Qualitative distance: seven classes tiling [0, ∞), three derived ranges, composition
computed from the class bounds by the triangle inequality, and the calculus and prover
over vaelii.impl.qcn-kb. See docs/space.md.
Qualitative distance: seven classes tiling `[0, ∞)`, three derived ranges, composition computed from the class bounds by the triangle inequality, and the calculus and prover over `vaelii.impl.qcn-kb`. See docs/space.md.
The seven classes: the universe of the algebra.
The seven classes: the universe of the algebra.
Distance class keyword → the binary predicate a fact about it is stored under.
Distance class keyword → the binary predicate a fact about it is stored under.
Each class as the bounds [lo hi] of the half-open interval (lo, hi] of distances it
covers. The intervals tile the non-negative reals in class-order, and :co runs from
-∞ so that it denotes exactly zero. Scaling every finite bound by one factor leaves
compose unchanged.
Each class as the bounds `[lo hi]` of the half-open interval `(lo, hi]` of distances it covers. The intervals tile the non-negative reals in `class-order`, and `:co` runs from -∞ so that it denotes exactly zero. Scaling every finite bound by one factor leaves `compose` unchanged.
The seven classes, nearest first: the order classify and compose walk.
The seven classes, nearest first: the order `classify` and `compose` walk.
(classify d)The single class a numeric distance d falls in. The classes tile [0, ∞), so this is
total over real distances — and nil for a negative number, which is no distance at all
and which :co's unbounded lower end would otherwise swallow.
The single class a numeric distance `d` falls in. The classes tile `[0, ∞)`, so this is total over real distances — and nil for a negative number, which is no distance at all and which `:co`'s unbounded lower end would otherwise swallow.
(compose s1 s2)The composition of two class sets: every class whose interval meets the triangle range of some pair of members.
The composition of two class sets: every class whose interval meets the triangle range of some pair of members.
(converse-set classes)The converse of a class set: itself, since d(a,b) = d(b,a).
The converse of a class set: itself, since d(a,b) = d(b,a).
Qualitative distance as a vaelii.impl.qcn relation algebra.
Qualitative distance as a `vaelii.impl.qcn` relation algebra.
Every distance predicate, the seven base and the three derived ranges, mapped to the set of classes it denotes.
Every distance predicate, the seven base and the three derived ranges, mapped to the set of classes it denotes.
(distance-prover)The qualitative-distance entailment prover, which vaelii.core/add-reasoner registers
as :distance.
The qualitative-distance entailment prover, which `vaelii.core/add-reasoner` registers as `:distance`.
Qualitative distance as a vaelii.impl.qcn-kb calculus.
Qualitative distance as a `vaelii.impl.qcn-kb` calculus.
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