Attributed Description Logics: Reasoning on Knowledge Graphs Markus - - PowerPoint PPT Presentation

Attributed Description Logics: Reasoning on Knowledge Graphs

Markus Krötzsch1 Maximilian Marx1 Ana Ozaki2 Veronika Thost3

1Knowledge-Based Systems Group, TU Dresden 2KRDB Research Centre for Knowledge and Data, Free University of Bolzano 3MIT-IBM Watson AI Lab, IBM Research

27th International Joint Conference on Artificial Intelligence

Full paper: https://iccl.inf.tu-dresden.de/web/Inproceedings3045/en

Maximilian Marx (TU Dresden) DL@: Reasoning on Knowledge Graphs IJCAI 2018 1 / 6

Knowledge Graphs

Wikidata: the free and open Knowledge Graph of the Wikimedia Foundation meitner planckMedal lawrence fermiAward time : 1949 awarded time : 1957 for : cyclotron awarded

Maximilian Marx (TU Dresden) DL@: Reasoning on Knowledge Graphs IJCAI 2018 2 / 6

Knowledge Graphs

Wikidata: the free and open Knowledge Graph of the Wikimedia Foundation meitner planckMedal lawrence fermiAward time : 1949 awarded time : 1957 for : cyclotron awarded

Maximilian Marx (TU Dresden) DL@: Reasoning on Knowledge Graphs IJCAI 2018 2 / 6

Knowledge Graphs

Wikidata: the free and open Knowledge Graph of the Wikimedia Foundation meitner planckMedal lawrence fermiAward time : 1949 awarded time : 1957 for : cyclotron awarded awarded(meitner, planckMedal)@⌊ ⌈time : 1949⌋ ⌉ awarded(lawrence, fermiAward)@⌊ ⌈time : 1957, for : cyclotron⌋ ⌉

Maximilian Marx (TU Dresden) DL@: Reasoning on Knowledge Graphs IJCAI 2018 2 / 6

Description Logics

Description Logics: decidable fragments of First-Order Logic variable-free syntax theoretical foundation of the Web Ontology Language (OWL)

Maximilian Marx (TU Dresden) DL@: Reasoning on Knowledge Graphs IJCAI 2018 3 / 6

Description Logics

Description Logics: decidable fragments of First-Order Logic variable-free syntax theoretical foundation of the Web Ontology Language (OWL) Example “Everybody who has received an award should be known for something”

Maximilian Marx (TU Dresden) DL@: Reasoning on Knowledge Graphs IJCAI 2018 3 / 6

Description Logics

Description Logics: decidable fragments of First-Order Logic variable-free syntax theoretical foundation of the Web Ontology Language (OWL) Example “Everybody who has received an award should be known for something” ∃awarded. Award ⊑ ∃knownFor. ⊤

Maximilian Marx (TU Dresden) DL@: Reasoning on Knowledge Graphs IJCAI 2018 3 / 6

Description Logics

Description Logics: decidable fragments of First-Order Logic variable-free syntax theoretical foundation of the Web Ontology Language (OWL) Example “Everybody who has received an award should be known for something” ∃awarded. Award ⊑ ∃knownFor. ⊤ Award(planckMedal)

Maximilian Marx (TU Dresden) DL@: Reasoning on Knowledge Graphs IJCAI 2018 3 / 6

Description Logics

Description Logics: decidable fragments of First-Order Logic variable-free syntax theoretical foundation of the Web Ontology Language (OWL) Example “Everybody who has received an award should be known for something” ∃awarded. Award ⊑ ∃knownFor. ⊤ Award(planckMedal) But what about the annotations?

Maximilian Marx (TU Dresden) DL@: Reasoning on Knowledge Graphs IJCAI 2018 3 / 6

Attributed Description Logics

Attributed Description Logics: Add annotations to concept names and role names Allow variables as placeholders for annotations

Maximilian Marx (TU Dresden) DL@: Reasoning on Knowledge Graphs IJCAI 2018 4 / 6

Attributed Description Logics

Attributed Description Logics: Add annotations to concept names and role names Allow variables as placeholders for annotations Example “Everybody who has received an award should be known for something, keeping the same annotation”

Maximilian Marx (TU Dresden) DL@: Reasoning on Knowledge Graphs IJCAI 2018 4 / 6

Attributed Description Logics

Attributed Description Logics: Add annotations to concept names and role names Allow variables as placeholders for annotations Example “Everybody who has received an award should be known for something, keeping the same annotation” ∃ awarded@S. Award ⊑ ∃ knownFor@S. ⊤

Maximilian Marx (TU Dresden) DL@: Reasoning on Knowledge Graphs IJCAI 2018 4 / 6

Attributed Description Logics

Attributed Description Logics: Add annotations to concept names and role names Allow variables as placeholders for annotations Example “Everybody who has received an award should be known for something, with a new annotation that has the same for value”

