Contextual knowledge
CC-BY
Fabian M. Suchanek
Knowledge about knowledge
2
Meta‐knowledge about a fact:
- provenance
- trust
- degree
- probability
the fact is part of the truth,
and we just say something about it
the statement is true only in a particular context
Rhazes was a Persian physician.
-
we know this from the book
A History of Islamic Philosophy
Contextual knowledge:
- beliefs
- hypotheses
- stories
- utterances
Rhazes can turn copper into gold.
- this is true only in contemporary thought
Masoud Mahmoudian and Parvaneh Rahimi-Moghaddam: “The life and work of Abu ul-Ala Shirazi”, 2008
Contextual knowledge
3
President Trump ends the Ukraine War on his 1st day in office.
- true only in Trump’s speeches before 1st day in office
Rhazes can turn copper into gold.
- this is true only in contemporary thought
Harry Potter has a magic wand.
- true only in the Harry Potter books
You can see only the shadows of people
- true only in Plato’s thought experiment
Contextual knowledge
is knowledge that is true only within a specific context,
and not necessarily in the real world.
4
real world
contexts
Contexts can be nested
Contextual knowledge
We can imagine contextual knowledge as knowledge
that lives in a “bubble” (the context).
RDF-Star
5
RDF-Star
(also previously written RDF
) is a W3C standard to express contextual knowledge.
<<
Rhazes transmutes copper
>> believedBy SamanidPrince
RDF-Star
6
RDF-Star
(also previously written RDF
) is a W3C standard to express contextual knowledge.
<<
Rhazes transmutes copper
>> believedBy SamanidPrince
statement of subject predicate object
contextual statement of
subject predicate object
RDF-Star
7
RDF-Star
(also previously written RDF
) is a W3C standard to express contextual knowledge.
Contextual knowledge can be nested.
<<
>> saidBy Fabian
<<
Rhazes transmutes copper
>> believedBy SamanidPrince
>demo
RDF-Star: Demo
8
We use the triple store GraphDB by OntoText
We add our statement
RDF-Star: Demo
9
We ask: Who believes what?
RDF-Star: Demo
10
We ask: Who believes what?
Answer: “Rhazes transmutes copper” is believed by Alice
RDF-Star: Demo
11
We ask: Who transmutes what?
RDF-Star: Demo
12
We ask: Who transmutes what?
Answer:
nobody transmutes anything
in real life
RDF-Star
13
RDF-Star
(also previously written RDF
) is a W3C standard to express contextual knowledge.
Advantages:
-
simple syntax
-
increasingly well‐established W3C standard
-
good software support (Jena, RDF4J, Blazegraph, AnzoGraph, Stardog, GraphDB, Neo4j)
Disadvantages:
-
hard to express anything else than statements of subject, predicate, and object
<< Rhazes transmutes copper >> believedBy SamanidPrince
RDF-Star has
superseded
the alternatives, Named Graphs, Singleton Properties, Reification.
Further reading:
W3C specification
,
Hartig’s presentation
,
OntoText summary
Complex contextual statements
14
ｗｒｏｔｅ（Ｎａｄｉｍ，
∀ ｘ： ｃｏｎｔｅｍｐｏｒａｒｙ（ｘ， Ｒｈａｚｅｓ）⇒ ｂｅｌｉｅｖｅｓ（ｘ， ｔｒａｎｓｍｕｔｅｓ（Ｒｈａｚｅｓ， Ｃｏｐｐｅｒ）））
Nadim wrote that all contemporaries of Rhazes
believed that Rhazes could transmute copper into gold.
Complex contextual statements
15
contextual statement
(a logical formula)
nested contextual statement
quantification over agents
agent
Nadim wrote that all contemporaries of Rhazes
believed that Rhazes could transmute copper into gold.
