This document presents a survey of temporal extensions of description logics (DLs) conducted by Daniele Dell'Aglio, Fariz Darari and Davide Lanti. It begins with an overview and outline of the topics that will be covered, including a running example to model how to become a doctor. The paper then surveys existing solutions for extending DLs with temporal aspects, including state-change based DLs, temporal DLs with an internal approach, point-based temporal DLs and interval-based temporal DLs. It concludes with a discussion of current hot topics and future directions for research on temporal extensions of DLs.

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
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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
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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
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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
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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
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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
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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
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9. Classification of the DL temporal extensions
Daniele Dell’Aglio, Fariz Darari and Davide Lanti
A Survey of Temporal Extensions of DLs
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10. Classification of the DL temporal extensions
Daniele Dell’Aglio, Fariz Darari and Davide Lanti
A Survey of Temporal Extensions of DLs
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11. Classification of the DL temporal extensions
Daniele Dell’Aglio, Fariz Darari and Davide Lanti
A Survey of Temporal Extensions of DLs
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12. Classification of the DL temporal extensions
Daniele Dell’Aglio, Fariz Darari and Davide Lanti
A Survey of Temporal Extensions of DLs
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13. Classification of the DL temporal extensions
Daniele Dell’Aglio, Fariz Darari and Davide Lanti
A Survey of Temporal Extensions of DLs
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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
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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
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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
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17. C LASP [DL96]
Daniele Dell’Aglio, Fariz Darari and Davide Lanti
A Survey of Temporal Extensions of DLs
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18. C LASP [DL96]
Daniele Dell’Aglio, Fariz Darari and Davide Lanti
A Survey of Temporal Extensions of DLs
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19. C LASP [DL96]
Daniele Dell’Aglio, Fariz Darari and Davide Lanti
A Survey of Temporal Extensions of DLs
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20. C LASP [DL96]
Daniele Dell’Aglio, Fariz Darari and Davide Lanti
A Survey of Temporal Extensions of DLs
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21. C LASP [DL96]
Daniele Dell’Aglio, Fariz Darari and Davide Lanti
A Survey of Temporal Extensions of DLs
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22. C LASP [DL96]
Daniele Dell’Aglio, Fariz Darari and Davide Lanti
A Survey of Temporal Extensions of DLs
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23. C LASP [DL96]
Daniele Dell’Aglio, Fariz Darari and Davide Lanti
A Survey of Temporal Extensions of DLs
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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
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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
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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
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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
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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
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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
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31. T-R EX [WL92]
Daniele Dell’Aglio, Fariz Darari and Davide Lanti
A Survey of Temporal Extensions of DLs
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32. T-R EX [WL92]
Daniele Dell’Aglio, Fariz Darari and Davide Lanti
A Survey of Temporal Extensions of DLs
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33. T-R EX [WL92]
Daniele Dell’Aglio, Fariz Darari and Davide Lanti
A Survey of Temporal Extensions of DLs
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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