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- 1. A Survey of Temporal Extensions of DLs Research school: Foundations and Challenges of Change in Ontologies and Databases 2014 Free University of Bozen-Bolzano, Italy Group 6: Daniele Dell’Aglio DEIB – Politecnico di Milano daniele.dellaglio@polimi.it Fariz Darari ` KRDB – Universita di Bolzano fadirra@gmail.com Davide Lanti ` KRDB – Universita di Bolzano davide.lanti.sersante@gmail.com Mentor: Michael Zakharyaschev Birkbeck College Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 1 – 39
- 2. What we will see The paper: Alessandro Artale and Enrico Franconi. A survey of temporal extensions of description logics. Annals of Mathematics and Artiﬁcial Intelligence, 30(1-4):171-210, 2000. Outline: Overview Running Example A Survey on Existing Solutions Current Hot Topics, Future Directions Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 2 – 39
- 3. Outline Overview Running Example A Survey on Existing Solutions State-change based DLs Temporal DLs with internal approach Point-based temporal DLs Interval-based temporal DLs Current Hot Topics, Future Directions Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 3 – 39
- 4. Temporal extensions of DLs How can time be modelled? Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 4 – 39
- 5. Temporal extensions of DLs How can time be modelled? Point-based notion of time Interval-based notion of time Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 4 – 39
- 6. Temporal extensions of DLs How can time be modelled? Point-based notion of time Interval-based notion of time How can the temporal dimension be handled? Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 4 – 39
- 7. Temporal extensions of DLs How can time be modelled? Point-based notion of time Interval-based notion of time How can the temporal dimension be handled? Implicit notion of time: sequences of events through state-change representations Explicit notion of time: deﬁnition of temporal operators and new formulae Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 4 – 39
- 8. Temporal extensions of DLs How can time be modelled? Point-based notion of time Interval-based notion of time How can the temporal dimension be handled? Implicit notion of time: sequences of events through state-change representations Explicit notion of time: deﬁnition of temporal operators and new formulae Internal point of view: different states of an individual are modelled as different individual components External point of view: an individual has different states in different moments Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 4 – 39
- 9. Classiﬁcation of the DL temporal extensions Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 5 – 39
- 10. Classiﬁcation of the DL temporal extensions Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 5 – 39
- 11. Classiﬁcation of the DL temporal extensions Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 5 – 39
- 12. Classiﬁcation of the DL temporal extensions Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 5 – 39
- 13. Classiﬁcation of the DL temporal extensions Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 5 – 39
- 14. Outline Overview Running Example A Survey on Existing Solutions State-change based DLs Temporal DLs with internal approach Point-based temporal DLs Interval-based temporal DLs Current Hot Topics, Future Directions Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 6 – 39
- 15. Running example How to become a doctor: Be a PhD student for some years (3-4) Defend a thesis Become a doctor Let’s try to model it with different temporal logics! Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 7 – 39
- 16. Outline Overview Running Example A Survey on Existing Solutions State-change based DLs Temporal DLs with internal approach Point-based temporal DLs Interval-based temporal DLs Current Hot Topics, Future Directions Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 8 – 39
- 17. C LASP [DL96] Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 9 – 39
- 18. C LASP [DL96] Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 9 – 39
- 19. C LASP [DL96] Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 9 – 39
- 20. C LASP [DL96] Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 9 – 39
- 21. C LASP [DL96] Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 9 – 39
- 22. C LASP [DL96] Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 9 – 39
