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A Transition from RDF to Petri Nets Jan Paredaens Universiteit - - PowerPoint PPT Presentation

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A Transition from RDF to Petri Nets Jan Paredaens Universiteit Antwerpen 11.11.11 Jan Paredaens A Transition from RDF to Petri Nets 1/44 RDF Constraints in RDF WikiPedia Petri Nets Decidability - Axioms Conclusion Jan Paredaens A

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A Transition from RDF to Petri Nets

Jan Paredaens

Universiteit Antwerpen

11.11.11

Jan Paredaens A Transition from RDF to Petri Nets 1/44

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RDF Constraints in RDF WikiPedia Petri Nets Decidability - Axioms Conclusion

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RDF

Ramanathan V. Guha 1965 - 1997 RDF - Netscape Corp.

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RDF

RDF (Resource Description Framework) is a W3C recommendation for publishing structured data on the web. RDF databases arrange information in simple triples consisting of a subject, a predicate and an object.

exstaff:85740 exterms:addressUSA _:johnaddress . exstaff:85741 exterms:addressUSA _:anaddress . _:johnaddress exterms:street "1501 Grant Avenue" . _:johnaddress exterms:city "Bedford" . _:johnaddress exterms:state "Massachusetts" . _:johnaddress exterms:postalCode "01730" . _:exterms:addressUSA exterms:country "USA" . _:exterms:addressNL exterms:country "NL" . Jan Paredaens A Transition from RDF to Petri Nets 4/44

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RDF

An RDF-Graph is a finite set of triples (s, p, o).

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RDF

An RDF-Graph is a finite set of triples (s, p, o). As such it is one big ternary relation.

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RDF

An RDF-Graph is a finite set of triples (s, p, o). As such it is one big ternary relation. Semantically we cannot use the relational model.

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RDF

An RDF-Graph is a finite set of triples (s, p, o). As such it is one big ternary relation. Semantically we cannot use the relational model. For constraints we cannot use keys, functional dependencies, referential integrity, ...

Jan Paredaens A Transition from RDF to Petri Nets 8/44

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RDF

An RDF-Graph is a finite set of triples (s, p, o). As such it is one big ternary relation. Semantically we cannot use the relational model. For constraints we cannot use keys, functional dependencies, referential integrity, ... We have to use patterns and embeddings.

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Constraints in RDF

Ted Codd 1923 - 2003 1970 Relational DB

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Constraints in RDF

Constraints in RDF are mainly used for:

◮ Consistency checking. ◮ Consistent query answering. ◮ Data cleaning. ◮ Semantic query optimization. ◮ Distributed data management.

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Constraints in RDF

exstaff:85740 exterms:addressUSA _:johnaddress . exstaff:85741 exterms:addressUSA _:anaddress . _:johnaddress exterms:street "1501 Grant Avenue" . _:johnaddress exterms:city "Bedford" . _:johnaddress exterms:state "Massachusetts" . _:johnaddress exterms:postalCode "01730" . _:exterms:addressUSA exterms:country "USA" . _:exterms:addressNL exterms:country "NL" .

Triple Generating Constraint

For every address in the USA we need a state. TGC = {($x, exterms:addressUSA, $y)}, {($y, exterms:state, $z)} {($x, exterms:addressUSA, $y)}, {($y, exterms:state, $z)}

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Constraints in RDF

exstaff:85740 exterms:addressUSA _:johnaddress . exstaff:85741 exterms:addressUSA _:anaddress . _:johnaddress exterms:street "1501 Grant Avenue" . _:johnaddress exterms:city "Bedford" . _:johnaddress exterms:state "Massachusetts" . _:johnaddress exterms:postalCode "01730" . _:exterms:addressUSA exterms:country "USA" . _:exterms:addressNL exterms:country "NL" .

Functional Constraint

Every address in the USA has at most one state. FC = {($x, exterms:addressUSA, $y), ($y, exterms:state, $z)}, y → z

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Constraints in RDF

exstaff:85740 exterms:addressUSA _:johnaddress . exstaff:85741 exterms:addressUSA _:anaddress . _:johnaddress exterms:street "1501 Grant Avenue" . _:johnaddress exterms:city "Bedford" . _:johnaddress exterms:state "Massachusetts" . _:johnaddress exterms:postalCode "01730" . _:exterms:addressUSA exterms:country "USA" . _:exterms:addressNL exterms:country "NL" .

Forbidding Constraint

Every address in the Netherlands has no state. FBC = {($x, exterms:addressNL, $y)}, {($y, exterms:state, $z)}

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Constraints in RDF

exstaff:85740 exterms:addressUSA _:johnaddress . exstaff:85741 exterms:addressUSA _:anaddress . _:johnaddress exterms:street "1501 Grant Avenue" . _:johnaddress exterms:city "Bedford" . _:johnaddress exterms:state "Massachusetts" . _:johnaddress exterms:postalCode "01730" . _:exterms:addressUSA exterms:country "USA" . _:exterms:addressNL exterms:country "NL" .

(in)Equality Generating Constraint

For every address in the USA the city and the state are different EGC = {($x, exterms:addressUSA, $y)}, {($y, exterms:state, $z), ($y, exterms:city, $z′)}, $z = $z′

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WikiPedia

Jimmy Wales 1966 - 2003 Wikipedia

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WikiPedia

DBpedia is an open-access, large RDF repository that stores encyclopedic information retrieved from Wikipedia, and other

  • URLs. It contains 1 billion triples.

