[PPT] - News on Temporal Conjunctive Queries Veronika Thost TU Dresden PowerPoint Presentation

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News on Temporal Conjunctive Queries

Veronika Thost TU Dresden WSP@ISWC October 22, 2017

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Ontology-Based Data Access

Use Case: Finding Participants for Clinical Trial Example1

Previously infected with VZV or previously vaccinated with VZV vaccine
No Allergy to VZV vaccine

1https://clinicaltrials.gov/ct2/show/NCT01953900 2 / 8

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Ontology-Based Data Access

PID Name 1 Ann 2 Bob 3 Chris PID Finding Date 1 Chickenpox 08/2017 2 VZV-Infection 01/2010 3 VZV-Infection 11/2011 PID AllergyTest Date 1 neg 07/2017 2 pos 09/2017 3 neg 06/1970 Patient Test Finding Patients infected with VZV?

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Ontology-Based Data Access

PID Name 1 Ann 2 Bob 3 Chris PID Finding Date 1 Chickenpox 08/2017 2 VZV-Infection 01/2010 3 VZV-Infection 11/2011 PID AllergyTest Date 1 neg 07/2017 2 pos 09/2017 3 neg 06/1970 Patient Test Finding Patients infected with VZV? SELECT ID FROM Pat WHERE Pat.PID=Find.PID & Find.TYPE=VZVInfect

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Ontology-Based Data Access

PID Name 1 Ann 2 Bob 3 Chris PID Finding Date 1 Chickenpox 08/2017 2 VZV-Infection 01/2010 3 VZV-Infection 11/2011 PID AllergyTest Date 1 neg 07/2017 2 pos 09/2017 3 neg 06/1970 Patient Test Finding Patients infected with VZV? Patient VZV Virus Chickenpox VZVInfection HasFinding Allergy ∃AllergyTo

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Ontology-Based Data Access

PID Name 1 Ann 2 Bob 3 Chris PID Finding Date 1 Chickenpox 08/2017 2 VZV-Infection 01/2010 3 VZV-Infection 11/2011 PID AllergyTest Date 1 neg 07/2017 2 pos 09/2017 3 neg 06/1970 Patient Test Finding Patients infected with VZV? Patient VZV Virus Chickenpox VZVInfection HasFinding Allergy ∃AllergyTo

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Ontology-Based Data Access

PID Name 1 Ann 2 Bob 3 Chris PID Finding Date 1 Chickenpox 08/2017 2 VZV-Infection 01/2010 3 VZV-Infection 11/2011 PID AllergyTest Date 1 neg 07/2017 2 pos 09/2017 3 neg 06/1970 Patient Test Finding

AllergyTest = pos

Patients infected with VZV? Patient VZV Virus Chickenpox VZVInfection HasFinding Allergy ∃AllergyTo

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Ontology-Based Data Access

PID Name 1 Ann 2 Bob 3 Chris PID Finding Date 1 Chickenpox 08/2017 2 VZV-Infection 01/2010 3 VZV-Infection 11/2011 PID AllergyTest Date 1 neg 07/2017 2 pos 09/2017 3 neg 06/1970 Patient Test Finding Patients infected with VZV? Patient VZV Virus Chickenpox VZVInfection HasFinding Allergy ∃AllergyTo Patient(ann) ¬∃AllergyTo(ann) HasFinding(ann, f1) Chickenpox(f1) Patient(bob)

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Ontology-Based Data Access

PID Name 1 Ann 2 Bob 3 Chris PID Finding Date 1 Chickenpox 08/2017 2 VZV-Infection 01/2010 3 VZV-Infection 11/2011 PID AllergyTest Date 1 neg 07/2017 2 pos 09/2017 3 neg 06/1970 Patient Test Finding Patients infected with VZV? Answer: x Patient(x) ∧ ∃y.HasFinding(x, y) ∧ VZVInfection(y) Patient VZV Virus Chickenpox VZVInfection HasFinding Allergy ∃AllergyTo Patient(ann) ¬∃AllergyTo(ann) HasFinding(ann, f1) Chickenpox(f1) Patient(bob)

