n-ary relations
• OWL modeling problem when n≥3
– E.g. complex events
– Known solution with reification and binary
projections
• The situation content pattern and its
specializations (time-indexed situations,
various event models, etc.) are a good
approximation, modulo argument ordering,
and identity constraint
– two new patterns: ordereddescription, and
orderedsituation
1
ordered description pattern
• enables to represent e.g.:
– buys(x,y,z,t,p)
only contextual distinctions in basic n-ary pattern
no distinction in basic n-ary pattern!
– Buyer(x), Seller(y), Product(z),
Time(t), Place(p)
– Person(x), Person(y)
– Time(t*)
2
ordered situation pattern
QuickTime™ and a
Photo - JPEG decompressor
are needed to see this picture.
OWL2 punning here
for a version directed
at situations directly
3
still missing identity constraint
• still misses identity constraint, e.g.
– given the predicate: buys(x,y,z,t,p) [P1]
– axiom A1 (identity constraint) holds: ∀(x,y,z,t,p)(buys(x,y,z,t,p) = buys(x,y,z,t,p)) [A1]
• A1 is trivial in FOL
– now, if P1 is morphed by the following predicates:
• buys(r), buys1(r,x), buys2(r,y), buys3(r,z), buys4(r,t), buys5(r,p) [P2]
– axiom A1 needs be morphed as follows (in case no list variables are present):
• buys(r) ⟷ ∃!(x,y,z,t,p)(buys1(r,x) ∧ buys2(r,y) ∧ buys3(r,z) ∧ buys4(r,t) ∧ buys5(r,p)) [A2]
• but axiom A2 cannot be expressed in OWL; we need either a rule, or a programmatic
mechanism (e.g. a wizard, or a manual procedure) that ensures that any buys_n is
functional
• since OWA holds for OWL, no reasoner will infer that two individuals A and B occurring both
in the place of e.g. x in buys1(r,x) are the same individual; it’ll only detect an inconsistency
in case A owl:differentFrom B
• still, this pattern does not ensure (in a model-theoretical way) that two instances B1 and B2
of buys(r) with the same relations to the same individuals are the same individual: for this
additional inference, we need either a SPARQL or RIF formula (here a RIF example in next
slide)
4
forall ?e
(?b1 [owl:sameAs :?b2]
←
and (
?e [:hasSetting ?b1]
?e [:hasSetting ?b2]
not (
and (
?f [:hasSetting ?b1]
not (?f [:hasSetting ?b2])))
•in case of list variables, a more complex pattern should be devised forall ?s ?e ?c
5
... however ...
• Many problem-solving tasks require
reasoning over alternative
conceptualizations of a same situation or a
set of facts
– classical problem: views, schema evolution,
multiple ontologies over the same data, ontology
matching, ...
– traditionally, the universe of facts is not the same
as the universe of concepts
6
... however/2 ...
• Semantic web and punning capabilities prove it’s
important to have a clear shared universe of discourse
• Also traditional “hard” tasks need it
– legal knowledge (facts vs. cases vs. norms vs.
meta-norms)
– services, planning and control (actual vs. expected
facts)
– diagnoses and situation awareness (ground vs.
(un)wanted facts)
– hypothesis testing and CBR (building/testing
interpretations from facts)
7
– ...
Situation classification
• A common abstract task
– “Classifying a situation” according to possibly incomplete, alternative or
loose constraints and concepts
– Constraints must be explicit and explicitly linked to the representation of a
situation
• descriptionandsituation pattern enables the representation of
situations and descriptions, and their given links
– entities of a situation that play roles from a description, values of a situation
that fit parameters from a description, etc.).
• But it's very hard to represent in general how to:
1. make a situation emerge out of scattered facts
2. decide if a situation can be (partly or fully) classified under a description
3. evaluate which description fits best a certain set of facts
8
Example
• I can get classification from this (also via rule)
– RegularSale equivalentClass
(isSettingFor some
(isClassifiedBy some
(isConceptUsedIn value SaleModel)))
• But I cannot state that each thing in the setting
(or at least n things) must be classified by a
concept that is used in SaleModel
9
D&S example
isConceptUsedIn
Seller
Buyer
Product
Time
Place
satisfies
isClassifiedBy
Apple
Mustafa
iPad
Nov2010
Shanghai
Sale#1
isSettingFor
rdf:type
RegularSale
10
[1] OWL: minimal restriction or property
chain
RegularSale equivalentClass
(isSettingFor some
(isClassifiedBy some
(isConceptUsedIn value SaleModel)))
(isSettingFor o isClassifiedBy o
isConceptUsedIn) subPropertyOf satisfies
11
[1b] OWL: maximal restriction (does not
work because of OWA)
RegularSale equivalentClass
(isSettingFor only
(isClassifiedBy some
(isConceptUsedIn value SaleModel)))
12
[2] OWL: detailed list of restrictions or
property chains
RegularSale equivalentClass
(
(isSettingFor some
(isClassifiedBy some
(Seller and (isConceptUsedIn value SaleModel)))
(isSettingFor some
(isClassifiedBy some
(Buyer and (isConceptUsedIn value SaleModel)))
(isSettingFor some
(isClassifiedBy some
(Product and (isConceptUsedIn value SaleModel)))
...
)
•property chain here needs special properties to chain, for each concept
13
[3] SPARQL
– basic with SELECT or ASK; CONSTRUCT also possible to mimick a rule, but requires both
positive and negative conditions
• SELECT ?s
• WHERE {
•
?s rdf:type :Situation .
•
?s:isSettingFor ?e .
•
OPTIONAL {?e :isClassifiedBy ?c . ?c :isConceptUsedIn :SaleModel } .
•
FILTER (!bound(?c))
• }
– OWL2 version
• SELECT ?s
• WHERE {
•
?s rdf:type :Situation .
•
?s:isSettingFor ?e .
•
OPTIONAL {?e rdf:type ?c . ?c :isConceptUsedIn :SaleModel } .
•
FILTER (!bound(?c))
• }
14
[4] RIF
– OWL1 version
forall ?s ?e ?c
(?s [:satisfies :SaleModel]
| ?s [rdf:type :RegularSale]
←
and (
?e [:hasSetting ?s]
?e [:isClassifiedBy ?c]
?c [:isConceptUsedIn :SaleModel]))
– OWL2 version
forall ?s ?e ?c
(?s [:satisfies :SaleModel]
| ?s [rdf:type :RegularSale]
←
and (
?e [:hasSetting ?s]
?e [rdf:type ?c]
?c [:isConceptUsedIn :SaleModel]))
15