Identity on the Web @ KR on the Web

April 2nd, 2016

Wouter Beek (wbeek@vu.nl)

Open World Assumption (OWA)
Closed World Assumption (CWA)

Database: “Some apples are green.”
Question: “Are some apples delicious?”
CWA answer: “No.”
OWA answer: “I don't known.”

Why does the SW use OWA and not CWA?

Domain & range

              
                〈foaf:knows, rdfs:domain, foaf:Person〉
                〈ex:john, foaf:knows, ex:mary〉
                ⊨ 〈ex:john, rdf:type, foaf:Person〉
              
            
              
                〈foaf:knows, rdfs:range, foaf:Person〉
                〈ex:john, foaf:knows, ex:mary〉
                ⊨ 〈ex:mary, rdf:type, foaf:Person〉
              
            

What's wrong here?

Example drawn from BioPortal.

              
                〈bpo:has_event, rdfs:domain, bpo:person〉
                〈bpo:has_event, rdfs:domain, bpo:event〉
                〈bpo:has_event, rdfs:domain, bpo:disease〉
              
            

What is the formal meaning?

What is the intended meaning?

How is this related to the OWA?

Semantics of identity

Indiscernibility of identicals (Leibniz's Law)

$$a = b \rightarrow (\forall \phi \in \Psi)(\phi(a) = \phi(b))$$

Identity of indiscernibles

$$(\forall \phi \in \Psi)(\phi(a) = \phi(b)) \rightarrow a = b$$



Why is this formula trivial?

The SW
‘identity crisis’

Semantics of owl:sameAs

$$a = b \leftrightarrow (\forall \phi \in \Psi)(\phi(a) = \phi(b))$$

Pragmatics of owl:sameAs

Linked Data:

  1. Use URIs as names for things
  2. Use HTTP URIs so that people can look up those names
  3. When someone looks up a URI, provide useful information, using the standards (RDF*, SPARQL)
  4. Include links to other URIs. so that they can discover more things


Tim Berners-Lee, Linked Data, 2016

AAA

Anyone can say anything about anything

AAA

Anyone can say that anything is identical to anything else
(and they do)

Relatedness cannot replace identity

SKOS exactMatch indicates a high degree of confidence that two concepts can be used interchangeably across a wide range of information retrieval applications
From the SKOS standard

bbc:sameAs

bbc:sameAs

owl:sameAs

?

Problems of identity

[1] Identity does not hold across modal contexts

Lois Lane was rescued by Superman
Superman is Clark Kent
⊨ Lois Lane was rescued by Clark Kent

Lois Lane believes that she was rescued by Superman
Superman is Clark Kent
⊭ Lois Lane believes that she was rescued by Clark Kent

[2] Indentity is context-dependent

Baspirin™ is the same as Caspirin™

Baspirin™ is not the same as Caspirin™

[3] Identity over time

[4] Identity under counterfactual assertion

Any property ascribed can be negated in a counterfactual


Example: “If my parents would not have met then I would not have been born.”

Formal Concept Analysis (FCA)

Context: instances (X), properties (Y), mapping (m)

$$X' \,:=\, \{ y \in Y \,\vert\, (\forall x \in X)(m(x,y)) \}$$

$$Y' \,:=\, \{ x \in X \,\vert\, (\forall y \in Y)(m(x,y)) \}$$

Formal concept 〈X,Y〉: X'=Y and Y'=X

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