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HyperordersandTransclusion:
JamesGouldingTimBrailsfordHelenAshman
understandingdimensionalhypertext
hyperordersandtransclusionThenext20‐ishminutes:
• ....willwindit’smerrywaythrough:
–Whyhyperstructuresareimportant
–hyperstructuresarenotjustRDF
–IntroducingHyperorders
–Transclusionanditsproblems
–Wherewecouldgonext...
hyperordersandtransclusionOntheshouldersof...
tednelson‐hypertexttransclusionzigzag
DougEnglebart‐augmentinghumanintellectcollaborationnetworks
tedcodd‐predicatelogicrelationalmodel...hyperstructure?
hyperordersandtransclusionComputerScience
4
EdsgerDijkstradijkstra’salgorithm‐“GoTostatementconsideredharmful”‐clarityofthought
astronomy
telescopescience
hyperordersandtransclusionComputerScienceisabout...
5
INFORMATION
structure
integrity
manipula<on
hyperordersandtransclusionHyperstructures
• hyperstructures‐hypertextswheretheitemofconcernisnotadocumentbutadatum‐seem,therefore,crucialtocomputerscience.
– interconnectivity
– querying
– navigation
– discoverability
– Blexibility
hyperordersandtransclusionTernaryHyperstructures
• <subject,predicate,object>
HM ternary = 〈 S, P, O, E 〉
whereE⊂S×P×O– Sisthesetofpossiblesubjectvertices– Pisthesetofpossiblepredicates(linktypes)– Oisthesetofallpossibleobjectvertices– Eisaternaryrelationactingacrossthem
hyperordersandtransclusionTernaryHyperstructures
• <subject,predicate,object>
HM ternary = 〈 V, P, E 〉
whereE⊂V×P×V– Visthesetofpossiblevertices– Pisthesetofpossiblepredicates(linktypes)– Eisaternaryrelationactingacrossthem
hyperordersandtransclusionTernaryHyperstructures
• <subject,predicate,object>
–
• ButisthistheonlywayofdeEiningandcreatinghyperstructures?
• No,therearemanyotheroptions,ofwhichZigZagisjustone....
hyperordersandtransclusion
• Zzstructureisahyperstructurewhere...‣ dataiscontainedininterconnectedcells.‣ cellsarearrangedintoparallellistsinagivendimension.‣ acellcanonlyhaveamaximumofoneforwardconnectionandonebackwardconnectionineachdimension.
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James Goulding
d.lastname
‣ theremaybeanynumberofdimensions.
Tim Brailsford
Helen Ashman
d.people
ZigZagandZZstructure
hyperordersandtransclusion
11
• ZigZag‣ zzstructureoverlaidwithextrafunctionality‣mostimportantlytransclusion(cloning)
d.clone
Goulding
d.authorHyperstructures Coactive Intelligence
ZigZagandZZstructure
Goulding
hyperordersandtransclusionDefiningZigZagformally:
– IthasnonotionofaEirstorderlink(Nelson’sprescriptionthatoneofZigZag’sfundamentalrulesisthat“therearenolinktypes”).
– InsteadZigZaghassetsofadjacencies,describinghownodesareordered.Anindividualsetisadimension.
• ZigZagisactuallyquitehardtocategorize:
– Itisabinary,notternary,structure.
hyperordersandtransclusionBinaryHyperstructures
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<subject (negward cell), object (posward cell)>
Asimplebinaryhyperstructuremaybedescribedasastandardbipartitegraph:HM binary = 〈 S, O, E 〉
where E ⊂ S ×O
Butzzstructureisnotjustabinaryrelationalmodel‐itsassociationsareallocatedintosubsetswithcommonsemantics.
DimensionalHyperstructures:
HM dimensional = 〈 S, O, { D1, D2, ..., Dn } 〉
where Di ⊂ S × O.
hyperordersandtransclusionHyperorders
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Ifweonlyhaveonesetofnodes:
HMhyperorder = 〈 C, { D1, D2, ..., Dn } 〉
where Di ⊂ C2.
hyperordersandtransclusion2.Transclusion
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–TransclusionhasalwaysbeenakeycomponentinNelson’svisionofhypertext.
