News on Temporal Conjunctive Queries
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1 News on Temporal Conjunctive Queries Veronika Thost TU Dresden October 22, 2017
2 Ontology-Based Data Access Use Case: Finding Participants for Clinical Trial Example 1 Previously infected with VZV or previously vaccinated with VZV vaccine No Allergy to VZV vaccine / 8
3 Ontology-Based Data Access Patients infected with VZV? PID Name 1 Ann 2 Bob 3 Chris Patient PID Finding Date 1 Chickenpox 08/ VZV-Infection 01/ VZV-Infection 11/2011 Finding PID AllergyTest Date 1 neg 07/ pos 09/ neg 06/1970 Test 3 / 8
4 Ontology-Based Data Access Patients infected with VZV? SELECT ID FROM Pat WHERE Pat.PID=Find.PID & Find.TYPE=VZVInfect PID Name 1 Ann 2 Bob 3 Chris Patient PID Finding Date 1 Chickenpox 08/ VZV-Infection 01/ VZV-Infection 11/2011 Finding PID AllergyTest Date 1 neg 07/ pos 09/ neg 06/1970 Test 3 / 8
5 Ontology-Based Data Access Patients infected with VZV? Patient VZV Virus Chickenpox VZVInfection HasFinding Allergy AllergyTo PID Name 1 Ann 2 Bob 3 Chris Patient PID Finding Date 1 Chickenpox 08/ VZV-Infection 01/ VZV-Infection 11/2011 Finding PID AllergyTest Date 1 neg 07/ pos 09/ neg 06/1970 Test 3 / 8
6 Ontology-Based Data Access Patients infected with VZV? Patient VZV Virus Chickenpox VZVInfection HasFinding Allergy AllergyTo PID Name 1 Ann 2 Bob 3 Chris Patient PID Finding Date 1 Chickenpox 08/ VZV-Infection 01/ VZV-Infection 11/2011 Finding PID AllergyTest Date 1 neg 07/ pos 09/ neg 06/1970 Test 3 / 8
7 Ontology-Based Data Access Patients infected with VZV? Patient VZV Virus Chickenpox VZVInfection HasFinding Allergy AllergyTo PID Name 1 Ann 2 Bob 3 Chris Patient PID Finding Date 1 Chickenpox 08/ VZV-Infection 01/ VZV-Infection 11/2011 Finding AllergyTest = pos PID AllergyTest Date 1 neg 07/ pos 09/ neg 06/1970 Test 3 / 8
8 Ontology-Based Data Access Patients infected with VZV? Patient VZV Virus Chickenpox VZVInfection HasFinding Allergy AllergyTo PID Name PID Finding Date PID AllergyTest Date Patient(ann) 1 Ann 1 Chickenpox 08/ neg 07/2017 AllergyTo(ann) 2 Bob 2 VZV-Infection HasFinding(ann, 01/2010 f1) 2 pos 09/ Chris 3 VZV-Infection Chickenpox(f1) 11/ Patient(bob) neg 06/1970 Patient Finding Test 3 / 8
9 Ontology-Based Data Access Patients infected with VZV? Patient(x) y.hasfinding(x, y) VZVInfection(y) Answer: x Patient VZV Virus Chickenpox VZVInfection HasFinding Allergy AllergyTo PID Name PID Finding Date PID AllergyTest Date Patient(ann) 1 Ann 1 Chickenpox 08/ neg 07/2017 AllergyTo(ann) 2 Bob 2 VZV-Infection HasFinding(ann, 01/2010 f1) 2 pos 09/ Chris 3 VZV-Infection Chickenpox(f1) 11/ Patient(bob) neg 06/1970 Patient Finding Test 3 / 8
10 Ontology-Based Data Access Patients infected with VZV? Patient(x) y.hasfinding(x, y) VZVInfection(y) Answer: x Patient x.vzv(x) Virus(x) x.chickenpox(x) VZVInfection(x) HasFinding Allergy AllergyTo Patient(ann) AllergyTo(ann) HasFinding(ann, f1) Chickenpox(f1) Patient Finding Test Patient(bob) 3 / 8
11 Ontology-Based Data Access Patients infected with VZV? Patient(x) y.hasfinding(x, y) VZVInfection(y) Answer: 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 Finding Test Patient(bob) 3 / 8
12 Ontology-Based Data Access Patients infected with VZV? Patient(x) y.hasfinding(x, y) VZVInfection(y) Answer: x = ann 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 Finding Test Patient(bob) 3 / 8