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Ontology-Based Data Access

Patient Test Finding Patients infected with VZV? Answer: x Patient(x) ∧ ∃y.HasFinding(x, y) ∧ VZVInfection(y) Patient ∀x.VZV(x) → Virus(x) ∀x.Chickenpox(x) → VZVInfection(x) HasFinding Allergy ∃AllergyTo Patient(ann) ¬∃AllergyTo(ann) HasFinding(ann, f1) Chickenpox(f1) Patient(bob)

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Ontology-Based Data Access

Patient Test Finding Patients infected with VZV? Answer: x Patient(x) ∧ ∃y.HasFinding(x, y) ∧ VZVInfection(y) Patient ∀x.VZV(x) → Virus(x) ∀x.Chickenpox(x) → VZVInfection(x) ∀xy.HasFinding(x, y) ∧ Allergy(y) → ∃AllergyTo(x) Patient(ann) ¬∃AllergyTo(ann) HasFinding(ann, f1) Chickenpox(f1) Patient(bob)

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Ontology-Based Data Access

Patient Test Finding Patients infected with VZV? Answer: x = ann Patient(x) ∧ ∃y.HasFinding(x, y) ∧ VZVInfection(y) Patient ∀x.VZV(x) → Virus(x) ∀x.Chickenpox(x) → VZVInfection(x) ∀xy.HasFinding(x, y) ∧ Allergy(y) → ∃AllergyTo(x) Patient(ann) ¬∃AllergyTo(ann) HasFinding(ann, f1) Chickenpox(f1) Patient(bob)

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Ontology-Based Data Access: Temporal Queries

Patient Test Finding Patients infected with VZV previously, not allergic to VZV vaccine (now)? Patient ∀x.VZV(x) → Virus(x) ∀x.Chickenpox(x) → VZVInfection(x) ∀xy.HasFinding(x, y) ∧ Allergy(y) → ∃AllergyTo(x) Patient(ann) ¬∃AllergyTo(ann) HasFinding(ann, f1) Chickenpox(f1) Patient(bob)

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Ontology-Based Data Access: Temporal Queries

Patient Test Finding Patients infected with VZV previously, not allergic to VZV vaccine (now)? Patient ∀x.VZV(x) → Virus(x) ∀x.Chickenpox(x) → VZVInfection(x) ∀xy.HasFinding(x, y) ∧ Allergy(y) → ∃AllergyTo(x) Patient(ann) ¬∃AllergyTo(ann) HasFinding(ann, f1) Chickenpox(f1) Patient(bob) 07/17 08/17 09/17

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Ontology-Based Data Access: Temporal Queries

Patient Test Finding Patients infected with VZV previously, not allergic to VZV vaccine (now)? Patient(x) ∧ P∃y.HasFinding(x, y) ∧ VZVInfection(x) Patient ∀x.VZV(x) → Virus(x) ∀x.Chickenpox(x) → VZVInfection(x) ∀xy.HasFinding(x, y) ∧ Allergy(y) → ∃AllergyTo(x) Patient(ann) ¬∃AllergyTo(ann) HasFinding(ann, f1) Chickenpox(f1) Patient(bob) 07/17 08/17 09/17

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Ontology-Based Data Access: Temporal Queries

Patient Test Finding Patients infected with VZV previously, not allergic to VZV vaccine (now)? Patient(x) ∧ P∃y.HasFinding(x, y) ∧ VZVInfection(x) ∧ ¬∃y.AllergyTo(x, y) ∧ VZVVaccine(y) Patient ∀x.VZV(x) → Virus(x) ∀x.Chickenpox(x) → VZVInfection(x) ∀xy.HasFinding(x, y) ∧ Allergy(y) → ∃AllergyTo(x) Patient(ann) ¬∃AllergyTo(ann) HasFinding(ann, f1) Chickenpox(f1) Patient(bob) 07/17 08/17 09/17

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Ontology-Based Data Access: Temporal Queries

Patient Test Finding Patients infected with VZV previously, not allergic to VZV vaccine (now)? Patient(x) ∧ P∃y.HasFinding(x, y) ∧ VZVInfection(x) ∧ ¬∃y.AllergyTo(x, y) ∧ VZVVaccine(y) Patient ∀x.VZV(x) → Virus(x) ∀x.Chickenpox(x) → VZVInfection(x) ∀xy.HasFinding(x, y) ∧ Allergy(y) → ∃AllergyTo(x) Patient(ann) Patient(ann) Patient(ann) ¬∃AllergyTo(ann) HasFinding(ann, f1) Chickenpox(f1) Patient(bob) 07/17 08/17 09/17