ｗｒｏｔｅ（Ｎａｄｉｍ，
∀ ｘ： ｃｏｎｔｅｍｐｏｒａｒｙ（ｘ， Ｒｈａｚｅｓ）⇒ ｂｅｌｉｅｖｅｓ（ｘ， ｔｒａｎｓｍｕｔｅｓ（Ｒｈａｚｅｓ， Ｃｏｐｐｅｒ）））
Complex contextual statements
16
∀ φ： ｗｒｏｔｅ（Ｎａｄｉｍ， φ） ⇒ φ
quantification over contextual statements
extraction of statement φ from context to reality
What Nadim writes is true.
Nadim wrote that all contemporaries of Rhazes
believed that Rhazes could transmute copper into gold.
ｗｒｏｔｅ（Ｎａｄｉｍ，
∀ ｘ： ｃｏｎｔｅｍｐｏｒａｒｙ（ｘ， Ｒｈａｚｅｓ）⇒ ｂｅｌｉｅｖｅｓ（ｘ， ｔｒａｎｓｍｕｔｅｓ（Ｒｈａｚｅｓ， Ｃｏｐｐｅｒ）））
Complex contextual statements
17
ｃｏｎｔｅｍｐｏｒａｒｙ（Ａｌｉｃｅ， Ｒｈａｚｅｓ）
Nadim wrote that all contemporaries of Rhazes
believed that Rhazes could transmute copper into gold.
What Nadim writes is true.
Alice was a contemporary of Rhazes.
∀ φ： ｗｒｏｔｅ（Ｎａｄｉｍ， φ） ⇒ φ
ｗｒｏｔｅ（Ｎａｄｉｍ，
∀ ｘ： ｃｏｎｔｅｍｐｏｒａｒｙ（ｘ， Ｒｈａｚｅｓ）⇒ ｂｅｌｉｅｖｅｓ（ｘ， ｔｒａｎｓｍｕｔｅｓ（Ｒｈａｚｅｓ， Ｃｏｐｐｅｒ）））
Complex contextual statements
18
ｃｏｎｔｅｍｐｏｒａｒｙ（Ａｌｉｃｅ， Ｒｈａｚｅｓ）
Nadim wrote that all contemporaries of Rhazes
believed that Rhazes could transmute copper into gold.
What Nadim writes is true.
Alice was a contemporary of Rhazes.
∀ φ： ｗｒｏｔｅ（Ｎａｄｉｍ， φ） ⇒ φ
∀ ｘ： ｃｏｎｔｅｍｐｏｒａｒｙ（ｘ， Ｒｈａｚｅｓ）⇒ ｂｅｌｉｅｖｅｓ（ｘ， ｔｒａｎｓｍｕｔｅｓ（Ｒｈａｚｅｓ， Ｃｏｐｐｅｒ））
ｗｒｏｔｅ（Ｎａｄｉｍ，
∀ ｘ： ｃｏｎｔｅｍｐｏｒａｒｙ（ｘ， Ｒｈａｚｅｓ）⇒ ｂｅｌｉｅｖｅｓ（ｘ， ｔｒａｎｓｍｕｔｅｓ（Ｒｈａｚｅｓ， Ｃｏｐｐｅｒ）））
Complex contextual statements
19
ｃｏｎｔｅｍｐｏｒａｒｙ（Ａｌｉｃｅ， Ｒｈａｚｅｓ）
Nadim wrote that all contemporaries of Rhazes
believed that Rhazes could transmute copper into gold.
What Nadim writes is true.
Alice was a contemporary of Rhazes.