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WikiPedia

Every person in DBpedia should have at most one birth date. {($person, dbo : birthDate, $y), ($person, dbo : birthDate, $z)}, {($y = $z)}}. Ask {?person dbo:birthDate ?y. ?person dbo:birthDate ?z. FILTER(?y != ?z)} As the total number of people with a recorded birth date is 465498, we conclude that 0.72% of all people on DBpedia violate this constraint!

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WikiPedia

The next constraint expresses that no person is born after his/her death: Ask {?person dbo:birthDate ?birth . ?person dbo:deathDate ?death . FILTER (?death<?birth)} This constraint is violated 150 times.

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WikiPedia

When checking the constraint that no extinct bird still live we get a violation: Ask{?animal dbpprop:extinct ?z. ?animal dbpprop:classis :Bird. ?animal dbpprop:status ?y FILTER (?y != "EX"@en )} This constraint is not satisfied by the Antillean Cave Rail (Nesotrochis debooyi).

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Petri Nets

Carl Adam Petri 1926 - 2010 1962 Petri Net

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Petri Nets

We represent a Petri Net ¡¡TEKENING¿¿ by an RDF Graph:

$p_1$ $t$ $p3$ Jan Paredaens A Transition from RDF to Petri Nets 22/44

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Petri Nets

TGC1 = {($p1, $t, $p3), ($p2, $t, $p4)}, {($p1, $t, $p4)}

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Petri Nets

TGC1 = {($p1, $t, $p3), ($p2, $t, $p4)}, {($p1, $t, $p4)} TGC2 = {($p1, $t, $p2)}, {($p1, Place, $p1), ($p2, Place, $p2),

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Petri Nets

TGC1 = {($p1, $t, $p3), ($p2, $t, $p4)}, {($p1, $t, $p4)} TGC2 = {($p1, $t, $p2)}, {($p1, Place, $p1), ($p2, Place, $p2), FB1 = {($p1, $t, $p2), ($t, Place, $t)}

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Petri Nets

TGC1 = {($p1, $t, $p3), ($p2, $t, $p4)}, {($p1, $t, $p4)} TGC2 = {($p1, $t, $p2)}, {($p1, Place, $p1), ($p2, Place, $p2), FB1 = {($p1, $t, $p2), ($t, Place, $t)} Connected.

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Petri Nets

Two problems ¡¡TEKENING¿¿ TGC1 = {($p, Input, $t)}, {($p, Place, $p)}

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Petri Nets

Two problems ¡¡TEKENING¿¿ TGC1 = {($p, Input, $t)}, {($p, Place, $p)} TGC2 = {($t, Output, $p)}, {($p, Place, $p)}

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Petri Nets

Two problems ¡¡TEKENING¿¿ TGC1 = {($p, Input, $t)}, {($p, Place, $p)} TGC2 = {($t, Output, $p)}, {($p, Place, $p)} FBC1 = {($p, Input, $t), ($t, Place, $t)}

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Petri Nets

Two problems ¡¡TEKENING¿¿ TGC1 = {($p, Input, $t)}, {($p, Place, $p)} TGC2 = {($t, Output, $p)}, {($p, Place, $p)} FBC1 = {($p, Input, $t), ($t, Place, $t)} FBC2 = {($t, Output, $p), ($t, Place, $t)}

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Petri Nets

Two problems ¡¡TEKENING¿¿ TGC1 = {($p, Input, $t)}, {($p, Place, $p)} TGC2 = {($t, Output, $p)}, {($p, Place, $p)} FBC1 = {($p, Input, $t), ($t, Place, $t)} FBC2 = {($t, Output, $p), ($t, Place, $t)} EGC = {($x1, $x2, $x3)}, $x2 = Input ∨ $x2 = Output ∨ $x2 = Place

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Petri Nets

Two problems ¡¡TEKENING¿¿ TGC1 = {($p, Input, $t)}, {($p, Place, $p)} TGC2 = {($t, Output, $p)}, {($p, Place, $p)} FBC1 = {($p, Input, $t), ($t, Place, $t)} FBC2 = {($t, Output, $p), ($t, Place, $t)} EGC = {($x1, $x2, $x3)}, $x2 = Input ∨ $x2 = Output ∨ $x2 = Place Connected.

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Decidability - Axioms

Alan Turing 1912 - 1954 1936 Turing Machine

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Decidability - Axioms

◮ More constraints on RDF;

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Decidability - Axioms

◮ More constraints on RDF; ◮ Also a recursive constraint;

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Decidability - Axioms

◮ More constraints on RDF; ◮ Also a recursive constraint; ◮ Taking blanc nodes into account;

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Decidability - Axioms

◮ More constraints on RDF; ◮ Also a recursive constraint; ◮ Taking blanc nodes into account; ◮ Decidability Results;

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Decidability - Axioms

◮ More constraints on RDF; ◮ Also a recursive constraint; ◮ Taking blanc nodes into account; ◮ Decidability Results; ◮ Complexity Results;

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Decidability - Axioms

◮ More constraints on RDF; ◮ Also a recursive constraint; ◮ Taking blanc nodes into account; ◮ Decidability Results; ◮ Complexity Results; ◮ Sound and Complete Sets of Axioms.

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Conclusion

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Conclusion

1879 - 1955

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Conclusion

1879 - 1955

Theories should be as simple as possible ...

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Conclusion

1879 - 1955

Theories should be as simple as possible ... ... but not simpler.

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Conclusion

Video

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