Logic on MARS: Ontologies for Generalised Property Graphs
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(2) What do these people have in common?. Marx, Krötzsch, Thost (TU Dresden). Logic on MARS. IJCAI 2017. 2/9.
(3) What do these people have in common?. People that have won two Nobel prizes. Marx, Krötzsch, Thost (TU Dresden). Logic on MARS. IJCAI 2017. 2/9.
(4) Laureates in Knowledge Graphs Wikidata: a free and open Knowledge Graph year : 1903 with : PierreCurie with : Becquerel nobelPhysics. year : 1911. award. award. nobelChemistry. Curie. Marx, Krötzsch, Thost (TU Dresden). Logic on MARS. IJCAI 2017. 3/9.
(5) Laureates in Knowledge Graphs Wikidata: a free and open Knowledge Graph year : 1903 with : PierreCurie with : Becquerel nobelPhysics. year : 1911. award. award. nobelChemistry. Curie. Marx, Krötzsch, Thost (TU Dresden). Logic on MARS. IJCAI 2017. 3/9.
(6) Laureates in Knowledge Graphs Wikidata: a free and open Knowledge Graph year : 1903 with : PierreCurie with : Becquerel nobelPhysics. year : 1911. award. award. nobelChemistry. Curie. Marx, Krötzsch, Thost (TU Dresden). Logic on MARS. IJCAI 2017. 3/9.
(7) Laureates in Knowledge Graphs Wikidata: a free and open Knowledge Graph year : 1903 with : PierreCurie with : Becquerel nobelPhysics. year : 1911. award. award. nobelChemistry. Curie fact notation: award(Curie, nobelChemistry)@{year : 1911}. Marx, Krötzsch, Thost (TU Dresden). Logic on MARS. IJCAI 2017. 3/9.
(8) Laureates in Knowledge Graphs Wikidata: a free and open Knowledge Graph year : 1903 with : PierreCurie with : Becquerel nobelPhysics. year : 1911. award. award. nobelChemistry. Curie fact notation: award(Curie, nobelChemistry)@{year : 1911} Knowledge Graph: labeled graph; edges carry annotation sets (finite sets of attribute–value pairs) Marx, Krötzsch, Thost (TU Dresden). Logic on MARS. IJCAI 2017. 3/9.
(9) Laureates in Knowledge Graphs Wikidata: a free and open Knowledge Graph year : 1903 with : PierreCurie with : Becquerel nobelPhysics. year : 1911. award. award. nobelChemistry. Curie fact notation: award(Curie, nobelChemistry)@{year : 1911} Knowledge Graph: labeled graph; edges carry annotation sets (finite sets of attribute–value pairs) MARS: multi-attributed relational structure (annotated hypergraph) Marx, Krötzsch, Thost (TU Dresden). Logic on MARS. IJCAI 2017. 3/9.
(10) Annotation-aware reasoning Example: for sole “award” winners, infer “laureate,” i.e., from. award(Curie, nobelChemistry)@{year : 1911}. Marx, Krötzsch, Thost (TU Dresden). Logic on MARS. IJCAI 2017. 4/9.
(11) Annotation-aware reasoning Example: for sole “award” winners, infer “laureate,” i.e., from infer. award(Curie, nobelChemistry)@{year : 1911}, laureate(nobelChemistry, Curie)@{year : 1911}. Marx, Krötzsch, Thost (TU Dresden). Logic on MARS. IJCAI 2017. 4/9.
(12) Annotation-aware reasoning Example: for sole “award” winners, infer “laureate,” i.e., from infer. award(Curie, nobelChemistry)@{year : 1911}, laureate(nobelChemistry, Curie)@{year : 1911}. Rule: ∀x, y.∀S. award(x, y)@S ∧ (bc \ bwith : +c)(S) → laureate(y, x)@S. Marx, Krötzsch, Thost (TU Dresden). Logic on MARS. IJCAI 2017. 4/9.
(13) Annotation-aware reasoning Example: for sole “award” winners, infer “laureate,” i.e., from infer. award(Curie, nobelChemistry)@{year : 1911}, laureate(nobelChemistry, Curie)@{year : 1911}. Rule: ∀x, y.∀S. award(x, y)@S ∧ (bc \ bwith : +c)(S) → laureate(y, x)@S Specifier (bc \ bwith : +c): any annotation set without attribute “with” !{year : 1911} %{year : 1903, with : PierreCurie, with : Becquerel}. Marx, Krötzsch, Thost (TU Dresden). Logic on MARS. IJCAI 2017. 4/9.