∀ φ： ｗｒｏｔｅ（Ｎａｄｉｍ， φ） ⇒ φ
ｂｅｌｉｅｖｅｓ（Ａｌｉｃｅ， ｔｒａｎｓｍｕｔｅｓ（Ｒｈａｚｅｓ， Ｃｏｐｐｅｒ））
∀ ｘ： ｃｏｎｔｅｍｐｏｒａｒｙ（ｘ， Ｒｈａｚｅｓ）⇒ ｂｅｌｉｅｖｅｓ（ｘ， ｔｒａｎｓｍｕｔｅｓ（Ｒｈａｚｅｓ， Ｃｏｐｐｅｒ））
ｗｒｏｔｅ（Ｎａｄｉｍ，
∀ ｘ： ｃｏｎｔｅｍｐｏｒａｒｙ（ｘ， Ｒｈａｚｅｓ）⇒ ｂｅｌｉｅｖｅｓ（ｘ， ｔｒａｎｓｍｕｔｅｓ（Ｒｈａｚｅｓ， Ｃｏｐｐｅｒ）））
Complex contextual statements
20
ｃｏｎｔｅｍｐｏｒａｒｙ（Ａｌｉｃｅ， Ｒｈａｚｅｓ）
Nadim wrote that all contemporaries of Rhazes
believed that Rhazes could transmute copper into gold.
What Nadim writes is true.
Alice was a contemporary of Rhazes.
∀ φ： ｗｒｏｔｅ（Ｎａｄｉｍ， φ） ⇒ φ
ｔｒａｎｓｍｕｔｅｓ（Ｒｈａｚｅｓ， Ｃｏｐｐｅｒ）
x
ｂｅｌｉｅｖｅｓ（Ａｌｉｃｅ， ｔｒａｎｓｍｕｔｅｓ（Ｒｈａｚｅｓ， Ｃｏｐｐｅｒ））
∀ ｘ： ｃｏｎｔｅｍｐｏｒａｒｙ（ｘ， Ｒｈａｚｅｓ）⇒ ｂｅｌｉｅｖｅｓ（ｘ， ｔｒａｎｓｍｕｔｅｓ（Ｒｈａｚｅｓ， Ｃｏｐｐｅｒ））
ｗｒｏｔｅ（Ｎａｄｉｍ，
∀ ｘ： ｃｏｎｔｅｍｐｏｒａｒｙ（ｘ， Ｒｈａｚｅｓ）⇒ ｂｅｌｉｅｖｅｓ（ｘ， ｔｒａｎｓｍｕｔｅｓ（Ｒｈａｚｅｓ， Ｃｏｐｐｅｒ）））
Complex contextual statements
21
ｃｏｎｔｅｍｐｏｒａｒｙ（Ａｌｉｃｅ， Ｒｈａｚｅｓ）
Nadim wrote that all contemporaries of Rhazes
believed that Rhazes could transmute copper into gold.
What Nadim writes is true.
Alice was a contemporary of Rhazes.
∀ φ： ｗｒｏｔｅ（Ｎａｄｉｍ， φ） ⇒ φ
ｔｒａｎｓｍｕｔｅｓ（Ｒｈａｚｅｓ， Ｃｏｐｐｅｒ）
x
Such reasoning is not possible in standard First-Order Logic!
But such statements can be
translated
to First-Order Logic!
ｂｅｌｉｅｖｅｓ（Ａｌｉｃｅ， ｔｒａｎｓｍｕｔｅｓ（Ｒｈａｚｅｓ， Ｃｏｐｐｅｒ））
∀ ｘ： ｃｏｎｔｅｍｐｏｒａｒｙ（ｘ， Ｒｈａｚｅｓ）⇒ ｂｅｌｉｅｖｅｓ（ｘ， ｔｒａｎｓｍｕｔｅｓ（Ｒｈａｚｅｓ， Ｃｏｐｐｅｒ））
ｗｒｏｔｅ（Ｎａｄｉｍ，
∀ ｘ： ｃｏｎｔｅｍｐｏｒａｒｙ（ｘ， Ｒｈａｚｅｓ）⇒ ｂｅｌｉｅｖｅｓ（ｘ， ｔｒａｎｓｍｕｔｅｓ（Ｒｈａｚｅｓ， Ｃｏｐｐｅｒ）））
Complex contextual statements: Translation
22
Nadim wrote that all contemporaries of Rhazes believed that Rhazes could transmute copper
into gold. Whatever Nadim writes is true. Alice was a contemporary of Rhazes.