–Thetermwasoriginallyusedtodenotetheinclusion,byreferentialaddressing,ofpartofonedocumentwithinanother.
– Itsusagehasnowexpandedtoencompassthepresentationofdatainacontextotherthantheoneoriginallyintended.
–CanbeusedinZigZagtosolvetheproblemofnotbeingallowed1‐manylinks.
hyperordersandtransclusionAnexampleenJty...
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AStructureforDNA
year
type
journal
author
author
Paper
1953
Nature
JamesWatson
FrancisCrick
hyperordersandtransclusionDealingwith1‐manyinZigZag
17
A Structure for DNA Paper
Nature
1953
James Watson
Francis Crick
d.type
d.journal
d.year
d.author1
d.author2
hyperordersandtransclusionDealingwith1‐manyinZigZag
18
A Structure for DNA Paper
Nature
1953
James Watson
Francis Crick
d.type
d.journal
d.year
d.author1
d.author2
d.author
d.author
hyperordersandtransclusionDealingwith1‐manyinZigZag
19
A Structure for DNA Paper
Nature
1953
James Watson
Francis Crick
d.type
d.journal
d.year
d.author
d.group
hyperordersandtransclusionDealingwith1‐manyinZigZag
20
A Structure for DNA Paper
Nature
1953
d.type
d.journal
d.year
James Watson
d.clone
d.author
d.clone
Francis Crickd.author
hyperordersandtransclusionIdenJtyTransclusion
• Thislastapproachisinteresting‐zzstructureisrelegatedtoastructural,notalogicallevel.
• The“paperentity”isnownotrepresentedbyasinglecell,butthreethatmustbereconstructedtogether.
• However,thereisonlyonepaper‐allofthetranscludedcellsshareexactlythesamenumericalidentity.
• WehencerefertothisuseofnodeandcontentreuseasIdentityTransclusion.
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hyperordersandtransclusionAllconnec<onsareshared
22
A Structure for DNA Paper
Nature
1953
d.type
d.journal
d.year
James Watson
d.clone
d.author
d.clone
Francis Crickd.author
hyperordersandtransclusionInstanceTransclusion
23
hyperordersandtransclusionInstanceTransclusion
24
James Bond Flemingd.creator
d.actor
d.period
d.no films
Connery
1960’s
6
d.clone
James Bond
d.actor
d.period
d.no films
Moore
1970’s
7
d.clone
James Bond
hyperordersandtransclusionInstanceTransclusion
• Thistimethetranscludedcellsrepresentdifferentinstancesof“Bond”.
• Theydon’tshareacompleteidentity.
• instancetransclusiondoesnotshareallitsrelationsacrossallofitscontexts,whereasanidentitytransclusiondoes,becauseforthelatteronlyoneentityisbeingmodeled.
25
hyperordersandtransclusionDisasterStrikes...
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Swan
Swan Whited.clone
d.colour
Swan Blackd.clone
d.colour
Swan Black
White
d.cloned.colour
d.colourSwan
d.clone
• Thisjustwon’tworkbecauseIamtryingtouseinstanceandidentitytransclusionatthesametime.
...inswanform
hyperordersandtransclusionothertransclusioncollisions
27
Head of State Head of State
MonarchBritain
Head of State
PresidentUSA
King George V
1936
Queen Elizabeth II
1952
d.clone
d.country d.title
d.clone
d.country d.title
d.cloned.name
d.coronated
d.cloned.name
d.coronated
hyperordersandtransclusionCollisioninotherHyperstructures
• Butthisisnotjustaproblemforzigzag.It’saproblemforotherhyperstructurestoo...
28
tedcodd‐predicatelogicrelationalmodel...hyperstructure?
RelaJonalDatabases
...butdoesRMactuallydefineahyperstructureoflinksandcontent?
hyperordersandtransclusionRelaJonalHyperstructure?
• arecordisalinkacrossitsitems.
• foreignkeysarelinksacrossrecords.
• rela<onalalgebracreatesdynamicandcomputedlinks.
• ONUPDATECASCADEcreatestransclusionlinks.
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• “Rela<onalhyperstructures”cancopewiththeheadofstateexample,butnottheswans,withoutusinganar9ficialkey.
N‐aryHyperstructures