(14) What else do we need? year : 1956 with : Brattain with : Shockley award award. nobelPhysics. Bardeen year : 1972 with : Cooper with : Schrieffer. Marx, Krötzsch, Thost (TU Dresden). Logic on MARS. IJCAI 2017. 5/9.
(15) What else do we need? year : 1956 with : Brattain with : Shockley award award. nobelPhysics. Bardeen year : 1972 with : Cooper with : Schrieffer. Marx, Krötzsch, Thost (TU Dresden). Logic on MARS. IJCAI 2017. 5/9.
(16) What else do we need? year : 1956 with : Brattain with : Shockley award award. nobelPhysics. Bardeen year : 1972 with : Cooper with : Schrieffer. Marx, Krötzsch, Thost (TU Dresden). Logic on MARS. IJCAI 2017. 5/9.
(17) What else do we need? year : 1956 with : Brattain with : Shockley award award. nobelPhysics. Bardeen year : 1972 with : Cooper with : Schrieffer Goal: derive “award” for co-laureates copying annotation sets is not enough, we need to compute a new annotation set Marx, Krötzsch, Thost (TU Dresden). Logic on MARS. IJCAI 2017. 5/9.
(18) A Logic for Knowledge Graphs Goal: annotation-aware reasoning derived knowledge may depend on annotation sets. Marx, Krötzsch, Thost (TU Dresden). Logic on MARS. IJCAI 2017. 6/9.
(19) A Logic for Knowledge Graphs Goal: annotation-aware reasoning derived knowledge may depend on annotation sets compute new annotation sets. Marx, Krötzsch, Thost (TU Dresden). Logic on MARS. IJCAI 2017. 6/9.
(20) A Logic for Knowledge Graphs Goal: annotation-aware reasoning derived knowledge may depend on annotation sets compute new annotation sets MAPL: multi-attributed predicate logic. Marx, Krötzsch, Thost (TU Dresden). Logic on MARS. IJCAI 2017. 6/9.
(21) A Logic for Knowledge Graphs Goal: annotation-aware reasoning derived knowledge may depend on annotation sets compute new annotation sets MAPL: multi-attributed predicate logic enrich edges with finite binary relations (annotation sets). Marx, Krötzsch, Thost (TU Dresden). Logic on MARS. IJCAI 2017. 6/9.
(22) A Logic for Knowledge Graphs Goal: annotation-aware reasoning derived knowledge may depend on annotation sets compute new annotation sets MAPL: multi-attributed predicate logic enrich edges with finite binary relations (annotation sets) quantification over annotation sets. Marx, Krötzsch, Thost (TU Dresden). Logic on MARS. IJCAI 2017. 6/9.
(23) A Logic for Knowledge Graphs Goal: annotation-aware reasoning derived knowledge may depend on annotation sets compute new annotation sets MAPL: multi-attributed predicate logic enrich edges with finite binary relations (annotation sets) quantification over annotation sets Theorem MAPL has the same expressivity as weak second-order logic. Entailment for MAPL theories is not semi-decidable.. Marx, Krötzsch, Thost (TU Dresden). Logic on MARS. IJCAI 2017. 6/9.
(24) A Logic for Knowledge Graphs Goal: annotation-aware reasoning derived knowledge may depend on annotation sets compute new annotation sets MAPL: multi-attributed predicate logic enrich edges with finite binary relations (annotation sets) quantification over annotation sets Theorem MAPL has the same expressivity as weak second-order logic. Entailment for MAPL theories is not semi-decidable. Idea: Encode arbitrary arity predicates in annotation sets. Marx, Krötzsch, Thost (TU Dresden). Logic on MARS. IJCAI 2017. 6/9.
(25) MAPL Rules A decidable fragment Specifiers express constraints on annotation sets. Marx, Krötzsch, Thost (TU Dresden). Logic on MARS. IJCAI 2017. 7/9.
(26) MAPL Rules A decidable fragment Specifiers express constraints on annotation sets Function definitions derive new annotation sets. Marx, Krötzsch, Thost (TU Dresden). Logic on MARS. IJCAI 2017. 7/9.