- 23. C LASP [DL96] Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 9 – 39
- 24. C LASP A system to reason about plans, proposed by Devambu and Litman (ﬁrst half of 90s) Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 10 – 39
- 25. C LASP A system to reason about plans, proposed by Devambu and Litman (ﬁrst half of 90s) Two formalisms The C LASSIC DL to deﬁne states, actions, plans and relation among them A set of operators to specify the plan expressions SEQUENCE, LOOP, TEST, OR, . . . The plan expression is converted in a ﬁnite automata Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 10 – 39
- 26. C LASP A system to reason about plans, proposed by Devambu and Litman (ﬁrst half of 90s) Two formalisms The C LASSIC DL to deﬁne states, actions, plans and relation among them A set of operators to specify the plan expressions SEQUENCE, LOOP, TEST, OR, . . . The plan expression is converted in a ﬁnite automata C LASP performs Plan subsumption Plan recognition: determines if a scenario belong to a given plan Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 10 – 39
- 27. C LASP considerations Actions are instantaneous The temporal expressivity of Clasp is implicit in the language Alternatives can be expressed through disjunctions (OR) Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 11 – 39
- 28. C LASP considerations Actions are instantaneous The temporal expressivity of Clasp is implicit in the language Alternatives can be expressed through disjunctions (OR) Explicit temporal constraints are not expressible The terminological representation of states: is not as expressive as the predicate calculus representation used in STRIPS avoids doing general theorem proving when computing state subsumption Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 11 – 39
- 29. Outline Overview Running Example A Survey on Existing Solutions State-change based DLs Temporal DLs with internal approach Point-based temporal DLs Interval-based temporal DLs Current Hot Topics, Future Directions Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 12 – 39
- 30. T-R EX [WL92] Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 13 – 39
- 31. T-R EX [WL92] Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 13 – 39
- 32. T-R EX [WL92] Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 13 – 39
- 33. T-R EX [WL92] Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 13 – 39
- 34. T-R EX A system to represent and reason about plans developed by Weida and Litman (90s) Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 14 – 39
- 35. T-R EX A system to represent and reason about plans developed by Weida and Litman (90s) Like C LASP, two different formalisms are used The K-R EP or the C LASSIC DLs to describe the actions A temporal constraint network to represent the plans Constraints deﬁned through the Allen’s relationships before, meets, after, ﬁnishes, . . . Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 14 – 39
- 36. T-R EX A system to represent and reason about plans developed by Weida and Litman (90s) Like C LASP, two different formalisms are used The K-R EP or the C LASSIC DLs to describe the actions A temporal constraint network to represent the plans Constraints deﬁned through the Allen’s relationships before, meets, after, ﬁnishes, . . . T-R EX performs the following reasoning tasks: subsumption plan recognition: the system determines if a set of observations are compatible with (i.e., could instantiate) the plan set plans are classiﬁed in possible, necessary and impossible Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 14 – 39
- 37. T-R EX considerations T-Rex conceptual model captures the actions States are not represented Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 15 – 39
- 38. T-R EX considerations T-Rex conceptual model captures the actions States are not represented T-Rex is an example of external notion of time with an internal approach It uses the Allen’s relationships to specify the constraints (explicit notion of time) Plans capture the time notion (internal approach) Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 15 – 39
- 39. T-R EX considerations T-Rex conceptual model captures the actions States are not represented T-Rex is an example of external notion of time with an internal approach It uses the Allen’s relationships to specify the constraints (explicit notion of time) Plans capture the time notion (internal approach) The plan subsumption is NP-Complete The crux is to determine the mappings between plans Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 15 – 39
