I claim that none of the commonly used embedding methods capture any semantics. It's fine if you want to move from a symbolic to a numeric or geometric representation, but when you do, don't throw the semantic baby out with the symbolic bathwater. I argue that a useful definition of semantics is "predictable inference". This makes it possible to have semantics outside a logical framework. A methodological warning from 1976: don't fool yourself that wishful mnemonics in your knowledge graph are "semantics". Therefore, knowledge graphs without a schema/ontology is just a data graph, without much semantics. Finally, a discussion of some embedding methods that do manage to take semantics into account (TransOWL, ball embeddings like ELEm and EmEL++, and box embeddings like BoxEL and Box^2EL. So: even if you do move to a non-symbolic representation (numerical, geometric), make sure you keep the semantics: don't throw the semantic baby out with the symbolic bathwater.

1. The K in “neuro-symbolic”
stands for “knowledge” *
Frank van Harmelen,
Learning & Reasoning Group
Vrije Universiteit Amsterdam
Creative Commons License
CC BY 3.0:
Allowed to copy, redistribute
remix & transform
But must attribute
1
* With thanks to Wouter Beek

2. Highlights
• Bluffer’s guide to KG embedding
• What is semantics?
• What is not a knowledge graph
• A very fishy picture
• A lesson from 1976
• A baby in a bath
• Some hope for the K in neuro-symbolic
2

3. The K in “neuro-symbolic”
stands for “knowledge” *
Warning: no generative AI, no ChatGPT, no Large Language Models….

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Is neuro-symbolic really important for SemWeb?
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7. Bluffer’s Guide to KG Embedding
https://docs.ampligraph.org/
basedIn ?

8. Drug1
Protein2
Protein1
Drug2
binds
Bluffer’s Guide to KG Embedding
• Link prediction
But also:
• Entity classification
• Relation extraction
• ….
binds

9. prediction
algorithm
9
Some things are better done geometrically (and not symbolically):
• Link prediction 
• Node classification
• Relation extraction
Bluffer’s Guide to KG Embedding:
From Symbols to Vectors and back again

10. 10
Bluffer’s Guide to KG Embedding:
Different ways to compute the embeddings
TransE: |h+r-t|
RotateE:
symmetrie 
<h,r,t> and <t,r,h>
composition 
father’s mother =
mother’s father

11. Claim
None of the commonly used embeddings
capture any semantics
What is “semantics”?
11

12. This is not semantics
12

13. It is “wishful mnemonics”
13
13

14. Artificial Intelligence meets natural stupidity,
Drew McDermott, 1976
14

15. Artificial Intelligence meets natural stupidity,
Drew McDermott, 1981
15
Wishful Mnemonics
A major source of confusion in AI programs is the use of
mnemnonics like “UNDERSTAND” or “GOAL”. If a
programmer calls the main loop of their program
“UNDERSTAND”, they may mislead a lot of people, most
prominently themselves.
What they should do instead is refer to this main loop as
“G0034” and see if they can convince themselves or
anyone else that G0034 implements some part of
understanding.
It is much harder to do this when using terms like “G0034”.
When you say UNDERSTAND(x), you can just feel the

16. Artificial Intelligence meets natural stupidity,
Drew McDermott, 1981
16
As a field, AI has always been on the border of
respectability,
and therefore on the border of crackpottery.
……..
In this paper, I have criticised AI researchers (including
myself) very harshly. To say anything good about anyone is
beyond the scope of this paper.
Prescription medicine for every AI researcher:
In order to maintain your mental hygiene, read
“Artificial Intelligence meets natural stupidity”
once yearly

17. So, this is “wishful mnemonics”
17
17

18. “wishful mnemonics” is not semantics
for your computer
18
G0034
H9945
XB56B
RB56
B599
Z077
W87
U654
B6 7B3
86G
86G
86G
86G
KL64
BA21
BA51
86H

19. 19
“logical semantics” is also not semantics
for your computer

20. So what is semantics for your computer?
Frank Bussum
birth-place

21. So what is semantics for your computer?
Frank Bussum
has-birth-place
domain: person
range: location
Frank is person
lowerbound
Has-birth-place