∀ φ： ｗｒｏｔｅ（Ｎａｄｉｍ， φ） ⇒ φ
ｃｏｎｔｅｍｐｏｒａｒｙ（Ａｌｉｃｅ， Ｒｈａｚｅｓ）
translation
First-Order Logic
reasoning
with a tool called Qiana
with a standard automated reasoner
ｗｒｏｔｅ（Ｎａｄｉｍ，
∀ ｘ： ｃｏｎｔｅｍｐｏｒａｒｙ（ｘ， Ｒｈａｚｅｓ）⇒ ｂｅｌｉｅｖｅｓ（ｘ， ｔｒａｎｓｍｕｔｅｓ（Ｒｈａｚｅｓ， Ｃｏｐｐｅｒ）））
ｂｅｌｉｅｖｅｓ（Ａｌｉｃｅ， ｔｒａｎｓｍｕｔｅｓ（Ｒｈａｚｅｓ， Ｃｏｐｐｅｒ））
>demo
>demo&sum
Complex contextual statements: Demo
23
!wrote(nadim,
forall(x, contemporary(x, rhazes)
=> !believes(x, transmutes(rhazes, copper)))).
!wrote(nadim, x) => x
contemporary(alice,rhazes)
1. Express in logical terms
Nadim wrote that all contemporaries of Rhazes believed that Rhazes could transmute copper
into gold. Whatever Nadim writes is true. Alice was a contemporary of Rhazes.
Complex contextual statements: Demo
24
fof(h0,axiom,
ist(wrote(nadim), q_Forall(q_x0,
q_Not(q_And(q_contemporary(q_x0, rhazes),
q_Not(q_ist(q_believes(q_x0), q_transmutes(rhazes, copper)))))))
).
fof(h1,axiom,! [X] : (ist(wrote(nadim), X) => truthPredicate(X))).
fof(h2,axiom, contemporary(alice,rhazes)).
fof(axiom5,axiom,![XC, X1, X2] :(ist(XC, q_And(X1, X2))
=> (ist(XC, X1) & ist(XC, X2)))).
fof(axiom6,axiom,![XC, X1, X2] :(ist(XC, q_And(X1, X2))
<=> ist(XC, q_And(X2, X1)))).
fof(axiom7,axiom,![XC, X1] :(ist(XC, q_Neg(q_Neg(X1)))
<=> ist(XC, X1))).
...
1. Express in logical terms
2. Translate with Qiana
Nadim wrote that all contemporaries of Rhazes believed that Rhazes could transmute copper
into gold. Whatever Nadim writes is true. Alice was a contemporary of Rhazes.
Complex contextual statements: Demo
25
result: proof found
proof:
1: [in,h0] ist(wrote(nadim),q_Forall(q_x0,q_Not(q_And(
q_contemporary(q_x0,rhazes),q_Not(q_ist(q_believes(q_x0),
q_transmutes(rhazes,copper))))))).
2: [in,axiom16_ist] -ist(X,Y) | ist(Z,U).
3: [in,h3] -ist(believes(alice),q_transmutes(rhazes,copper)).
4: [mp, 1, 2, 3] false
1. Express in logical terms
2. Translate with Qiana
3. Use a classical reasoner
Nadim wrote that all contemporaries of Rhazes believed that Rhazes could transmute copper
into gold. Whatever Nadim writes is true. Alice was a contemporary of Rhazes.
Complex contextual statements with Qiana
Qiana
is a method to translate logical formulas that can contain contexts, quantifications over
agents and formulas, and truth extractions into first‐order logic (where the reasoning can be done
by off‐the‐shelf automated reasoners).
