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Temporally qualified continuants for BFO 2 OWL A bottom-up view

Temporally qualified continuants for BFO 2 OWL A bottom-up view. Stefan Schulz, Janna Hastings, Fabian Neuhaus May 20, 2013 (updated). Relations between continuants. Binary relations between occurrents non-ambiguous: partOf² ( Battle_of_Stalingrad , Second_World_War )

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Temporally qualified continuants for BFO 2 OWL A bottom-up view

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  1. Temporally qualified continuants for BFO 2 OWLA bottom-up view Stefan Schulz, Janna Hastings, FabianNeuhaus May 20, 2013 (updated)

  2. Relations between continuants • Binary relations between occurrents non-ambiguous: partOf² (Battle_of_Stalingrad, Second_World_War) • Binary relations between continuants ambiguous: partOf² (Lviv, Poland) • Ternary relations between continuants non-ambiguous: partOf³(Lviv, Austria, 1900) partOf³(Lviv, Poland, 1925) partOf³(Lviv, URSS, 1950) partOf³(Lviv, Ukraine, 2000)

  3. Problem: restriction to binary relations in OWL • Instantiation ambiguous: • Lvivrdf:typeCity • Ukraine rdf:typeCountry • Relations ambiguous: • LvivpartOf URSS • LvivpartOf Austria • Assertion that URSS and Austriadon't overlap:Inconsistency 

  4. Class level axioms • How to interpret standard OWL axioms like: City subClassOf partOf some Country ? • Temporary relatedness: every city is part of some country at least at some time"a"t1 $t2:inst³ (a,A,t1) Ù inst³ (a,A,t2)®$b: (inst³ (b,B,t2)Ùrel³ (a,b,t1)) • Permanent generic relatedness: at all times, every city is part of some country"a"t:inst³ (a,A,t)®$b:inst³ (b,B,t)Ù rel³ (a,b,t) • Permanent specific relatedness: at all times, every city is part of the same country"a"t1: [inst³(a,A,t) ®$b:(inst³(b,B,t)Ùrel³(a,b,t) "t: (inst³ (a,A,t) ® (rel³(a,b,t) Ù inst³ (b, B, t))))]

  5. Possible solutions • Use binary relations and interpret them as permanent generically related (as most of DL community has done for decades): may be acceptable as long no non-rigid classes and no instances are used (?) • Reify ternary relations: (n-ary relations ODP) Complicated, user-unfriendly and difficult to get transitivity into it • Use temporalized relations (as in BFO 2 OWL Graz version): works only for temporary relatedness and permanent specific relatedness, but not for permanent generic relatedness. • Four-dimensionalism (?): represent histories instead of objects • Use temporally qualified continuants. See following slides

  6. ContinuantTQ • Continuants in OWL ontology can be referred to in the context of a time frame:Continuant TQ = continuant, temporally qualified • "façon de parler" • Examples: • Lviv during the First World War • Ukraine during Feb 1, 1995 • The URSS during its whole existence (1917 – 1991) • Mr. X's heart transplant, occupying an operation room at May 20, 2013, 12pm • my left thumb now • my heart, since my birth

  7. ContinuantTQ • ContinuantTQs are specific DL constructs • ContinuantTQs in DL axioms translate into a sequence of FOL statements with ternary relations • ContinuantTQs are ontological neutral:c@t1 = c at time t1 is not a different individual than c@t2. It is only referred to at a different time • In OWL, a ContinuantTQ class can be instantiated by any kind of (contiguous) temporal references at any time

  8. ExamplesforcontinuantTQs 1917 1991 2013 1261 Ukraine (max) Ukraine @[1917;1991] Ukraine @[1991;2013] Ukraine rdf:typeGeoPoliticalEntity Ukraine@[19171001;19910715] rfd:typeSovietRepublic Ukraine @[19910716;20130513] rfd:typeSovereignState Ukraine @[19910716;20130513] rfd:typeLviv@[19910716;20130513] Austria@[18660101;19170930] hasPartLviv@[18660101;19170930]

  9. ExamplesforcontinuantTQs 1994 1998 2013 1980 John John@[1980;1994] John@[1994;1998] John rfd:typeHuman John@[1980;1994] rfd:typeChild John@[1994;1998] rfd:typeTeenager John@[1998;2013] rfd:typeAdult John@[201305201000; 201305201100] rfd:typepatientOfsome (AppendectomyandhasAgentvalueDrSmith@[201305201000; 201305201100] "PhasedSortals"