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Ontology-Based Data Access: Temporal Queries

Patient Test Finding Patients infected with VZV previously, not allergic to VZV vaccine (now)? Patient(x) ∧ P∃y.HasFinding(x, y) ∧ VZVInfection(x) ∧ ¬∃y.AllergyTo(x, y) ∧ VZVVaccine(y) Patient ∀x.VZV(x) → Virus(x) ∀x.Chickenpox(x) → VZVInfection(x) ∀xy.HasFinding(x, y) ∧ Allergy(y) → ∃AllergyTo(x) Patient(ann) Patient(ann) Patient(ann) ¬∃AllergyTo(ann) HasFinding(ann, f1) ¬∃AllergyTo(ann) Chickenpox(f1) Patient(bob) 07/17 08/17 09/17

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Ontology-Based Data Access: Temporal Queries

with Rigid Symbols

Patient Test Finding Patients infected with VZV previously, not allergic to VZV vaccine (now)? Patient(x) ∧ P∃y.HasFinding(x, y) ∧ VZVInfection(x) ∧ ¬∃y.AllergyTo(x, y) ∧ VZVVaccine(y) Patient ∀x.VZV(x) → Virus(x) ∀x.Chickenpox(x) → VZVInfection(x) ∀xy.HasFinding(x, y) ∧ Allergy(y) → ∃AllergyTo(x) Patient(ann) Patient(ann) Patient(ann) ¬∃AllergyTo(ann) HasFinding(ann, f1) ¬∃AllergyTo(ann) Chickenpox(f1) Patient(bob) 07/17 08/17 09/17

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Ontology-Based Data Access: Temporal Queries

Temporal conjunctive queries: conjunctive queries (CQs) + LTL

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Ontology-Based Data Access: Temporal Queries

Temporal conjunctive queries: conjunctive queries (CQs) + LTL

TCQ q1, q2 := CQ q | ¬q1 (not) | q1 ∧ q2 (and) | q1 ∨ q2 (or) |

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Ontology-Based Data Access: Temporal Queries

Temporal conjunctive queries: conjunctive queries (CQs) + LTL

TCQ q1, q2 := CQ q | ¬q1 (not) | q1 ∧ q2 (and) | q1 ∨ q2 (or) | F q1 (next) | Pq1 (previous) | q1 Pq1

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Ontology-Based Data Access: Temporal Queries

Temporal conjunctive queries: conjunctive queries (CQs) + LTL

TCQ q1, q2 := CQ q | ¬q1 (not) | q1 ∧ q2 (and) | q1 ∨ q2 (or) | F q1 (next) | Pq1 (previous) | q1 U q2 (until) | q1 S q2 (since) q1 Pq1 q1 S q2 q2 q1

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Ontology-Based Data Access: Temporal Queries

Temporal conjunctive queries: conjunctive queries (CQs) + LTL

TCQ q1, q2 := CQ q | ¬q1 (not) | q1 ∧ q2 (and) | q1 ∨ q2 (or) | F q1 (next) | Pq1 (previous) | q1 U q2 (until) | q1 S q2 (since) q1 Pq1 q1 S q2 q2 q1 → Pq2 := true S q2 (some time in the past)

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Ontology-Based Data Access: Temporal Queries

Temporal conjunctive queries: conjunctive queries (CQs) + LTL

TCQ q1, q2 := CQ q | ¬q1 (not) | q1 ∧ q2 (and) | q1 ∨ q2 (or) | F q1 (next) | Pq1 (previous) | q1 U q2 (until) | q1 S q2 (since) q1 Pq1 q1 S q2 q2 q1 → Pq2 := true S q2 (some time in the past) Semantics: sequences of DL interpretations I = (∆, Ii)i∈N

Example

I, 3 | = PPatient(ann) iff I2 | = Patient(ann)

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Ontology-Based Data Access: Temporal Queries

Temporal conjunctive queries: conjunctive queries (CQs) + LTL
Ontology: lightweight description logics (DLs)
Temporal data: sequence of fact bases

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Ontology-Based Data Access: Temporal Queries

Temporal conjunctive queries: conjunctive queries (CQs) + LTL
Ontology: lightweight description logics (DLs)
Temporal data: sequence of fact bases

