Historical and archaeological dates are rarely crisp. A radiocarbon sample gives "around 1200, give or take sixty years"; a regnal date is "circa 600 BCE". ISO 8601-2 writes that uncertainty with a margin of error — 1200±60 — and Tempo parses it, carries it, and lets you ask graded questions about it: not just "do these overlap?" but "could they overlap, and must they?".
The margin is carried, not guessed
A ± value is a first-class Tempo value. It round-trips, it survives arithmetic, and — importantly — it does not silently widen your bounds:
import Tempo.Sigils
~o"1200±60Y" #=> ~o"1200±60Y" # round-trips
Tempo.shift(~o"1200±60Y", ~o"P5Y") #=> ~o"1205±60Y" # the margin travels alongThe crisp span of 1200±60 is exactly the span of 1200 — the ±60 is metadata about where that span sits, not a wider span. So the exact interval algebra stays exact, and the uncertainty only speaks up when you ask a graded question.
Certain, possible, impossible
Every graded relation answers three-valued. Take a dig with two radiocarbon-dated contexts, a clearly later wall, and the site's known occupation span:
hearth = ~o"1200±60Y" # a hearth, dated to ~1200, give or take 60 years
midden = ~o"1240±40Y" # a midden, ~1240 ± 40
later_wall = ~o"1500±20Y" # a wall, clearly later, ~1500 ± 20
occupation = ~o"1000/1500" # the site was occupied 1000–1500Now ask the questions a site director would ask:
Tempo.possibly_overlaps?(hearth, midden) #=> true
Tempo.certainly_overlaps?(hearth, midden) #=> false
Tempo.overlap_certainty(hearth, midden) #=> :possible
Tempo.relation_certainty(hearth, later_wall, :precedes) #=> :certain
Tempo.certainly_within?(hearth, occupation) #=> true"The hearth and the midden might be contemporary, but the dates aren't tight enough to be sure. The hearth is certainly earlier than the later wall, and certainly falls within the site's occupation."
That callout is the whole point: each line reads as a sentence a historian would actually say.
What the three verdicts mean
A margin widens each endpoint into a range of where it could really sit. A relation is then:
:certain— it holds for every placement consistent with the margins.:possible— it holds for some placements but not all.:impossible— it holds for no placement.
overlap_certainty/2 and within_certainty/2 are the three-valued counterparts of overlaps?/2 and within?/2; relation_certainty/3 asks about any Allen relation (or list of them); and the certainly_*?/possibly_*? predicate pairs read the verdict off as a boolean when that is all you need.
Crisp dates fall back to yes and no
When neither operand carries a margin there is only one possible placement, so a graded relation collapses to the ordinary predicate — :possible never arises:
Tempo.certainly_overlaps?(~o"2000Y", ~o"2000Y") #=> true # == Tempo.overlaps?/2
Tempo.certainly_overlaps?(~o"2000Y", ~o"2001Y") #=> false
Tempo.overlap_certainty(~o"2000Y", ~o"2001Y") #=> :impossibleSo you can reach for the graded verdicts everywhere and pay nothing on crisp data.
Underspecification is uncertainty too
A margin is not the only way a date is vague. ISO 8601-2 also lets a value leave digits unspecified — ~o"20XXY" is some year in 2000–2099, ~o"2020YXXM" some month of 2020 — and a value may be un-anchored, carrying a month or day with no year at all. Tempo reads these the same three-valued way, over the set of dates the value could actually be:
# "Some year in 2000–2099" — certainly within that span, but not every
# grounding survives a window that opens a year later.
Tempo.certainly_within?(~o"20XXY", ~o"2000Y/2100Y") #=> true
Tempo.within_certainty(~o"20XXY", ~o"2001Y/2101Y") #=> :possible
# A masked year may precede a date inside its span, or follow it.
Tempo.relation_certainty(~o"20XXY", ~o"2050Y", :precedes) #=> :possible
Tempo.certainly_before?(~o"20XXY", ~o"2200Y") #=> true"A find dated only to 'the 2000s' is certainly within 2000–2100, only possibly before 2050, and certainly before 2200."
Un-anchored values — a recurring month or day with no year — compare on a shared leading unit, the same-axis rule the set operations use:
Tempo.certainly_before?(~o"1M31D", ~o"3M15D") #=> true"The 31st of January is before the 15th of March in any year."
Comparing across resolution axes — an un-anchored month against an anchored year — has no answer without knowing the year, so Tempo says so rather than guess:
Tempo.within_certainty(~o"2M", ~o"2050Y")
#=> {:error, %Tempo.RequiresAnchorError{}}What this is not (yet)
The verdicts are three-valued, not numeric — Tempo will tell you an overlap is possible, but not that it is "70% likely". A probability needs a prior over where the true date sits, and a soft, fades-at-the-edges approximately needs a membership function; both are planned for a companion library rather than the crisp core. For today, ± is inert in your bounds and your exact relations, and speaks only through the graded questions above.