## A Temporal Description Logic for Reasoning about Actions and Plans (1998)

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Venue: | Journal of Artificial Intelligence Research |

Citations: | 87 - 18 self |

### BibTeX

@ARTICLE{Artale98atemporal,

author = {Alessandro Artale and Enrico Franconi},

title = {A Temporal Description Logic for Reasoning about Actions and Plans},

journal = {Journal of Artificial Intelligence Research},

year = {1998},

volume = {9},

pages = {463--506}

}

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### Abstract

A class of interval-based temporal languages for uniformly representing and reasoning about actions and plans is presented. Actions are represented by describing what is true while the action itself is occurring, and plans are constructed by temporally relating actions and world states. The temporal languages are members of the family of Description Logics, which are characterized by high expressivity combined with good computational properties. The subsumption problem for a class of temporal Description Logics is investigated and sound and complete decision procedures are given. The basic language TL-F is considered #rst: it is the composition of a temporal logic TL # able to express interval temporal networks # together with the non-temporal logic F # a Feature Description Logic. It is proven that subsumption in this language is an NP-complete problem. Then it is shown how to reason with the more expressive languages TLU-FU and TL-ALCF . The former adds disjunction both at...

### Citations

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Citation Context ..., actions and plans in a uniform way. The most common approaches to model actions are based on the notion of state change { e.g., the formal models based on the original situation calculus (McCarthy &=-=Hayes, 1969-=-; Sandewall & Shoham, 1994) or the Strips-like planning systems (Fikes & Nilsson, 1971; Lifschitz, 1987) { in which actions are generally considered instantaneous and de ned as functions from one stat... |

377 |
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Citation Context ...g an action to more elementary actions, decomposing 501sArtale & Franconi it in partially ordered steps (Artale &Franconi, 1995). This kind of reasoning is found in hierarchical planners like Nonlin (=-=Tate, 1977-=-), Sipe (Wilkins, 1988) and Forbin (Dean, Firby, & Miller, 1990). Acknowledgements This paper is a substantial extension and revision of (Artale & Franconi, 1994). The work was partially supported by ... |

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Citation Context ... is the minimal Description Logic including full negation and disjunction { i.e., propositional calculus, and it is a notational variant of the propositional modal logic K (m) (Halpern & Moses, 1985; =-=Schild, 1991-=-). The basic types of a Description Logic are concepts, roles, features, and individuals. A concept is a description gathering the common properties among a collection of individuals; from a logical p... |

234 | Action and Events in Interval Temporal Logic - Allen, Gerguson - 1994 |

228 | The complexity of concept languages
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(Show Context)
Citation Context ...tend Description Logics with an interval{based temporal logic. The temporal variant of the Description Logic is equipped with a model-theoretic semantics. The underlying Description Logic is FLENR , (=-=Donini et al., 1995-=-): it di ers from ALCF in that it does not contain the > and ? concepts, it does not have neither negation nor disjunction, and it has cardinality restrictions and conjunction over roles. The new temp... |

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Citation Context ...notion of state change { e.g., the formal models based on the original situation calculus (McCarthy &Hayes, 1969; Sandewall & Shoham, 1994) or the Strips-like planning systems (Fikes & Nilsson, 1971; =-=Lifschitz, 1987-=-) { in which actions are generally considered instantaneous and de ned as functions from one state to another by means of pre- and post-conditions. Here, an explicit notion of time is introduced in th... |

126 | A formal theory of plan recognition and its implementation
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Citation Context ...es can be organized in a subsumption-based taxonomy, which plays the role of an action/plan library to be used for the tasks known in the literature as plan retrieval and individual plan recognition (=-=Kautz, 1991-=-). A re nement of the plan recognition notion is proposed, by splitting it into the di erent tasks of plan description classi cation { involving a plan type { and speci c plan recognition with respect... |

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Citation Context ...the possibility ofrepresenting persistent properties in the language, this Section considers how to solve the frame problem, and in particular the famous example of the Yale Turkey Shooting Scenario (=-=Sandewall, 1994; All-=-en & Ferguson, 1994), formerly known as the Yale Shooting Problem. An inertia operator \= " is introduced here. Intuitively, =C is currently true if it was true at a preceding interval { sayi{and... |

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Citation Context ...pt may appear at most once as the left-hand side of an axiom, and no terminological cycles are allowed, i.e., no de ned concept may occur { neither directly nor indirectly { within its own de nition (=-=Nebel, 1991-=-). An interpretation I satis esA : =C if and only if A I =C I . As an example, consider the unary relation (i.e., a concept) denoting the class of happy fathers, de ned using the atomic predicates Man... |

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Citation Context ...with TL-F , a language being the composition of a temporal logic TL -- able to express interval temporal networks -- together with the non-temporal Description Logic F -- a Feature Description Logic (=-=Smolka, 1992-=-). It turns out that subsumption for TL-F is an NP-complete problem. Then, we show how to reason with more expressive languages: TLU-FU , which adds disjunction both at the temporal and non-temporal s... |

82 | TBox and ABox reasoning in expressive description logics - Giacomo, Lenzerini - 1996 |

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Citation Context ...age for our proposal. As for the formal apparatus, the formalism introduced by (Schmidt-Schau & Smolka, 1991) and further elaborated by (Donini, Hollunder, Lenzerini, Spaccamela, Nardi, & Nutt, 1992; =-=Donini et al., 1994-=-, 1995; Buchheit et al., 1993; De Giacomo & Lenzerini, 1995, 1996) is followed: in this way, Description Logics are considered as a structured fragment of predicate logic. ALC (Schmidt-Schau & Smolka,... |

