## A Contextualized Semantics for owl:sameAs

##### Wouter Beek (w.g.j.beek@vu.nl), Stefan Schlobach, Frank van Harmelen

wouterbeek.github.io

## Two types of meaning

### Formal meaning

DL, OWL, Model Theory

## owl:sameAs has 2 meanings

### Formal meaning

$$a = b \,\longleftrightarrow\, (\forall P)(Pa = Pb)$$

OWL 2 specification, 2012

### Social meaning

“Include links to other URIs, to discover more things.”

Tim Berners-Lee, 4th Linked Data principle, 2006

# Existing solutions

## Use weaker alternatives(e.g. relatedness)

Everything is related to everything.

SKOS exactMatch indicates a high degree of confidence that two concepts can be used interchangeably across a wide range of information retrieval applications
SKOS specification, 2009

## Use domain-specific identity relations

“the same chemical” (ex:sameChemical)

“the same product” (ex:sameProduct)

## Change modeling practice

Adding an owl:sameAs link requires approval from the authority that is being linked to.

# Our solution

## Preserve equivalence properties

The identity relation is the smallest equivalence relation.

Every equivalence relation is also an identity relation, but w.r.t. a subset of the properties.

If A and B have the same income, I cannot infer identity.

But if I am reasoning about income groups, then they are identical.

Identity subrelations that are also equivalence relations can, in some contexts, be used i.o. the identity relation.

### The same chemical compound ($=_{\{\text{chemical}\}}$)

ns1:Aspirin,ns2:Aspirin〉and 〈ns1:Nicotine,ns2:Nicotine〉 are the same according to the same criteria.

## Lattice of identity subrelations

Identity context: A consistent collection of identity subrelations from the identity lattice

# Pros & cons

• We do not change the schema
• We do not change the data
• We do not lose equivalence properties
• Consistently reason over inconsistent data
• Very few things are the same sui generis
• Highly non-monotonic: identity subrelations change when statements are added/removed
• Computationally challenging (parallel FCA computation)

# Questions?

### Formal meaning

$$a = b \,\longleftrightarrow\, (\forall P)(Pa = Pb)$$