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## DL-Lite and Interval Temporal Logics: a Marriage Proposal (extended version) (2014)

### Citations

2936 | Maintaining knowledge about temporal intervals - Allen - 1983 |

495 | Tractable reasoning and efficient query answering in description logics: The DL-Lite family
- Calvanese, Giacomo, et al.
- 2007
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Citation Context ... can assert membership of objects (constants) in concepts, or that a pair of objects is connected by a role. The name DL-Lite identifies a family of description logics, proposed for the first time in =-=[22, 23]-=- and characterized by a good computational behaviour combined with a relatively high expressive power. To describe the DL-Lite family, whose intended applications include capturing typical concept mod... |

210 | DL-Lite: Tractable description logics for ontologies
- Calvanese, Giacomo, et al.
- 2005
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Citation Context ... can assert membership of objects (constants) in concepts, or that a pair of objects is connected by a role. The name DL-Lite identifies a family of description logics, proposed for the first time in =-=[22, 23]-=- and characterized by a good computational behaviour combined with a relatively high expressive power. To describe the DL-Lite family, whose intended applications include capturing typical concept mod... |

200 | The DL-Lite family and relations
- Artale, Calvanese, et al.
- 2009
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Citation Context ... number restrictions and role inclusions are fully available). A comprehensive survey of the variety of the formalisms that belong to DL-Lite, their properties, and their applications can be found in =-=[3]-=-. Temporal extensions of DLs have been studied in [4, 6, 7, 9, 11, 12, 33] (see [5, 26, 29] for a detailed survey). In particular, in [8] logics of the family DL-Lite have been been combined with a va... |

190 |
Many-dimensional modal logics: Theory and applications.
- Gabbay, Kurucz, et al.
- 2003
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Citation Context ...ey of the variety of the formalisms that belong to DL-Lite, their properties, and their applications can be found in [3]. Temporal extensions of DLs have been studied in [4, 6, 7, 9, 11, 12, 33] (see =-=[5, 26, 29]-=- for a detailed survey). In particular, in [8] logics of the family DL-Lite have been been combined with a variety of point-based temporal logics, ranging from LTL with Future and Past to full LTL wit... |

157 | A propositional modal logic of time intervals.
- Halpern, Shoham
- 1991
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Citation Context .... As for the underlying temporal structure, in [8] all results are given for Z. In this paper, we study interval-based extensions of DL-Lite logics based on fragments of Halpern and Shoham’s logic HS =-=[28]-=-. We make the following assumptions: (i) we take Z as the temporal domain; (ii) we consider only HS fragments that can express the so-called length constraints; (iii) we distinguish between rigid role... |

98 | A temporal description logic for reasoning about actions and plans.
- Artale
- 1998
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Citation Context ...ailable). A comprehensive survey of the variety of the formalisms that belong to DL-Lite, their properties, and their applications can be found in [3]. Temporal extensions of DLs have been studied in =-=[4, 6, 7, 9, 11, 12, 33]-=- (see [5, 26, 29] for a detailed survey). In particular, in [8] logics of the family DL-Lite have been been combined with a variety of point-based temporal logics, ranging from LTL with Future and Pas... |

57 | Temporal description logics: A survey.”
- Lutz, Wolter, et al.
- 2008
(Show Context)
Citation Context ...ey of the variety of the formalisms that belong to DL-Lite, their properties, and their applications can be found in [3]. Temporal extensions of DLs have been studied in [4, 6, 7, 9, 11, 12, 33] (see =-=[5, 26, 29]-=- for a detailed survey). In particular, in [8] logics of the family DL-Lite have been been combined with a variety of point-based temporal logics, ranging from LTL with Future and Past to full LTL wit... |

56 | Temporal description logics
- Artale, Franconi
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Citation Context ...ey of the variety of the formalisms that belong to DL-Lite, their properties, and their applications can be found in [3]. Temporal extensions of DLs have been studied in [4, 6, 7, 9, 11, 12, 33] (see =-=[5, 26, 29]-=- for a detailed survey). In particular, in [8] logics of the family DL-Lite have been been combined with a variety of point-based temporal logics, ranging from LTL with Future and Past to full LTL wit... |