13 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 Finding Test Patient(bob) 3 / 8
14 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) 07/17 08/17 09/17 Patient(ann) AllergyTo(ann) HasFinding(ann, f1) Chickenpox(f1) Patient(bob) Patient Finding Test 3 / 8
15 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) 07/17 08/17 09/17 Patient(ann) AllergyTo(ann) HasFinding(ann, f1) Chickenpox(f1) Patient(bob) Patient Finding Test 3 / 8
16 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) 07/17 08/17 09/17 Patient(ann) AllergyTo(ann) HasFinding(ann, f1) Chickenpox(f1) Patient(bob) Patient Finding Test 3 / 8
17 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) 07/17 08/17 09/17 Patient(ann) Patient(ann) Patient(ann) AllergyTo(ann) HasFinding(ann, f1) Chickenpox(f1) Patient(bob) Patient Finding Test 3 / 8
18 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) 07/17 08/17 09/17 Patient(ann) Patient(ann) Patient(ann) AllergyTo(ann) HasFinding(ann, f1) AllergyTo(ann) Chickenpox(f1) Patient(bob) Patient Finding Test 3 / 8
19 with Rigid Symbols 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) 07/17 08/17 09/17 Patient(ann) Patient(ann) Patient(ann) AllergyTo(ann) HasFinding(ann, f1) AllergyTo(ann) Chickenpox(f1) Patient(bob) Patient Finding Test 3 / 8
20 Temporal conjunctive queries: conjunctive queries (CQs) + LTL 4 / 8
21 Temporal conjunctive queries: conjunctive queries (CQs) + LTL TCQ q 1, q 2 := CQ q q 1 (not) q 1 q 2 (and) q 1 q 2 (or) 4 / 8
22 Temporal conjunctive queries: conjunctive queries (CQs) + LTL TCQ q 1, q 2 := CQ q q 1 (not) q 1 q 2 (and) q 1 q 2 (or) F q 1 (next) P q 1 (previous) q 1 P q 1 4 / 8
23 Temporal conjunctive queries: conjunctive queries (CQs) + LTL TCQ q 1, q 2 := CQ q q 1 (not) q 1 q 2 (and) q 1 q 2 (or) F q 1 (next) P q 1 (previous) q 1 U q 2 (until) q 1 S q 2 (since) q 1 q q 1 2 P q 1 q 1 S q 2 4 / 8
24 Temporal conjunctive queries: conjunctive queries (CQs) + LTL TCQ q 1, q 2 := CQ q q 1 (not) q 1 q 2 (and) q 1 q 2 (or) F q 1 (next) P q 1 (previous) q 1 U q 2 (until) q 1 S q 2 (since) q 1 q q 1 2 P q 1 q 1 S q 2 P q 2 := true S q 2 (some time in the past) 4 / 8
25 Temporal conjunctive queries: conjunctive queries (CQs) + LTL TCQ q 1, q 2 := CQ q q 1 (not) q 1 q 2 (and) q 1 q 2 (or) F q 1 (next) P q 1 (previous) q 1 U q 2 (until) q 1 S q 2 (since) q 1 q q 1 2 P q 1 q 1 S q 2 P q 2 := true S q 2 (some time in the past) Semantics: sequences of DL interpretations I = (, I i) i N Example I, 3 = P Patient(ann) iff I 2 = Patient(ann) 4 / 8
26 Temporal conjunctive queries: conjunctive queries (CQs) + LTL Ontology: lightweight description logics (DLs) Temporal data: sequence of fact bases 4 / 8
27 Temporal conjunctive queries: conjunctive queries (CQs) + LTL Ontology: lightweight description logics (DLs) Temporal data: sequence of fact bases Problem: Results: Application: I Temporal query entailment Computational complexity Choose languages according to available resources (time and memory) 4 / 8
28 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) 4 / 8
29 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) + rewrite TCQ q Ontology O Query q Rewritability: Answers to q w.r.t. O, (D) 0 i n = Answers to q over (D) 0 i n 4 / 8
