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) Buyer(x), Seller(y), Product(z), Time(t), Place(p) Person(x), Person(y) Time(t*) only contextual distinctions in basic n-ary pattern no distinction in basic n-ary pattern! 2

ordered situation pattern OWL2 punning here for a version directed at situations directly

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 ( ?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: make a situation emerge out of scattered facts decide if a situation can be (partly or fully) classified under a description 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 SaleModel isClassifiedBy satisfies Apple Mustafa iPad Nov2010 Shanghai Sale#1 isSettingFor rdf:type RegularSale

[1] OWL: minimal restriction or property chain RegularSale equivalentClass (isSettingFor some (isClassifiedBy some (isConceptUsedIn value SaleModel))) (isSettingFor o isClassifiedBy o isConceptUsedIn) subPropertyOf satisfies

[1b] OWL: maximal restriction (does not work because of OWA) RegularSale equivalentClass (isSettingFor only (isClassifiedBy some (isConceptUsedIn value SaleModel)))

[2] OWL: detailed list of restrictions or property chains RegularSale equivalentClass ( (isSettingFor some (isClassifiedBy some (Seller and (isConceptUsedIn value SaleModel))) (Buyer and (isConceptUsedIn value SaleModel))) (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 OPTIONAL {?e rdf:type ?c . ?c :isConceptUsedIn :SaleModel } . 14

[4] RIF OWL1 version OWL2 version forall ?s ?e ?c (?s [:satisfies :SaleModel] | ?s [rdf:type :RegularSale] ← and ( ?e [:hasSetting ?s] ?e [:isClassifiedBy ?c] ?c [:isConceptUsedIn :SaleModel])) OWL2 version ?e [rdf:type ?c] 15