41 | LTL over description logic axioms
- Baader, Ghilardi, et al.
- 2012
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Citation Context ...ailable). A comprehensive survey of the variety of the formalisms that belong to DL-Lite, their properties, and their applications can be found in [3]. Temporal extensions of DLs have been studied in =-=[4, 6, 7, 9, 11, 12, 33]-=- (see [5, 26, 29] for a detailed survey). In particular, in [8] logics of the family DL-Lite have been been combined with a variety of point-based temporal logics, ranging from LTL with Future and Pas... |

35 | A Temporal Terminological Logic
- Schmiedel
(Show Context)
Citation Context ...ailable). A comprehensive survey of the variety of the formalisms that belong to DL-Lite, their properties, and their applications can be found in [3]. Temporal extensions of DLs have been studied in =-=[4, 6, 7, 9, 11, 12, 33]-=- (see [5, 26, 29] for a detailed survey). In particular, in [8] logics of the family DL-Lite have been been combined with a variety of point-based temporal logics, ranging from LTL with Future and Pas... |

20 |
D.: A description logic of change
- Artale, Lutz, et al.
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17 | Temporal description logic for ontology-based data access. In:
- Artale, Kontchakov, et al.
- 2013
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17 | G.: Decidable and Undecidable Fragments of Halpern and Shoham’s Interval Temporal Logic: Towards a Complete Classification
- Bresolin, Monica, et al.
- 2008
(Show Context)
Citation Context ...ily follows that THSDL-LiteHNbool is undecidable as well. However, a number of recent results show that various fragments of HS offer a good balance between expressiveness and decidability/complexity =-=[13, 14, 17, 19, 30, 31, 32]-=-, suggesting that we can weaken the temporal part, by considering decidable fragments ofHS, without sacrificing expressiveness. Even if we fix the underlying interval-based temporal languages, there a... |

16 | Temporalizing ontology-based data access. In: - Baader, Borgwardt, et al. - 2013 |

14 | Maximal decidable fragments of Halpern and Shoham’s modal logic of intervals
- Montanari, Puppis, et al.
- 2010
(Show Context)
Citation Context ...ily follows that THSDL-LiteHNbool is undecidable as well. However, a number of recent results show that various fragments of HS offer a good balance between expressiveness and decidability/complexity =-=[13, 14, 17, 19, 30, 31, 32]-=-, suggesting that we can weaken the temporal part, by considering decidable fragments ofHS, without sacrificing expressiveness. Even if we fix the underlying interval-based temporal languages, there a... |

11 | Metric Propositional Neighborhood Logics: Expressiveness, Decidability, and Undecidability
- Bresolin, Monica, et al.
- 2010
(Show Context)
Citation Context ...to express length constraints, the situation is slightly more complex. The most general way to deal with length constraints is to explicitly introduce a predicate, len∼k, with the following semantics =-=[18]-=-: M, [i, j] |= len∼k iff δ(i, j) ∼ k. where δ is a distance function δ : Z× Z→ N, defined as δ(i, j) = |i− j|, for each ∼∈ {<, ≤, =, ≥, >}1. As showed in [18, 20], the language of AA can be extended w... |

9 |
Time-dependent concepts: Representation and reasoning using temporal description logics
- Bettini
- 1997
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7 | A cookbook for temporal conceptual data modelling with description logics
- Artale, Kontchakov, et al.
- 2014
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Citation Context ...Lite, their properties, and their applications can be found in [3]. Temporal extensions of DLs have been studied in [4, 6, 7, 9, 11, 12, 33] (see [5, 26, 29] for a detailed survey). In particular, in =-=[8]-=- logics of the family DL-Lite have been been combined with a variety of point-based temporal logics, ranging from LTL with Future and Past to full LTL with Since 1 and Until (see, e.g., [27]). Differe... |

7 | G.: The dark side of Interval Temporal Logic: sharpening the undecidability border
- Bresolin, Monica, et al.
- 2011
(Show Context)
Citation Context ...ily follows that THSDL-LiteHNbool is undecidable as well. However, a number of recent results show that various fragments of HS offer a good balance between expressiveness and decidability/complexity =-=[13, 14, 17, 19, 30, 31, 32]-=-, suggesting that we can weaken the temporal part, by considering decidable fragments ofHS, without sacrificing expressiveness. Even if we fix the underlying interval-based temporal languages, there a... |