  10. Relations hasMax, maxOf, atSomeTime, hasTime • hasMax (inverse maxOf) relates a ContinuantTQ instance to its related instance with the maximal temporal extension • atSomeTimerelatesa ContinuantTQ with each other a ContinuantTQ related to the same continuant • atSomeTime hasMax  maxOf • maxOfsubPropertyOfatSomeTime(not necessaryifhasMaxis reflexive) • hasTimerelates a continuantTQwithitsdefining time interval

  11. Relations hasMax, maxOf, atSomeTime, hasTime 1994 1998 2013 1980 John John@[1980;1994] John@[1994;1998] John maxOf John@[1994;1998] John@[1998;2013] atSomeTime John@[201305201000; 201305201100] John@[1998;2013] hasTime [1998; 2013]

  12. Translations FOL, ternary DL, binary partOf³ (Lviv, Austria, 1900) partOf³ (Lviv, Poland, 1925) instanceOf³ (Lviv, Settlement, 1100) instanceOf³ (Lviv, City, 1925) partOf (Lviv@1900, Austria@1900)hasTime (Lviv@1900, 1900)hasMax (Lviv@1900, Lviv)hasTime (Austria@1900, 1900)hasMax (Austria@1900, Austria) partOf (Lviv@1925, Poland@1925)hasTime (Lviv@1925, 1925)hasMax (Lviv@1925, Lviv)hasTime(Poland@1925, 1925)hasMax (Poland@1925, Poland) Lviv@1100 rdf:Type SettlementhasTime(Lviv@1100, 1100)hasMax (Lviv@1100, Lviv) Lviv@1925 rdf:Type CityhasTime (Lviv@1925, 1925)hasMax (Lviv@1925, Lviv)

  13. Examples, Class level "Each city is always part of some country""a,t:inst³(x,City,t)®$b:inst³(b,Country,t)Ù part of³ (x,y,t) "Each medieval city has had a gate at some time""a,t1 $t2:inst³(x,MCity,t1) Ù inst³(x,MCity,t2)®$b: (inst(y,Gate,t2)ÙhasPart³(x,y,t1)) Permanent parthood City subClassOf partOf some Country partOfeq inverse(hasPart) partOf Domain ContinuantQC or Occurrent partOf Range ContinuantQC or Occurrent MCity subClassOf atSomeTime some (hasPart some Gate) Temporary parthood

  14. Examples City subClassOf partOf some Country CountrysubClassOf partOf some Continent CitysubClassOf subClassOfpartOfsome Continent Not necessarily always the same country CityGatesubClassOf atSomeTime some (partOfsome City) CityGateDoorsubClassOf partOf some CityGate Does not entail that CityGateDooris part of a city at some time (door built in after destruction of city) CellNucleolussubClassOf partOf some CellNucleus CellNucleussubClassOf partOf some Cell CellNucleolussubClassOf partOfsome Cell(not necessary that the cell is always the same, e.g. after division) Apple subClassOf atSomeTime some (partOfsome AppleTree) AppleSeedsubClassOf atSomeTime some (partOfsome Apple) Does not entail that part Apple seeds are parts of apple trees • Permanent generic relatedness • Temporary relatedness • Permanent generic relatedness • Permanent generic relatedness • Permanent generic relatedness • Temporary relatedness • Temporary relatedness

  15. Consistencyof A-boxes r1: partOf (Lviv@1900, Austria@1900)r2: hasTime(Lviv@1900, 1900)r3: hasMax (Lviv@1900, Lviv)r4: hasTime (Austria@1900, 1900)r5: hasMax (Austria@1900, Austria) r0: partOf³(Lviv, Austria, 1900) One ternary relation rel (a, b, t) is translated into a set of five binary relations. r1: rel (a@t, b@t)r2: hasTime(a@t, t)r3: hasMax (a@t, a)r4: hasTime (b@t , t)r5: hasMax (b@t, b) OWL Rule for consistency checking:TemporallyQualifiedContinuant(?x), TemporallyQualifiedContinuant(?y), hasTime (?x,?t1), hasTime(?y,?t2), topObjectProperty(?x,?y) - > equal(?t1,?t2)

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