ｗｒｏｔｅ（Ｎａｄｉｍ， ∀ ｘ： ｃｏｎｔｅｍｐｏｒａｒｙ（ｘ， Ｒｈａｚｅｓ）⇒ ｂｅｌｉｅｖｅｓ（ｘ， ｔｒａｎｓｍｕｔｅｓ（Ｒｈａｚｅｓ， Ｃｏｐｐｅｒ）））
Advantages:
-
adapted to complex reasoning tasks
-
ample software support (any standard logical reasoner will do)
Disadvantages:
-
made for reasoning, not for storing factoids
Qiana subsumes previous works on context logics and modal logic. Further reading:
paper
,
GitHub
Contextual knowledge: Summary
27
Contextual knowledge
is knowledge that is
true only within a specific context,
and not necessarily in the real world:
- beliefs
- hypotheses
- stories
- utterances
RDF-Star
is a W3C standard to express contextual knowledge.
Qiana
is a method to translate contextual knowledge to first‐order logic for reasoning.
contexts
<<
Rhazes transmutes copper
>> believedBy SamanidPrince
ｗｒｏｔｅ（Ｎａｄｉｍ，
∀ ｘ： ｃｏｎｔｅｍｐｏｒａｒｙ（ｘ， Ｒｈａｚｅｓ）⇒ ｂｅｌｉｅｖｅｓ（ｘ， ｔｒａｎｓｍｕｔｅｓ（Ｒｈａｚｅｓ， Ｃｏｐｐｅｒ）））
Meta‐knowledge about facts
28
Meta‐knowledge about a fact:
- provenance
- trust
- degree of truth
- probability
Rhazes advocated evidence‐based medicine
-
we know this from the book
A History of Islamic Philosophy
Rhazes criticised revealed religion
- we trust this information to a degree of 0.6
Rhazes was a successful alchemist.
- this information is true to a degree of 0.3
Rhazes rolls a dice. The dice shows 6.
- the probability of this happening is 16%
Debatable if these are
still annotations of
a fact...
RDF-Star for provenance
29
RDF-Star can be used to express also provenance.
Rhazes advocated evidence‐based medicine
-
we know this from the book
A History of Islamic Philosophy
Rhazes advocated evidenceBasedMed {| from HistoryOfIslamicPhil |}
30
Rhazes advocated evidence‐based medicine
-
we know this from the book
A History of Islamic Philosophy
Rhazes advocated evidenceBasedMed {| from HistoryOfIslamicPhil |}
core statement
provenance statement
new syntax!
RDF-Star for provenance
RDF-Star can be used to express also provenance.
31
Rhazes advocated evidence‐based medicine
-
we know this from the book
A History of Islamic Philosophy
Rhazes advocated evidenceBasedMed {| from HistoryOfIslamicPhil |}
Rhazes advocated evidenceBasedMed
<< Rhazes advocated evidenceBasedMed >> from HistoryOfIslamicPhil
syntactic sugar for
core statement, i.e., the statement is true
meta-statement about the core statement
RDF-Star for provenance
RDF-Star can be used to express also provenance.
32
RDF-Star for provenance with PROV
Rhazes advocated evidenceBasedMed {|
from
HistoryOfIslamicPhil |}
Rhazes advocated evidence‐based medicine
-
we know this from the book
A History of Islamic Philosophy
Which terms should we use here?
RDF-Star for provenance with PROV
PROV
is an ontology (a vocabulary) to annotate a fact (or, more generally, any entity) with
information about the process that generated it.
Rhazes
advocated evidenceBasedMed {|
wasDerivedFrom
HistoryOfIslamicPhil ;
wasGeneratedBy
Fabian ;
generatedAtTime
2025
|}
33
Provenance: Summary
34
Provenance information is an annotation of a fact that says how we came to know this fact.
RDF-Star
is a W3C standard that can express provenance information. The vocabulary of
provenance annotations can be provided by the
PROV
ontology.
Rhazes
advocated evidenceBasedMed {|
wasDerivedFrom
HistoryOfIslamicPhil ;
wasGeneratedBy
Fabian ;
generatedAtTime
2025
|}
Further reading:
The PROV Ontology
,
RDF-star specification