I

Problem: Temporal query entailment Results: Computational complexity Application: Choose languages according to available resources (time and memory)

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Ontology-Based Data Access: Temporal Queries

Temporal conjunctive queries: conjunctive queries (CQs) + LTL
Ontology: lightweight description logics (DLs)
Temporal data: sequence of fact bases

I II

Problem: Temporal query entailment Temporal query answering Results: Computational complexity Rewritability Application: Choose languages according Hints for implementation to available resources (use existing tools) (time and memory)

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Ontology-Based Data Access: Temporal Queries

Temporal conjunctive queries: conjunctive queries (CQs) + LTL
Ontology: lightweight description logics (DLs)
Temporal data: sequence of fact bases

I II

Problem: Temporal query entailment Temporal query answering Results: Computational complexity Rewritability Application: Choose languages according Hints for implementation to available resources (use existing tools) (time and memory)

TCQ q + Ontology O rewrite Query q′ Rewritability: Answers to q w.r.t. O, (D)0≤i≤n = Answers to q′ over (D)0≤i≤n

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Ontology-Based Data Access: Temporal Queries

I Temporal Query Entailment

Given: Boolean TCQ q, O, (Di)0≤i≤n Problem: O, (Di)0≤i≤n, n | = q

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Ontology-Based Data Access: Temporal Queries

I Temporal Query Entailment

Given: Boolean TCQ q, O, (Di)0≤i≤n Problem: O, (Di)0≤i≤n, n | = q

Combined Complexity Data Complexity

Rigid Symbols none classes all none classes all DL-Lite[ |H]

[core|horn]

≥PSpace ? ? ? ? ? EL ≥PSpace ? ? ≥P ? ? DL-Lite[krom|bool] ≥PSpace ? ? ≥co-NP ? ? DL-LiteH

[krom|bool]

≥2-ExpTime ? ? ≥co-NP ? ? ALCHQ1 ExpTime co-NExpTime 2-ExpTime co-NP co-NP ≤ExpTime ALCHQ1 ≥2-ExpTime co-NExpTime co-NExpTime co-NP co-NP ≤ExpTime

1[Baader et al., JWS’15] 5 / 8

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Ontology-Based Data Access: Temporal Queries

I Temporal Query Entailment

Given: Boolean TCQ q, O, (Di)0≤i≤n Problem: O, (Di)0≤i≤n, n | = q

PSpace?

Combined Complexity Data Complexity

Rigid Symbols none classes all none classes all DL-Lite[ |H]

[core|horn]

≥PSpace ? ? ? ? ? EL ≥PSpace ? ? ≥P ? ? DL-Lite[krom|bool] ≥PSpace ? ≥co-NP ? ? DL-LiteH

[krom|bool]

≥2-ExpTime ? ? ≥co-NP ? ? ALCHQ1 ExpTime co-NExpTime 2-ExpTime co-NP co-NP ≤ExpTime ALCHQ1 ≥2-ExpTime co-NExpTime co-NExpTime co-NP co-NP ≤ExpTime

1[Baader et al., JWS’15] 5 / 8

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Ontology-Based Data Access: Temporal Queries

I Temporal Query Entailment

Given: Boolean TCQ q, O, (Di)0≤i≤n Problem: O, (Di)0≤i≤n, n | = q

PSpace? FO-rewritable?

Combined Complexity Data Complexity

Rigid Symbols none classes all none classes all DL-Lite[ |H]

[core|horn]

≥PSpace ? ? ? ? EL ≥PSpace ? ? ≥P ? ? DL-Lite[krom|bool] ≥PSpace ? ≥co-NP ? ? DL-LiteH

[krom|bool]

≥2-ExpTime ? ? ≥co-NP ? ? ALCHQ1 ExpTime co-NExpTime 2-ExpTime co-NP co-NP ≤ExpTime ALCHQ1 ≥2-ExpTime co-NExpTime co-NExpTime co-NP co-NP ≤ExpTime

1[Baader et al., JWS’15] 5 / 8

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Ontology-Based Data Access: Temporal Queries

I Temporal Query Entailment

Given: Boolean TCQ q, O, (Di)0≤i≤n Problem: O, (Di)0≤i≤n, n | = q

PSpace? FO-rewritable? Tractable?