- 40. Time as Concrete Domain [BH91] Idea: Abstract individuals are related to values in a concrete domain .. via features Tuples of concrete values identiﬁed by features can be constrained to belong to a predicate over the concrete domain Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 16 – 39
- 41. Example [AF00] . Poor-Manager = Manager ∀MONTHLY-BALANCE.∃(INCOME, EXPENSES). ≤ INCOME and EXPENSES are features from ∆I to the concrete domain R ≤ is a predicate deﬁned over the concrete domain ∆I R IN ≤ EXP M-B M-B IN ≤ EXP Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 17 – 39
- 42. ALC(D) [BH91] ALC extended with concrete predicates I I (∃(u1 , . . . , un ).P)I := {a ∈ ∆I | u1 (a), . . . , un (a) ∈ P D } u1 , . . . , un are compositions of features D is called concrete domain Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 18 – 39
- 43. Running Example Postdoc PHD-STATE : PhD-Student DOC-STATE : (Doctor ¬PhD-Student) ∃(PHD-STATE ◦ HAS-TIME, DOC-STATE ◦ HAS-TIME).meets ∆I Intervals H-T meets P-S D-S H-T Recall: “different states of an individual are modelled as different individuals” Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 19 – 39
- 44. Considerations ALC(D), ALCF (D) concept satisﬁability, subsumption, and ABox consistency PSPACE-complete .. under the assumption that satisﬁability in the concrete domain is in PSPACE ALCRP(D) Undecidable Decidability if avoiding the interaction of complex roles with existential and universal restrictions Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 20 – 39
- 45. Outline Overview Running Example A Survey on Existing Solutions State-change based DLs Temporal DLs with internal approach Point-based temporal DLs Interval-based temporal DLs Current Hot Topics, Future Directions Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 21 – 39
- 46. Combining Description Logics and Tense Operators: ALCT [Sch93] Combination of ALC with point-based modal temporal connectives 3P , 2P , cP , UP , UP Time part of the semantic structure AI ⊆ T × ∆I R I ⊆ T × ∆I × ∆I Recall: “an individual has different states at different moments” Temporal connectives can be applied only to concepts 3CtI := {a ∈ ∆I | ∃t . t ≤ t ∧ a ∈ CtI } Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 22 – 39
- 47. Running Example Every doctor has been a PhD student in the past Doctor 3P PhD-Student Every thesis defender is a PhD student that has been a PhD student in the past Thesis-Defender Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs PhD-Student 3P PhD-Student 23 – 39
- 48. Running Example Every doctor has been a PhD student in the past Doctor 3P PhD-Student Every thesis defender is a PhD student that has been a PhD student in the past Thesis-Defender Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs PhD-Student 3P PhD-Student 23 – 39
- 49. Running Example Every doctor has been a PhD student in the past Doctor 3P PhD-Student Every thesis defender is a PhD student that has been a PhD student in the past Thesis-Defender Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs PhD-Student 3P PhD-Student 23 – 39
- 50. Considerations ALCT Empty Abox Linear, unbounded and discrete time structure PSPACE-complete for statisﬁability checking Branching, unbounded and discrete time structure EXPTIME-hard Interval-based time structure Undecidable Open questions (still open?) Extending ALCT (N ) with past tense? Real numbers? Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 24 – 39
- 51. Outline Overview Running Example A Survey on Existing Solutions State-change based DLs Temporal DLs with internal approach Point-based temporal DLs Interval-based temporal DLs Current Hot Topics, Future Directions Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 25 – 39
- 52. Interval-based Temporal DLs Schmiedel’s Formalism Idea Examples The Undecidable Realm Idea Examples Towards Decidable Logic Idea Examples Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 26 – 39
- 53. Interval-based Temporal DLs: Characteristics Interval-based Explicit, eg: alltime, 3TE Follows the external approach, eg: C i, a for temporal concept assertions and R i, a, b for temporal role assertions Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 27 – 39