(27) MAPL Rules A decidable fragment Specifiers express constraints on annotation sets Function definitions derive new annotation sets Example: from award(Bardeen, nobelPhysics)@{year : 1956, with : Shockley, with : Brattain}. Marx, Krötzsch, Thost (TU Dresden). Logic on MARS. IJCAI 2017. 7/9.
(28) MAPL Rules A decidable fragment Specifiers express constraints on annotation sets Function definitions derive new annotation sets. Example: from award(Bardeen, nobelPhysics)@{year : 1956, with : Shockley, with : Brattain}, infer award(Shockley, nobelPhysics)@{year : 1956, with : Bardeen, with : Brattain}. Marx, Krötzsch, Thost (TU Dresden). Logic on MARS. IJCAI 2017. 7/9.
(29) MAPL Rules A decidable fragment Specifiers express constraints on annotation sets Function definitions derive new annotation sets. Example: from award(Bardeen, nobelPhysics)@{year : 1956, with : Shockley, with : Brattain}, infer award(Shockley, nobelPhysics)@{year : 1956, with : Bardeen, with : Brattain} Rule award(x, y)@S ∧ bwith : zc(S) → award(z, y)@CoLaureate(S, x, z). Marx, Krötzsch, Thost (TU Dresden). Logic on MARS. IJCAI 2017. 7/9.
(30) MAPL Rules A decidable fragment Specifiers express constraints on annotation sets Function definitions derive new annotation sets. Example: from award(Bardeen, nobelPhysics)@{year : 1956, with : Shockley, with : Brattain}, infer award(Shockley, nobelPhysics)@{year : 1956, with : Bardeen, with : Brattain} Rule award(x, y)@S ∧ bwith : zc(S) → award(z, y)@CoLaureate(S, x, z) with function definition CoLaureate(U, v, w): ⇒ insert(with : v) bwith : oc(U ), o 6≈ w ⇒ insert(with : o) byear : dc(U ) ⇒ insert(year : d) Marx, Krötzsch, Thost (TU Dresden). Logic on MARS. IJCAI 2017. 7/9.
(31) Reasoning in MARPL Overview Bottom-up materialisation: MARS chase. Marx, Krötzsch, Thost (TU Dresden). Logic on MARS. IJCAI 2017. 8/9.
(32) Reasoning in MARPL Overview Bottom-up materialisation: MARS chase Idea: never touch existing annotation sets, only derive new ones. Marx, Krötzsch, Thost (TU Dresden). Logic on MARS. IJCAI 2017. 8/9.
(33) Reasoning in MARPL Overview Bottom-up materialisation: MARS chase Idea: never touch existing annotation sets, only derive new ones Function definitions are evaluated during rule application. Marx, Krötzsch, Thost (TU Dresden). Logic on MARS. IJCAI 2017. 8/9.
(34) Reasoning in MARPL Overview Bottom-up materialisation: MARS chase Idea: never touch existing annotation sets, only derive new ones Function definitions are evaluated during rule application exponentially many possible annotation sets ensure termination. Marx, Krötzsch, Thost (TU Dresden). Logic on MARS. IJCAI 2017. 8/9.
(35) Reasoning in MARPL Overview Bottom-up materialisation: MARS chase Idea: never touch existing annotation sets, only derive new ones Function definitions are evaluated during rule application exponentially many possible annotation sets ensure termination Theorem MARPL entailment is ExpTime-complete for data & combined complexity.. Marx, Krötzsch, Thost (TU Dresden). Logic on MARS. IJCAI 2017. 8/9.
(36) Reasoning in MARPL Overview Bottom-up materialisation: MARS chase Idea: never touch existing annotation sets, only derive new ones Function definitions are evaluated during rule application exponentially many possible annotation sets ensure termination Theorem MARPL entailment is ExpTime-complete for data & combined complexity.. Theorem MARPL entailment is PTime-complete for data complexity if the size of annotation sets is bounded.. Marx, Krötzsch, Thost (TU Dresden). Logic on MARS. IJCAI 2017. 8/9.
(37) Conclusion & Outlook Summary: MAPL general, second-order based framework for attributed logics; not semi-decidable MARPL decidable, rule-shaped fragment; ExpTime-complete for data & combined complexity. Future Work: Create attributed ontologies, e.g., for Wikidata Implement a MARPL reasoner Identify more expressive decidable fragments of MAPL Study attributed versions of other KR formalisms Classify data complexities, identify tractable fragments. Marx, Krötzsch, Thost (TU Dresden). Logic on MARS. IJCAI 2017. 9/9.
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