30 I Temporal Query Entailment Given: Boolean TCQ q, O, (D i) 0 i n Problem: O, (D i) 0 i n, n = q 5 / 8
31 I Temporal Query Entailment Given: Boolean TCQ q, O, (D i) 0 i n Problem: O, (D i) 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-Lite H [krom bool] 2-ExpTime?? co-np?? ALCHQ 1 ExpTime co-nexptime 2-ExpTime co-np co-np ExpTime ALCHQ 1 2-ExpTime co-nexptime co-nexptime co-np co-np ExpTime 1 [Baader et al., JWS 15] 5 / 8
32 I Temporal Query Entailment Given: Boolean TCQ q, O, (D i) 0 i n Problem: O, (D i) 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? PSpace? co-np?? DL-Lite H [krom bool] 2-ExpTime?? co-np?? ALCHQ 1 ExpTime co-nexptime 2-ExpTime co-np co-np ExpTime ALCHQ 1 2-ExpTime co-nexptime co-nexptime co-np co-np ExpTime 1 [Baader et al., JWS 15] 5 / 8
33 I Temporal Query Entailment Given: Boolean TCQ q, O, (D i) 0 i n Problem: O, (D i) 0 i n, n = q Combined Complexity Data Complexity Rigid Symbols none classes all none classes all DL-Lite [ H] [core horn] PSpace???? FO-rewritable? EL PSpace?? P?? DL-Lite [krom bool] PSpace? PSpace? co-np?? DL-Lite H [krom bool] 2-ExpTime?? co-np?? ALCHQ 1 ExpTime co-nexptime 2-ExpTime co-np co-np ExpTime ALCHQ 1 2-ExpTime co-nexptime co-nexptime co-np co-np ExpTime 1 [Baader et al., JWS 15] 5 / 8
34 I Temporal Query Entailment Given: Boolean TCQ q, O, (D i) 0 i n Problem: O, (D i) 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? PSpace? co-np?? DL-Lite H [krom bool] 2-ExpTime?? co-np?? FO-rewritable? Tractable? ALCHQ 1 ExpTime co-nexptime 2-ExpTime co-np co-np ExpTime ALCHQ 1 2-ExpTime co-nexptime co-nexptime co-np co-np ExpTime 1 [Baader et al., JWS 15] 5 / 8
35 I Temporal Query Entailment Given: Boolean TCQ q, O, (D i) 0 i n Problem: O, (D i) 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? PSpace? co-np?? FO-rewritable? Tractable? DL-Lite H [krom bool] 2-ExpTime?? co-np?? co-np? ALCHQ 1 ExpTime co-nexptime 2-ExpTime co-np co-np ExpTime ALCHQ 1 2-ExpTime co-nexptime co-nexptime co-np co-np ExpTime 1 [Baader et al., JWS 15] 5 / 8
36 I Temporal Query Entailment Given: Boolean TCQ q, O, (D i) 0 i n Problem: O, (D i) 0 i n, n = q 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? PSpace? co-np?? FO-rewritable? Tractable? DL-Lite H [krom bool] 2-ExpTime?? co-np?? co-np? ALCHQ 1 ExpTime co-nexptime 2-ExpTime co-np co-np ExpTime ALCHQ 1 2-ExpTime co-nexptime co-nexptime co-np co-np ExpTime 1 [Baader et al., JWS 15] 5 / 8
37 I Temporal Query Entailment Given: Boolean TCQ q, O, (D i) 0 i n Problem: O, (D i) 0 i n, n = q 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 PSpace? co-np?? FO-rewritable? Tractable? DL-Lite H [krom bool] 2-ExpTime 2-ExpTime 2-ExpTime co-np?? co-np? ALCHQ 1 ExpTime co-nexptime 2-ExpTime co-np co-np ExpTime ALCHQ 1 2-ExpTime co-nexptime co-nexptime co-np co-np ExpTime Strong impact of rigid symbols 1 [Baader et al., JWS 15] 5 / 8
38 I Temporal Query Entailment Given: Boolean TCQ q, O, (D i) 0 i n Problem: O, (D i) 0 i n, n = q Combined Complexity Data Complexity Rigid Symbols none classes all none classes all DL-Lite [ H] [core horn] PSpace PSpace PSpace NC 1 NC 1 NC 1 EL PSpace PSpace co-nexptime P? Tractable? DL-Lite [krom bool] ExpTime co-nexptime 2-ExpTime PSpace? co-np?? DL-Lite H [krom bool] 2-ExpTime 2-ExpTime 2-ExpTime co-np?? co-np? ALCHQ 1 ExpTime co-nexptime 2-ExpTime co-np co-np ExpTime ALCHQ 1 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 NC 1 : efficient parallel algorithms exist 1 [Baader et al., JWS 15] 5 / 8