Combined Complexity Data Complexity

Rigid Symbols none classes all none classes all DL-Lite[ |H]

[core|horn]

≥PSpace ? ? ? ? EL ≥PSpace ? ? ≥P ? DL-Lite[krom|bool] ≥PSpace ? ≥co-NP ? ? DL-LiteH

[krom|bool]

≥2-ExpTime ? ? ≥co-NP ? ? ALCHQ1 ExpTime co-NExpTime 2-ExpTime co-NP co-NP ≤ExpTime ALCHQ1 ≥2-ExpTime co-NExpTime co-NExpTime co-NP co-NP ≤ExpTime

1[Baader et al., JWS’15] 5 / 8

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Ontology-Based Data Access: Temporal Queries

I Temporal Query Entailment

Given: Boolean TCQ q, O, (Di)0≤i≤n Problem: O, (Di)0≤i≤n, n | = q

PSpace? FO-rewritable? Tractable? co-NP?

Combined Complexity Data Complexity

Rigid Symbols none classes all none classes all DL-Lite[ |H]

[core|horn]

≥PSpace ? ? ? ? EL ≥PSpace ? ? ≥P ? DL-Lite[krom|bool] ≥PSpace ? ≥co-NP ? ? DL-LiteH

[krom|bool]

≥2-ExpTime ? ? ≥co-NP ? ? ALCHQ1 ExpTime co-NExpTime 2-ExpTime co-NP co-NP ≤ExpTime ALCHQ1 ≥2-ExpTime co-NExpTime co-NExpTime co-NP co-NP ≤ExpTime

1[Baader et al., JWS’15] 5 / 8

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Ontology-Based Data Access: Temporal Queries

I Temporal Query Entailment

Given: Boolean TCQ q, O, (Di)0≤i≤n Problem: O, (Di)0≤i≤n, n | = q

PSpace? FO-rewritable? Tractable? co-NP?

Combined Complexity Data Complexity

Rigid Symbols none classes all none classes all DL-Lite[ |H]

[core|horn]

PSpace PSpace PSpace ? ? EL PSpace PSpace ? ≥P ? DL-Lite[krom|bool] ≥PSpace ? ≥co-NP ? ? DL-LiteH

[krom|bool]

≥2-ExpTime ? ? ≥co-NP ? ? ALCHQ1 ExpTime co-NExpTime 2-ExpTime co-NP co-NP ≤ExpTime ALCHQ1 ≥2-ExpTime co-NExpTime co-NExpTime co-NP co-NP ≤ExpTime

1[Baader et al., JWS’15] 5 / 8

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Ontology-Based Data Access: Temporal Queries

I Temporal Query Entailment

Given: Boolean TCQ q, O, (Di)0≤i≤n Problem: O, (Di)0≤i≤n, n | = q

PSpace? FO-rewritable? Tractable? co-NP?

Combined Complexity Data Complexity

Rigid Symbols none classes all none classes all DL-Lite[ |H]

[core|horn]

PSpace PSpace PSpace ? ? EL PSpace PSpace co-NExpTime ≥P ? DL-Lite[krom|bool] ExpTime co-NExpTime 2-ExpTime ≥co-NP ? ? DL-LiteH

[krom|bool]

2-ExpTime 2-ExpTime 2-ExpTime ≥co-NP ? ? ALCHQ1 ExpTime co-NExpTime 2-ExpTime co-NP co-NP ≤ExpTime ALCHQ1 ≥2-ExpTime co-NExpTime co-NExpTime co-NP co-NP ≤ExpTime

Strong impact of rigid symbols

1[Baader et al., JWS’15] 5 / 8

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Ontology-Based Data Access: Temporal Queries

I Temporal Query Entailment

Given: Boolean TCQ q, O, (Di)0≤i≤n Problem: O, (Di)0≤i≤n, n | = q

PSpace? Tractable? co-NP?