Maximilian Marx (TU Dresden) DL@: Reasoning on Knowledge Graphs IJCAI 2018 4 / 6

Attributed Description Logics

Attributed Description Logics: Add annotations to concept names and role names Allow variables as placeholders for annotations Example “Everybody who has received an award should be known for something, with a new annotation that has the same for value” ∃ awarded@S. Award ⊑ ∃ knownFor@⌊ ⌈for : S.for⌋ ⌉

Maximilian Marx (TU Dresden) DL@: Reasoning on Knowledge Graphs IJCAI 2018 4 / 6

Attributed Description Logics

Attributed Description Logics: Add annotations to concept names and role names Allow variables as placeholders for annotations Example “Everybody who has received an award in 1949 should be known for something, with a new annotation that has the same values for for”

Maximilian Marx (TU Dresden) DL@: Reasoning on Knowledge Graphs IJCAI 2018 4 / 6

Attributed Description Logics

Attributed Description Logics: Add annotations to concept names and role names Allow variables as placeholders for annotations Example “Everybody who has received an award in 1949 should be known for something, with a new annotation that has the same values for for” S :⌊time : 1949⌋

• ∃ awarded@S. Award ⊑ ∃ knownFor@⌊

⌈for : S.for⌋ ⌉

• Maximilian Marx (TU Dresden)

DL@: Reasoning on Knowledge Graphs IJCAI 2018 4 / 6

Attributed Description Logics

Attributed Description Logics: Add annotations to concept names and role names Allow variables as placeholders for annotations Example “Everybody who has received an award in 1949 should be known for something, with a new annotation that has the same values for for” S :⌊time : 1949⌋

• ∃ awarded@S. Award ⊑ ∃ knownFor@⌊

⌈for : S.for⌋ ⌉

• Reasoning:

Ground all axioms Treat all annotated concepts and annotated roles as new names

Maximilian Marx (TU Dresden) DL@: Reasoning on Knowledge Graphs IJCAI 2018 4 / 6

Attributed Description Logics

Attributed Description Logics: Add annotations to concept names and role names Allow variables as placeholders for annotations Example “Everybody who has received an award in 1949 should be known for something, with a new annotation that has the same values for for” S :⌊time : 1949⌋

• ∃ awarded@S. Award ⊑ ∃ knownFor@⌊

⌈for : S.for⌋ ⌉

• Reasoning:

Ground all axioms Treat all annotated concepts and annotated roles as new names Add auxiliary axioms that handle inclusions of annotations

Maximilian Marx (TU Dresden) DL@: Reasoning on Knowledge Graphs IJCAI 2018 4 / 6

Complexities

Theorem Combined complexity of satisfiability for attributed Knowledge Bases non-attributed attributed DL ground restricted unrestricted P-complete ELH@ P-complete P-complete1 Exp-complete Exp-complete ALCH@ Exp-complete Exp-complete 2Exp-complete N2Exp-complete SROIQ@ N2Exp-complete N2Exp-complete N2Exp-complete

Maximilian Marx (TU Dresden) DL@: Reasoning on Knowledge Graphs IJCAI 2018 5 / 6

Complexities

Theorem Combined complexity of satisfiability for attributed Knowledge Bases non-attributed attributed DL ground restricted unrestricted P-complete ELH@ P-complete P-complete1 Exp-complete Exp-complete ALCH@ Exp-complete Exp-complete 2Exp-complete N2Exp-complete SROIQ@ N2Exp-complete N2Exp-complete N2Exp-complete Grounding is exponential in the size of the Knowledge Base

Maximilian Marx (TU Dresden) DL@: Reasoning on Knowledge Graphs IJCAI 2018 5 / 6

Complexities

Theorem Combined complexity of satisfiability for attributed Knowledge Bases non-attributed attributed DL ground restricted unrestricted P-complete ELH@ P-complete P-complete1 Exp-complete Exp-complete ALCH@ Exp-complete Exp-complete 2Exp-complete N2Exp-complete SROIQ@ N2Exp-complete N2Exp-complete N2Exp-complete Grounding is exponential in the size of the Knowledge Base Three syntactic restrictions ensure polynomial groundings

1: Except when violating one (specific) condition, where we show PSpace-hardness

Maximilian Marx (TU Dresden) DL@: Reasoning on Knowledge Graphs IJCAI 2018 5 / 6

Conclusion & Outlook

Conclusion: First-class support for annotations in Knowledge Bases Reasoning via translation into standard DLs Existing tools can be used for attributed reasoning Outlook: Further Extensions push DLs even closer to rule languages Focus on adapting rules for Knowledge Graphs? MARPL [Krötzsch, M., Thost IJCAI’17] is “Attributed Datalog” “Attributed Existential Rules”?

Maximilian Marx (TU Dresden) DL@: Reasoning on Knowledge Graphs IJCAI 2018 6 / 6