39 I Temporal Query Entailment Given: Boolean TCQ q, O, (D i) 0 i n Problem: O, (D i) 0 i n, n = q Combined Complexity Data Complexity Rigid Symbols none classes all none classes all DL-Lite [ H] [core horn] PSpace PSpace PSpace NC 1 NC 1 NC 1 EL PSpace PSpace co-nexptime P co-np co-np DL-Lite [krom bool] ExpTime co-nexptime 2-ExpTime PSpace? co-np?? DL-Lite H [krom bool] 2-ExpTime 2-ExpTime 2-ExpTime co-np?? co-np? ALCHQ 1 ExpTime co-nexptime 2-ExpTime co-np co-np ExpTime ALCHQ 1 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 NC 1 : efficient parallel algorithms exist 1 [Baader et al., JWS 15] 5 / 8
40 I Temporal Query Entailment Given: Boolean TCQ q, O, (D i) 0 i n Problem: O, (D i) 0 i n, n = q Combined Complexity Data Complexity Rigid Symbols none classes all none classes all DL-Lite [ H] [core horn] PSpace PSpace PSpace NC 1 NC 1 NC 1 EL PSpace PSpace co-nexptime P co-np co-np DL-Lite [krom bool] ExpTime co-nexptime 2-ExpTime PSpace? co-np co-np co-np DL-Lite H [krom bool] 2-ExpTime 2-ExpTime 2-ExpTime co-np co-np co-npco-np? ALCHQ 1 ExpTime co-nexptime 2-ExpTime co-np co-np ExpTime ALCHQ 1 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 NC 1 : 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
41 II Temporal Query Answering Given: TCQs, DL-Lite horn, SQL Problem: Is TCQ answering w.r.t. ontologies in DL-Lite horn rewritable to SQL? + rewrite TCQ q Ontology O SQL query q 6 / 8
42 II Temporal Query Answering Given: TCQs, DL-Lite horn, SQL Problem: Is TCQ answering w.r.t. ontologies in DL-Lite horn rewritable to SQL? + rewrite TCQ q Ontology O SQL query q Solution: Holds for positive TCQs (conjunctive queries + LTL w/o negation) 6 / 8
43 II Temporal Query Answering Given: TCQs, DL-Lite horn, SQL Problem: Is TCQ answering w.r.t. ontologies in DL-Lite horn rewritable to SQL? + rewrite TCQ q Ontology O 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. 6 / 8
44 II Temporal Query Answering Given: TCQs, DL-Lite horn, SQL Problem: Is TCQ answering w.r.t. ontologies in DL-Lite horn rewritable to SQL? + rewrite Temporal QL query q Ontology O in L 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. 6 / 8
45 II Temporal Query Answering Given: TCQs, DL-Lite horn, SQL Problem: Is TCQ answering w.r.t. ontologies in DL-Lite horn rewritable to SQL? + rewrite Temporal QL query q Ontology O in L 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! 6 / 8
46 II Temporal Query Answering L QL QL EL ++ subs. subs. DL-Lite R CQ UCQ ELH dr CQ FO = DL-Lite N horn CQ FO = DL-Lite R UCQ PEQ DL-Lite CQ UCQ ELHI CQ Datalog Horn-ALCHIQ CQ UCQ LDL + IQ IQ SROEL(, ) IQ IQ Datalog ± family CQ UCQ 7 / 8
47 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 8 / 8
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 ) 8 / 8
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? 8 / 8
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! 8 / 8
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, [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, [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 1 / 1
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