- 54. Schmiedel’s Formalism: Idea The ﬁrst of such an interval-based temporal DL (made in 1990) Underlying DL = F LEN R− (no on roles, and role conjunction) , ⊥, ¬, but with cardinality restrictions Temporal operators = at, alltime, sometime Subsumption is argued to be undecidable Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 28 – 39
- 55. Schmiedel’s Formalism: Examples Concept: PhD students during 1993 (at 1993 PhDStudent) Terminological Axiom: Doctors were PhD students Doctor (sometime(x)(metBy now x).(at x (PhDStudent))) Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 29 – 39
- 56. The Undecidable Realm: Idea Developed by Bettini Variable-free extension with existential and universal temporal quantiﬁcation Arbitrary relationships between more than two intervals can’t be represented Satisﬁability and subsumption are undecidable Starting from the DL ALCN Two concept constructors: 3TE.C and 2TE.C Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 30 – 39
- 57. The Undecidable Realm: Examples Concept: Persons who become a doctor sometime 3after.Doctor , eg: 1990, michael belongs to this, if 1992, michael belongs to Doctor Terminological Axiom: Doctors were PhD students Doctor 3(metBy).PhDStudent Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 31 – 39
- 58. Towards Decidable Logics: Idea Developed by Artale and Franconi Decidable: Expressivity is reduced, universal quantiﬁcation on temporal variables has been eliminated Underlying DL (most expressive): T L-ALCF Temporal variables are introduced by the temporal existential quantiﬁer 3, excluding the predeﬁned temporal var # Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 32 – 39
- 59. Towards Decidable Logics: Examples Terminological Axiom: Doctors were PhD students Doctor 3(x)(# metBy x).PhDStudent@x Terminological Axiom: PhD thesis defenders ﬁnish their PhDs PhDThesisDefender 3(x)(# ﬁnishes x).PhDStudent@x Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 33 – 39
- 60. Outline Overview Running Example A Survey on Existing Solutions State-change based DLs Temporal DLs with internal approach Point-based temporal DLs Interval-based temporal DLs Current Hot Topics, Future Directions Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 34 – 39
- 61. Hot Topics: Temporal DLs for OBDA OBDA over temporal data with validity time Ontologies capable of temporal conceptual modeling Developed TQL extending OWL 2 QL, still preserving FO rewritability Example: A fact with its validity time: givesBirth(diana, michael, 1970) A temporal axiom: 3p givesBirth Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs motherOf 35 – 39
- 62. Hot Topics: Stream Query Processing Query language for RDF streams Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 36 – 39
- 63. A Survey of Temporal Extensions of DLs Research school: Foundations and Challenges of Change in Ontologies and Databases 2014 Free University of Bozen-Bolzano, Italy Group 6: Daniele Dell’Aglio DEIB – Politecnico di Milano daniele.dellaglio@polimi.it Fariz Darari ` KRDB – Universita di Bolzano fadirra@gmail.com Davide Lanti ` KRDB – Universita di Bolzano davide.lanti.sersante@gmail.com Mentor: Michael Zakharyaschev Birkbeck College Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 37 – 39
- 64. [AF00] Alessandro Artale and Enrico Franconi. A survey of temporal extensions of description logics. Annals of Mathematics and Artiﬁcial Intelligence, 30(1-4):171–210, 2000. [BH91] Franz Baader and Philipp Hanschke. A scheme for integrating concrete domains into concept languages. In Proceedings of the 12th International Joint Conference on Artiﬁcial Intelligence - Volume 1, IJCAI’91, pages 452–457, San Francisco, CA, USA, 1991. Morgan Kaufmann Publishers Inc. [DL96] Premkumar T. Devanbu and Diane J. Litman. Taxonomic plan reasoning. Artif. Intell., 84(1-2):1–35, 1996. [Sch93] Klaus Schild. Combining terminological logics with tense logic. ˜ In Miguel Filgueiras and LuAs Damas, editors, Progress in Artiﬁcial Intelligence, volume 727 of Lecture Notes in Computer Science, pages 105–120. Springer Berlin Heidelberg, 1993. Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 38 – 39
- 65. [WL92] Robert A. Weida and Diane J. Litman. Terminological reasoning with constraint networks and an application to plan recognition. In Bernhard Nebel, Charles Rich, and William R. Swartout, editors, KR, pages 282–293. Morgan Kaufmann, 1992. Daniele Dell’Aglio, Fariz Darari and Davide Lanti A Survey of Temporal Extensions of DLs 39 – 39

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