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FX

:table1 a fx:root ;
  rdf:_1 [
    a fx:table1
    fx:col1 "colvalue" ;
    fx:col2 "12"^^xsd:int ;
    fx:col3 "12/12/2022"^^xsd:date
  ]

FX Relational Profile

Container: a FX container ContainerTable: URI of the entity representing the table (the root FX container) ContainerRow: a blank node representing any row in the table TypeProperty: the RDF type predicate TypeTable: the range of the RDF Type property, pointing to the table name in the database SlotRow: a container membership property linking a ContainerTable to any of its ContainerRow SlotColumn: an RDF property named after a table column linking a ContainerRow to the SlotValue (the typed literal from the column value) SlotValue: an RDF typed literal (the column value in the database table) Join: some roles can be joined together. E.g. ContainerRow(S) ^ ContainerRow(O). Not all assumption can be joined. Same assumptions in different triples can always be joined. Rules for inferring valid joined below.

Theorems for FX

Theorems for FX Relational Profile

Interpreting basic graph patterns

T <- ( S, P, O ) S <- URI|BN O <- URI|BN|TL CMP <- URI(rdf:_*) P <- URI BGP <- { T }

Generate constraints

;; Inferring the role of S ContainerTable(S) <- URI(S) | FXRoot(O) | SlotRow(P) | ContainerRow(O) ContainerRow(S) <- SlotColumn(P) | SlotValue(O) | TypeTable(O) ;; Inferring role of P SlotColumn(P) <- SlotValue(O) TypeProperty(P) <- TypeTable(O) | FXRoot(O) SlotRow(P) <- ContainerRow(O) SlotRow(P) <- CMP(P) SlotColumn(P) <- URI(fx:*) TypeProperty(P) <- URI(rdf:type) ;; Inferring the role of O SlotValue(O) <- SlotColumn(P) ContainerRow(O) <- SlotRow(P) TypeTable(O) <- URI(O) SlotValue(O) <- TL(O) ;; Making joins Join(n) <- Assumption(n) ^ Assumption(n) -- on different triples but same Assumption type ;; Inferring joins from different assumption types Join(n) <- ContainerRow(n) ^ ContainerRow(n) <- Subject(n) ^ Object(n) Join(n) <- ContainerRow(n) ^ ContainerRow(n) <- Object(n) ^ Subject(n) ;; there are not other cases where joins with different types make sense (proof!)

##Wrong: ##;; TypeTable(O) <- TypeProperty(P) ##;; ContainerRow(O) <- BN(O) // Not true, in SPARQL matches also values

Specialising in

Subject -> ContainerTable | ContainerRow Predicate -> SlotRow | SlotColumn | TypeProperty Object -> ContainerRow | SlotValue | FXRoot | TypeTable

Guards

ContainerTable(S) -> !SlotColumn(P) & !SlotValue(O)

Search the space of interpretations

State = Assumption[] ^ Hypothesis[] (the set of constraints) expand = generate next Stete by adding hypothesis (trying to specialise them as much as possible) Guard = checks for inconsistencies and avoids following inconsistent paths Visited = keeps the record of visited States (both valid and invalid) Proceed until all BGPInterpretations are visited (brute force)

next (x) Uses SpecialiseHypothesis to return a new State, which keeps track of the previous State Uses Guard to validate the new State returns False if invalid, otherwise the new State

follow(Stete y) while ( State s <- next(y) ) if visited(s) continue else follow(s)

Other notes

?s ?p ?o

S ?p ?o ?s P ?o -> IF P anySlot Then ?s is containerTable ELSE ?s is containerRow AND OP is column name AND ?o is columnValue(P) ?s ?p O

S P ?o ?s P O S ?p O

S P O

BGP -> BindingsWithRules ?s tableContainer && ?o valueFromTableXandColumnY && -> JoinAnalysis -> Query Assembly

Functions:

  • container to table -- OK
  • table to container -- OK
  • container to rownum -- OK
  • rownum to container -- OK
  • P to column
  • ?p to column set
  • P to rownum
  • ?p to row set
  • Ptype to tables (or P O to table)

[] a xyz:table1 ; fx:anySlot [ xyz:col1 ?value ] .

select table1.col1 from table1 limit 1 offset

?table rdf:_54 ?row . ?row xyz:col1 ?value

SELECT COL1 from table1 order by (primary key) limit 1 offset 54

?s fx:anySlot [ ?p ?o ]

NodeInterpretation:

  • ContainerTable (Only S) (KnownTable or AnyTable)
  • SlotRow (P) (KnownRow or AnyRow)
  • ContainerRow (O or S) (KnownTable or AnyTable, KnownRow or AnyRow)
  • SlotColumn (P) (KnownColumn or AnyColumn)
  • Value (O) (KnownValue or AnyValue)

TripleInterpretation: ContainerTable | ContainerRow SlotRow | SlotColumn ContainerTable | ContainerRow | Value

NodeVarJoin

  • var name
  • nodes

?s ?p ?o => ?s is table, ?p is CMP, ?o is row ?o ?x ?y => ?o is row, ?x is COLUMN, ?y is value ?g ?x ?q = ?r is row, ?x is COLUMN, ?q is value

Bindings (?s ?p ?o ?x ?y ?g ?q)

SELECT A.X FROM TABLE1 A, TABLE1 B where A.X=B.X SELECT A.X FROM TABLE2 A, TABLE2 B where A.X=B.X SELECT A.X FROM TABLE1 A, TABLE2 B where A.X=B.X

SELECT * FROM TABLE1 SELECT * FROM TABLE3

?p -> SlotColumn ( col1, col2, col3)