Combined Complexity Data Complexity

Rigid Symbols none classes all none classes all DL-Lite[ |H]

[core|horn]

PSpace PSpace PSpace NC1 NC1 NC1 EL PSpace PSpace co-NExpTime ≥P ? DL-Lite[krom|bool] ExpTime co-NExpTime 2-ExpTime ≥co-NP ? ? DL-LiteH

[krom|bool]

2-ExpTime 2-ExpTime 2-ExpTime ≥co-NP ? ? ALCHQ1 ExpTime co-NExpTime 2-ExpTime co-NP co-NP ≤ExpTime ALCHQ1 ≥2-ExpTime co-NExpTime co-NExpTime co-NP co-NP ≤ExpTime

Strong impact of rigid symbols
Horn DL-Lite: rigid symbols not critical, but no FO-rewritability

→ NC1: efficient parallel algorithms exist

1[Baader et al., JWS’15] 5 / 8

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Ontology-Based Data Access: Temporal Queries

I Temporal Query Entailment

Given: Boolean TCQ q, O, (Di)0≤i≤n Problem: O, (Di)0≤i≤n, n | = q

PSpace? co-NP?

Combined Complexity Data Complexity

Rigid Symbols none classes all none classes all DL-Lite[ |H]

[core|horn]

PSpace PSpace PSpace NC1 NC1 NC1 EL PSpace PSpace co-NExpTime P co-NP co-NP DL-Lite[krom|bool] ExpTime co-NExpTime 2-ExpTime ≥co-NP ? ? DL-LiteH

[krom|bool]

2-ExpTime 2-ExpTime 2-ExpTime ≥co-NP ? ? ALCHQ1 ExpTime co-NExpTime 2-ExpTime co-NP co-NP ≤ExpTime ALCHQ1 ≥2-ExpTime co-NExpTime co-NExpTime co-NP co-NP ≤ExpTime

Strong impact of rigid symbols
Horn DL-Lite: rigid symbols not critical, but no FO-rewritability

→ NC1: efficient parallel algorithms exist

1[Baader et al., JWS’15] 5 / 8

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Ontology-Based Data Access: Temporal Queries

I Temporal Query Entailment

Given: Boolean TCQ q, O, (Di)0≤i≤n Problem: O, (Di)0≤i≤n, n | = q

PSpace? co-NP?

Combined Complexity Data Complexity

Rigid Symbols none classes all none classes all DL-Lite[ |H]

[core|horn]

PSpace PSpace PSpace NC1 NC1 NC1 EL PSpace PSpace co-NExpTime P co-NP co-NP DL-Lite[krom|bool] ExpTime co-NExpTime 2-ExpTime co-NP co-NP co-NP DL-LiteH

[krom|bool]

2-ExpTime 2-ExpTime 2-ExpTime co-NP co-NP co-NP ALCHQ1 ExpTime co-NExpTime 2-ExpTime co-NP co-NP ≤ExpTime ALCHQ1 ≥2-ExpTime co-NExpTime co-NExpTime co-NP co-NP ≤ExpTime

Strong impact of rigid symbols
Horn DL-Lite: rigid symbols not critical, but no FO-rewritability

→ NC1: efficient parallel algorithms exist

Other DL-Lite variants comparable to very expressive DLs
Data complexity: temporal features for free!

1[Baader et al., JWS’15] 5 / 8

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Ontology-Based Data Access: Temporal Queries

II Temporal Query Answering

Given: TCQs, DL-Litehorn, SQL Problem: Is TCQ answering w.r.t. ontologies in DL-Litehorn rewritable to SQL?

TCQ q + Ontology O rewrite SQL query q′

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Ontology-Based Data Access: Temporal Queries

II Temporal Query Answering

Given: TCQs, DL-Litehorn, SQL Problem: Is TCQ answering w.r.t. ontologies in DL-Litehorn rewritable to SQL?

TCQ q + Ontology O rewrite SQL query q′

Solution: Holds for positive TCQs (conjunctive queries + LTL w/o negation)

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Ontology-Based Data Access: Temporal Queries

II Temporal Query Answering

Given: TCQs, DL-Litehorn, SQL Problem: Is TCQ answering w.r.t. ontologies in DL-Litehorn rewritable to SQL?

TCQ q + Ontology O rewrite SQL query q′

Solution: Holds for positive TCQs (conjunctive queries + LTL w/o negation)

Generic rewritability result

For positive temporal QL queries (QL queries + LTL w/o negation) and lightweight logics L if they satisfy certain conditions.

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Ontology-Based Data Access: Temporal Queries

II Temporal Query Answering

Given: TCQs, DL-Litehorn, SQL Problem: Is TCQ answering w.r.t. ontologies in DL-Litehorn rewritable to SQL?

