# heyting examples
Each example is runnable from the repo root. Output excerpts below are real,
captured from release runs. The two dataset examples are data-gated: without
their data they print fetch/train instructions and exit 0.
## Which example should I run?
| See the connectives on a ten-entity toy taxonomy | `taxonomy_query` |
| See interval-validity temporal hops, no training | `temporal_query` |
| Run the full stack on FB15k-237 with a trained DistMult | `fb15k237_clqa` |
| Run the temporal stack on ICEWS with a trained TComplEx | `icews14_temporal_clqa` |
| Score the published BetaE benchmark files, all 14 types | `betae_fb15k237` |
## `taxonomy_query`: the connectives on a toy graph
```bash
cargo run --release --example taxonomy_query
```
```text
1p dog is_a ? [Godel ] -> mammal (1.00)
2p dog is_a ? is_a ? [Product ] -> animal (1.00)
2i (dog is_a ?) AND (cat is_a ?) [Godel ] -> mammal (1.00)
2u (dog is_a ?) OR (sparrow is_a ?) [Godel ] -> mammal (1.00), bird (1.00)
not (dog eats ?) AND NOT (cat eats ?) [Lukasiewicz] -> plant (0.30)
```
## `temporal_query`: interval-validity hops on a hand-built graph
Time windows registered as virtual relation ids; the two-terms query is an
ordinary intersection of two differently-windowed hops.
```bash
cargo run --release --example temporal_query
```
```text
held office in the 1990s -> alice (1.00)
held office before 1990 AND after 2000 (two terms) -> bob (1.00)
held office after 2000 AND member of party_x -> bob (0.90), carol (0.90)
```
## `fb15k237_clqa`: the CQD recipe end to end
Trained DistMult (tranz CLI) supplies atom degrees; queries compose in the
Product and Gödel algebras; hard answers only, filtered; `!` types are
non-reducible (every atom needs a held-out edge, per the ICLR 2025
reducibility critique). Closes with a witness and conformal coverage.
```bash
scripts/fetch_fb15k237.sh # then train per the example header
cargo run --release --features tranz --example fb15k237_clqa
```
```text
type n MRR(P) H@1 H@3 H@10 MRR(G) H@10
1p 200 0.389 0.294 0.441 0.555 0.389 0.555
2p 165 0.238 0.157 0.269 0.393 0.224 0.375
2i 200 0.566 0.429 0.659 0.822 0.467 0.684
3i 200 0.731 0.600 0.843 0.948 0.553 0.767
2p! 168 0.232 0.155 0.257 0.374 0.216 0.354
2i! 200 0.361 0.257 0.383 0.606 0.388 0.604
3i! 200 0.385 0.277 0.416 0.621 0.426 0.661
conformal 1p answer sets: qhat 0.3043 on 300 valid pairs; held-out coverage 80% (nominal 80%)
```
The model is a DistMult d 256 trained with reciprocals and the weighted
nuclear-3 regularizer (`--reciprocals --n3-reg 0.0025 --init-scale 0.01`).
The plain-to-`!` drop (2i 0.566 -> 2i! 0.361) is the honest measure of
multi-hop composition.
## `icews14_temporal_clqa`: the temporal stack on real events
Trained TComplEx (tranz >= 0.7.2, with the Lacroix et al. regularizers;
link-prediction test MRR 0.520) supplies time-scoped atom degrees; windowed
and not-during query types run against an exact `TemporalKg` oracle; closes
with a witness, a time-projection demo, and conformal coverage.
```bash
scripts/fetch_icews14.sh # then train per the example header
cargo run --release --features tranz --example icews14_temporal_clqa
```
```text
type n MRR(P) H@1 H@3 H@10 MRR(G) H@10
1p 22 0.271 0.149 0.348 0.530 0.271 0.530
1p-t 86 0.440 0.337 0.500 0.605 0.440 0.605
2i-t 79 0.843 0.759 0.911 0.975 0.662 0.785
2i-t! 91 0.674 0.560 0.758 0.857 0.607 0.725
2u-t 49 0.187 0.095 0.196 0.394 0.210 0.426
time projection: when did (Ministry (Afghanistan), Make statement, Afghanistan) hold?
predicted top days: 2014-03-10 2014-01-05 2014-08-19 (true: 2014-03-06)
conformal windowed-1p answer sets: qhat 0.3372 on 300 valid pairs; held-out coverage 81% (nominal 80%)
```
ICEWS05-15 (5x the quads, an 11x time axis) runs through the same harness:
```bash
scripts/fetch_icews0515.sh # then train per the example header (batch 2048)
ICEWS_DATA=data/icews05-15 ICEWS_EMB=data/icews0515-tcomplex \
cargo run --release --features tranz --example icews14_temporal_clqa
```
## `betae_fb15k237`: the published benchmark files, evaluated exactly
Loads the KGReasoning pickles (queries + easy/hard answer sets) and scores
all 14 BetaE query types file-exactly, so rows compare directly against the
BetaE / CQD / QTO FB15k-237 tables (theirs use ComplEx-N3 at d >= 1000;
compare shapes, not absolutes). Negation rows exclude the negated branch's
top-50 candidates via a crisp `Query::given` mask; soft `1 - sigmoid`
negation over uncalibrated degrees measures at the random floor.
```bash
scripts/fetch_betae_fb15k237.sh # ~1.4 GB download
cargo run --release --features tranz --example betae_fb15k237
```
```text
type n MRR H@1 H@3 H@10 MRR(G) H@10
1p 300 0.329 (P) 0.235 0.374 0.500 0.329 0.500
2p 300 0.025 (P) 0.010 0.024 0.053 0.022 0.044
3p 300 0.040 (P) 0.018 0.036 0.076 0.036 0.073
2i 300 0.167 (P) 0.097 0.194 0.289 0.153 0.270
3i 300 0.180 (P) 0.122 0.199 0.282 0.157 0.259
pi 300 0.120 (P) 0.071 0.121 0.213 0.102 0.178
ip 300 0.126 (P) 0.075 0.129 0.230 0.088 0.193
2u 300 0.071 (P) 0.025 0.073 0.148 0.070 0.145
up 300 0.034 (P) 0.018 0.031 0.059 0.029 0.054
2in 300 0.010(P¬) 0.000 0.002 0.007 0.000 0.000
3in 300 0.011(P¬) 0.004 0.005 0.011 0.000 0.000
inp 300 0.016(P¬) 0.005 0.008 0.035 0.000 0.000
pin 300 0.009(P¬) 0.002 0.003 0.018 0.000 0.000
pni 300 0.022(P¬) 0.006 0.009 0.035 0.000 0.000
```