7 |
Tableau-based decision procedures for the logics of subinterval structures over dense orderings
- Bresolin, Goranko, et al.
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7 |
The ultimate undecidability result for the Halpern-Shoham logic
- Marcinkowski, Michaliszyn
- 2011
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6 |
Interval temporal logics over finite linear orders: the complete picture. In:
- Bresolin, Monica, et al.
- 2012
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Citation Context ...ned yet, but it is believed that the situation in the finite or discrete case should be similar. Out of these fragments, it has been possible to prove that exactly 62 are decidable in the finite case =-=[15]-=-, and 44 in the (strongly) discrete case (and in the case of Z) [16], all of which with complexities that range from NP-complete (in very simple cases) to NExpTime-complete, ExpSpace-complete, to non-... |

5 |
Interval temporal logics over strongly discrete linear orders: the complete picture. In:
- Bresolin, Monica, et al.
- 2012
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Citation Context ...rete case should be similar. Out of these fragments, it has been possible to prove that exactly 62 are decidable in the finite case [15], and 44 in the (strongly) discrete case (and in the case of Z) =-=[16]-=-, all of which with complexities that range from NP-complete (in very simple cases) to NExpTime-complete, ExpSpace-complete, to non-primitive recursive. The complete diagram that includes all decidabl... |

5 | Expressiveness of the interval logics of allen’s relations on the class of all linear orders: Complete classification
- Monica, Goranko, et al.
- 2011
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Citation Context ...to fix a class of linearly ordered sets right at the beginning. As a matter of fact, many interesting results have been found in the dense case or in the case of all linearly ordered sets (see, e.g., =-=[24]-=-). Second, we need to decide how to deal with ABox assertions. From [8] it seems clear that for useful applications the possibility of expressing that, for example, a certain individual has a given pr... |

4 |
What’s decidable about Halpern and Shoham’s interval logic? The maximal fragment ABBL
- Bresolin, Montanari, et al.
- 2011
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3 | Decidability of the interval temporal logic ABB over the natural numbers
- Montanari, Puppis, et al.
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1 |
Complete classification of the expressiveness of fragments of Halpern-Shoham logic over dense linear orders
- Aceto, Monica, et al.
- 2013
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Citation Context ...e call fragment F = X1X2 . . .Xn any subset of such modalities, displayed in alphabetical order. There are 212 such fragments. Some of these are expressively equivalent to each other; in [24] (resp., =-=[1]-=-) it is possible to find all possible inter-definability in the class of all linearly ordered sets (resp., all dense linearly ordered sets), giving rise to 1347 (resp., 966) expressively different fra... |

1 |
Optimal decision procedures for mpnl over finite structures, the natural numbers, and the integers
- Bresolin, Montanari, et al.
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Citation Context ...cate, len∼k, with the following semantics [18]: M, [i, j] |= len∼k iff δ(i, j) ∼ k. where δ is a distance function δ : Z× Z→ N, defined as δ(i, j) = |i− j|, for each ∼∈ {<, ≤, =, ≥, >}1. As showed in =-=[18, 20]-=-, the language of AA can be extended with explicit length constraints predicates when interpreted over N or Z without loosing the decidability of the fragment itself; its complexity, though, worsen fr... |

1 |
On Begins, Meets and Before
- Bresolin, Sala, et al.
- 2012
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Citation Context ...s a length constraint with a constant k, expressed in binary, will be exponentially longer than the constraint itself. To overcome this problem, we can use a more complicate logarithmic encoding (see =-=[21]-=-) that requires the use of both 〈A〉 and one among {〈B〉, 〈B〉, 〈E〉, 〈E〉}. In other cases, as showed in [18, 20] for the fragment AA, the language can be extended with length constraints without loosing ... |

1 | Crossing the undecidability border with extensions of propositional neighborhood logic over natural numbers
- Monica, Goranko, et al.
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Citation Context ...ready undecidable, that decidable fragments of it has been found only recently, and that even a very small first-order extension of a decidable fragment of HS has already been found to be undecidable =-=[25]-=-. The language of FO×HS contains predicates P0, P1, . . . of some given arity, variables x0, x1, . . ., and constants a0, a1, . . . A formula of FO×HS, generically denoted by f, g, . . ., is built fro... |