Temporal QL query q + Ontology O in L rewrite Temporal QL’ query q′

Solution: Holds for positive TCQs (conjunctive queries + LTL w/o negation)

Generic rewritability result

For positive temporal QL queries (QL queries + LTL w/o negation) and lightweight logics L if they satisfy certain conditions.

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Ontology-Based Data Access: Temporal Queries

II Temporal Query Answering

Given: TCQs, DL-Litehorn, SQL Problem: Is TCQ answering w.r.t. ontologies in DL-Litehorn rewritable to SQL?

Temporal QL query q + Ontology O in L rewrite Temporal QL’ query q′

Solution: Holds for positive TCQs (conjunctive queries + LTL w/o negation)

Generic rewritability result

For positive temporal QL queries (QL queries + LTL w/o negation) and lightweight logics L if they satisfy certain conditions. Many formalisms satisfy our conditions!

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Ontology-Based Data Access: Temporal Queries

II Temporal Query Answering

L QL QL′ EL++ subs. subs. DL-LiteR CQ UCQ ELHdr

⊥

CQ FO= DL-LiteN

horn

CQ FO= DL-LiteR UCQ PEQ DL-Lite CQ UCQ ELHI¬ CQ Datalog Horn-ALCHIQ CQ UCQ LDL+ IQ IQ SROEL(⊓, ×) IQ IQ Datalog± family CQ UCQ

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Summary & Outlook

Temporal query answering w.r.t. ontologies in lightweight logics
Focus on description logics
Complexity and rewritability results [Borgwardt et al., JWS’15, IJCAI’15, GCAI’15],

[T., WSP’17]

Others have also looked at temporal ontologies

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SLIDE 48

Summary & Outlook

Temporal query answering w.r.t. ontologies in lightweight logics
Focus on description logics
Complexity and rewritability results [Borgwardt et al., JWS’15, IJCAI’15, GCAI’15],

[T., WSP’17]

Others have also looked at temporal ontologies
Tailor formalisms to applications
Study metric temporal operators [Baader et al., FroCoS’17]

Treatment ⊓ F

(¬Treatment)U[45,180]Reaction
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SLIDE 49

Summary & Outlook

Temporal query answering w.r.t. ontologies in lightweight logics
Focus on description logics
Complexity and rewritability results [Borgwardt et al., JWS’15, IJCAI’15, GCAI’15],

[T., WSP’17]

Others have also looked at temporal ontologies
Tailor formalisms to applications
Study metric temporal operators [Baader et al., FroCoS’17]

Treatment ⊓ F

(¬Treatment)U[45,180]Reaction
Real stream reasoning?
What kind of ontology languages are needed?
Why are ontologies rarely applied?

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SLIDE 50

Summary & Outlook

Temporal query answering w.r.t. ontologies in lightweight logics
Focus on description logics
Complexity and rewritability results [Borgwardt et al., JWS’15, IJCAI’15, GCAI’15],

[T., WSP’17]

Others have also looked at temporal ontologies
Tailor formalisms to applications
Study metric temporal operators [Baader et al., FroCoS’17]

Treatment ⊓ F

(¬Treatment)U[45,180]Reaction
Real stream reasoning?
What kind of ontology languages are needed?
Why are ontologies rarely applied?

Thank you!

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SLIDE 51

References

[Baader et al., JWS’15] F. Baader, S. Borgwardt, M. Lippmann:

Temporal Query Entailments in the Description Logic SHQ. Journal of Web Semantics, 2015.

[Borgwardt et al., GCAI’15] S. Borgwardt, T:

Temporal Query Answering in DL-Lite with Negation. GCAI’15.

[Borgwardt et al., IJCAI’15] S. Borgwardt, T:

Temporal Query Answering in the Description Logic EL. IJCAI’15.

[T, WSP’17] T.:

News on Temporal Conjunctive Queries. WSP’17, to appear.

[Borgwardt et al., JWS’15] S. Borgwardt, M. Lippmann, T:

Temporalizing Rewritable Query Languages over Knowledge Bases. Journal of Web Semantics, 2015.

[Baader et al., FroCoS’17] F. Baader, S. Borgwardt, P. Koopmann, A. Ozaki, T:

Metric Temporal Description Logics with Interval-Rigid Names. FroCoS’17, to appear

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