77 | Exact and Approximate Reasoning about Temporal Relations - Beek, Cohen - 1990 |

71 | Reasoning with individuals in concept languages
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Citation Context ...tion Logics are their high expressivity combined with desirable computational properties { such as decidability, soundness and completeness of deduction procedures (Buchheit, Donini, & Schaerf, 1993; =-=Schaerf, 1994-=-; Donini, Lenzerini, Nardi, & Schaerf, 1994; Donini, Lenzerini, Nardi, & Nutt, 1995). The main purpose of this work is to investigate a class of decidable temporal Description Logics, and to provide c... |

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60 | Hierarchical Planning Involving Deadlines, Travel time and Resources - Dean, Firby, et al. - 1990 |

54 |
Temporal reasoning and planning
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(Show Context)
Citation Context ...this way, action types (resp. individual actions) can be represented in a uniform way by temporally related concepts (resp. individuals). For the basic temporal interval relations the Allen notation (=-=Allen, 1991-=-) (Figure 3) is used: before (b), meets (m), during (d), overlaps (o), starts (s), nishes (f), equal (=), after (a), met-by (mi), contains (di), overlapped-by (oi), started-by (si), nished-by ( ). Con... |

49 | Terminological knowledge representation: A proposal for a terminological logic. German Research Center for Artificial Intelligence (DFKI - Baader, Bürckert, et al. - 1991 |

49 |
Nonmonotonic temporal reasoning
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(Show Context)
Citation Context ...the possibility ofrepresenting persistent properties in the language, this Section considers how to solve the frame problem, and in particular the famous example of the Yale Turkey Shooting Scenario (=-=Sandewall, 1994; All-=-en & Ferguson, 1994), formerly known as the Yale Shooting Problem. An inertia operator \= " is introduced here. Intuitively, =C is currently true if it was true at a preceding interval { sayi{and... |

49 | The complexity of existential quantification in concept languages - Donini, Hollunder, et al. - 1992 |

48 | What’s in an aggregate: Foundations for description logics with tuples and sets - Giacomo, Lenzerini - 1995 |

43 | Combining terminological logics with tense logic - Schild - 1993 |

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(Show Context)
Citation Context ...covering fory. IfZ= ;, thenyis called uncovered, otherwiseyis said covered byZ. Proposition 6.3 (Covering procedure) Given a temporal constraint network hX;Tci in minimal form (see, e.g., (van Beek & =-=Manchak, 1996-=-)) and a nodey2X then the procedure described in Figure 12 returns all the possible coverings forywith size 2. The idea behind the covering is that whenever a set of nodes fz1;z2;:::;zpgis a covering ... |

40 | Plan-based terminological reasoning - Devanbu, Litman - 1991 |

34 |
A temporal terminological logic
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(Show Context)
Citation Context ...rom the assumption that an action has a duration in time, our proposal considers an interval-based modal temporal logic { in the spirit of Halpern and Shoham (1991) { and reduces the expressivity of (=-=Schmiedel, 1990-=-) in the direction of (Weida & Litman, 1992). While Schmiedel's work lacks computational machinery, and Halpern and Shoham's logic is undecidable, here an expressive decidable logic is obtained, provi... |

32 | A computational account for a description logic of time and action - Artale, Franconi - 1994 |

27 | Terminological logics with modal operators - Baader, Laux - 1995 |

26 |
Expressiveness and completeness of an interval tense logic
- Venema
- 1990
(Show Context)
Citation Context ...l temporal quanti er 2) makes the satis ability problem { and the subsumption { for propositionally complete languages undecidable in the most interesting temporal structures (Halpern & Shoham, 1991; =-=Venema, 1990-=-; Bettini, 1993). For the representation of actions and plans in the context of plan recognition, the universal temporal quanti er is not strictly necessary. This limitation makes these languages deci... |

24 | A unified framework for classbased representation formalisms - Calvanese - 1994 |

20 | D.J.: Taxonomic plan reasoning - Devanbu, Litman - 1996 |

19 | RAT: representation of actions using terminological logics - Heinsohn, Kudenko, et al. - 1992 |

14 | Subsumption and recognition of heterogeneous constraint networks - Weida, Litman - 1994 |

10 |
Time-dependent concepts: representation and reasoning using temporal description logics
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(Show Context)
Citation Context ...metime after the reference interval NOW. Schmiedel does not propose any algorithm for computing subsumption, but gives some preliminary hints. Actually, Schmiedel's logic is argued to be undecidable (=-=Bettini, 1997-=-), sacri cing the main bene t of Description Logics: the possibility ofhaving decidable inference techniques. Schmiedel's temporal Description Logic, when closed under complementation, contains as a p... |

8 | Fine grained theories of time
- Blackburn
- 2001
(Show Context)
Citation Context ...to hold over intervals, and events can be said to occur at intervals. His approach is very general, but it su ers from problems related to the semantic formalization of the predicates hold and occur (=-=Blackburn, 1992-=-). Moreover, computational properties of the formalism are not analyzed. The study of this latter aspect was, on the contrary, our main concern. In the Description Logic literature, other approaches f... |

8 | Interval situation calculus - Ternovskaia - 1994 |

7 | E.: Hierarchical plans in a Description Logic of time and action - Artale, Franconi - 1995 |