking one of them.
Seam three: keep the mentions or collapse them#
Provenance, in the sense of part 7, wants lineage: when an answer is computed, every contributing record should remain reachable from the result. The natural instinct is to keep everything.
Entity resolution wants the opposite. The field goes back to Ivan Fellegi and Alan Sunter's 1969 theory of record linkage, built for census files, and its whole job is to decide that "NYC," "New York City," and "Nueva York" are one thing, so that evidence about them can meet. The natural instinct is to collapse.
Run them together and the tension is immediate. A count of distinct cities is only correct if mentions were collapsed. A citation for that count is only honest if the collapsed mentions were kept. Worse, the collapse is a judgment, and judgments can be wrong, which means the lineage has to record not just which mentions contributed but which linking decision let them contribute at all.
The provenance side has better vocabulary for this than it usually gets credit for. Peter Buneman, Sanjeev Khanna and Wang-Chiew Tan's why-and-where characterization separates the witnesses that justify a result from the locations the data was copied from, and James Cheney, Laura Chiticariu and Wang-Chiew Tan's later survey sets why, how and where provenance against each other systematically. Those distinctions are exactly the right tools for the problem.
What they do not cover is a merge that was inferred rather than performed by a declared query operator. In the database setting the collapse is something the query did; here it is something the system concluded, on evidence, possibly wrongly. There is no operator in the algebra corresponding to "I judged these two mentions to be the same entity, and here is why." Somebody has to invent that record, and it has to survive every downstream computation.
The literature on each side is mature. The literature on the interaction is much thinner, and in my experience it is where a system quietly starts lying: the count looks right, the citation looks present, and the linking decision that produced both has vanished.
The seam nobody is standing on#
Then there is document geometry, part 8, which sits awkwardly next to all of this. Practically every formalism above assumes it is handed propositions, or at least linear text. A cell that means something because of its row, a clause that means something because it is under a heading marked superseded, a figure that means something because a footnote qualifies it: none of the classical treatments have a place to put that.
This one is not a disagreement so much as a missed connection. The document analysis community has separated geometric from logical structure since the 1980s and has a substantial literature on recovering the second from the first, including the table recognition survey that models the task as inference rather than parsing. The semantic formalisms that would most benefit were built alongside it, in a different venue, citing different people. Neither field is missing anything. They are simply not wired together, and the wiring is left as an exercise.
So here are the pieces, laid out in a row: a theory of when incomplete data supports a claim, a theory of what a sentence commits you to, a theory of how events hold their participants, a theory of two clocks, a theory of lineage through computation, a theory of identity across mentions, and a body of work on structured documents that was never asked to talk to any of the others.
That is the puzzle as the research leaves it. Each piece is genuinely solved in its own frame, by people who thought about it far longer than I have. What no paper hands you is a single record that can carry all of them at once without one commitment overwriting another while nobody is watching.
That has been the work, and most of it has consisted of reading carefully and then finding out where two sets of assumptions collide. I will keep publishing the pieces as I find them, including the ones that took me an embarrassingly long time.
Next in the series: the public data that makes all of this possible, and the license discipline that has to come with it.