22. So what is semantics for your computer?
Frank Bussum
has-birth-place
domain: person
range: location
Frank is person
Has-birth-place relates
min-cardinality: 1
max-cardinality: 1
 Bussum = Meren
lowerbound upperbound
Meren
Has-birth-place

23. RDF Schema
The semantics is in the Reserved Symbols
Ontology
Instance
Schema
Data

24. RDF Schema
The semantics is in the Reserved Symbols
Ontology
Instance
Schema
Data

25. Ontology
Instance
Schema
Data
RDF Schema
The semantics is in the Reserved Symbols

26. Claim
26
None of the commonly used embeddings
capture any semantics
Because none of the commonly used embeddings respect
any of the reserved symbols from RDF Schema or OWL.
Embeddings do “distributional semantics”, but
predictable co-occurrence ≠ predictable inference

27. Claim
None of the commonly used embeddings
capture any semantics
Because none of the commonly used embeddings
can represent universal quantification
(and that’s where the inference comes from)
Embeddings do “variable free sentences” only,
and those don’t allow for any inference. 27
has-birth-place
domain: person
range: location

28. This is not a knowledge graph
28
It is a data graph
because it doesn’t support any inference
and therefore doesn’t have any semantics

29. But surely other people
have noticed this before?
29

30. Make embeddings semantic again!
(Outrageaous Ideas paper at ISWC 2018)
Abstract
The original Semantic Web vision foresees to describe
entities in a way that the meaning can be interpreted both
by machines and humans. [But] embeddings describe an
entity as a numerical vector, without any semantics
attached to the dimensions. Thus, embeddings are as far
from the original Semantic Web vision as can be. In this
paper, we make a claim for semantic embeddings.
Proposal 1: A Posteriori Learning of Interpretations.
Reconstruct a human-readable interpretation from the
vector space.
Proposal 2: Pattern-based Embeddings.
Use patterns in the knowledge graph to choose
human-interpretable dimensions in the vector space.
30
Neither of these are aimed at predictable inference
-> no semantics 

31. From TransE to TransOWL
(and from TransR to TransROWL)
31
TransOWL:
TransE
Loss function
Summed over
all triples

32. More radical idea:
use more of the geometry
to capture the semantics
32
Male
Father
𝐹𝑎𝑡ℎ𝑒𝑟 ⊑ 𝑀𝑎𝑙𝑒
Parent
𝐹𝑎𝑡ℎ𝑒𝑟 ⊑ 𝑃𝑎𝑟𝑒𝑛𝑡
Spheres: ELEm, EmEL++
Male
Parent
Father
Boxes: BoxEL, Box2EL
𝑃𝑎𝑟𝑒𝑛𝑡 ⊓ 𝑀𝑎𝑙𝑒 ⊑ 𝐹𝑎𝑡ℎ𝑒𝑟 ?

33. More radical idea:
use more of the geometry
to capture the semantics

34. Highlights
Bluffer’s guide to KG embedding
What is semantics?
What is not a knowledge graph
A very fishy picture
A lesson from 1976
• A baby in a bath
• Some hope for the K in neuro-symbolic
34

35. 35
Symbolic
representation
Semantics

36. 36
Message 1:
Even if you throw out
the symbolic bathwater,
make sure to keep
the semantic baby.
#ISWS2023

37. 37
Message 2:
You can even keep
the symbolic bathwater!

38. Symbolic loss function
during training
See survey of 100+ systems in Von Rueden et al, Learning, 2019
flower?
cushion?
“Parts of a chair are:
cushion and armrest”
“Given the context of chair,
a cushion is much more likely
than a flower”
P(cushion|chair) >> P(flower|chair)

39. Symbolic consistency check
(during inference)
queen
crown
wears
39
shower
cap
?
Predict Select
crown?
showercap?

40. Symbolic justification
(after inference)
queen
wears
40
shower
cap
?
Predict Justify Explain
crown?

41. Takeaways
41
Some things are best done symbolically,
some numerically, some geometrically
The Semantic Web community is now truly a
“learning and reasoning” community
Semantics ≠ symbolic representation.
Instead: semantics = predictable inference
Whichever representation you choose,
make sure not to loose the predictable inference
There is more to neuro-symbolic methods
than embeddings