Maintaining knowledge about temporal intervals
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article Free Access Share on Maintaining knowledge about temporal intervals Author: James F. Allen Univ. of Rochester, Rochester, NY Univ. of Rochester, Rochester, NYView Profile Authors Info & Claims Communications of the ACMVolume 26Issue 11Nov. 1983 pp 832–843https://doi.org/10.1145/182.358434Online:01 November 1983Publication History 5,173citation11,531DownloadsMetricsTotal Citations5,173Total Downloads11,531Last 12 Months644Last 6 weeks101 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my Alerts New Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF
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Allen-relation selection on the operator output preserves the bitemporal-tuple type by closure of Allen's thirteen interval relations and the twelve-relation transitivity table that omits equality.
“Allen-relation selection on the operator output preserves the bitemporal-tuple type by closure of Allen's thirteen interval relations and the twelve-relation transitivity table that omits equality [3].”
From TOKI: A Bitemporal Operator Algebra for Contradiction Resolution in LLM-Agent Persistent Memory (2026) · cites this paper as [3]
Figure 2 identifies thirteen possible interval relationships, and Figure 4 is captioned as a transitivity table for twelve relations, omitting equality. The discussion of the basic algorithm describes transitive closure of temporal relations, but our copy does not establish that Allen-relation selection on an operator output preserves a bitemporal-tuple type. (LLM, conf=0.88)
Experimental — accuracy not yet measuredClosure under Allen-relation selection follows from the transitivity table over the twelve non-equality relations.
“Closure under Allen-relation selection follows from the transitivity table over the twelve non-equality relations [3].”
From TOKI: A Bitemporal Operator Algebra for Contradiction Resolution in LLM-Agent Persistent Memory (2026) · cites this paper as [3]
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“In the past, formalisms for relations have been limited to simple data types in a one-dimensional space such as integers, reals, or their combinations, e.g., as intervals (Allen, 1983).”
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“6 and the ensuing temporal CSP’s were introduced in Allen (1983). The eight spatial relations presented in Figure 2.7 and the composition table given in Figure 2.8 were introduced in Egenhofer (1991). In Egenhofer (1994a) these relations were systematically derived and in Egenhofer (1994b) a connection with the CSP’s…”
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“Allen’s interval calculus [2] is well known within AI; however, the credit for inventing such calculi is not due to him; [107] describes an interval calculus, while [91, chapter 2] is probably the earliest such system.”
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“Using the representation of [2], these relations are indicated graphically by a timeline representation of Figure 6a.”
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“The authors use thirteen temporal intervals defined by Allen [13] (e.”
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“Provided we are interested in temporal reasoning in the framework as described by Allen [2], one necessary requirement is that all basic relations are contained in the subclass.”
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“Qualitative approaches to temporal reasoning were introduced by Allen [13] with a specific algebra over intervals and a path consistency filtering algorithm.”
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“It uses ideas from Allen (1983), initially developed for reasoning about time intervals, and applies them to two dimensional space.”
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“This representation treats points as primitive (as do (Bennett and Partee 1972), (Dowty 1979), among others); other representations treat intervals as primitive, e.g., (Allen 1983).”
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“…subtasks are added to the entire temporal graph, it becomes possible to let confi-dence scores from the separate subtasks drive a constraint propagation algorithm as proposed in (Allen, 1983), in effect using high-precision relations to constrain lower-precision relations elsewhere in the graph.”
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“Meanwhile, [1] extended basic binary temporal relations discussed in [1] to n-ary temporal relations, and discussed reverse relations of them.”
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“However, no attempt has yet been made to determine the boundary between polynomial and NP-hard fragments of RCC-8, as it has been done for Allen's [1983] This research was partially supported by DFG as part of the project fast-qual-space, which is part of the DFG special research e(cid:11)ort on…”
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“The temporal relation is encoded with Allen’s temporal interval logic [Allen, 1983].”
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“Then, their intersection is de ned as C 0 C 00 = fxjx 2 I ; x 2 I g: The composition of C 0 and C 00 is de ned as C 0 C 00 = fzj9x 2 I ;9y 2 I ; x+ y = zg: Illustration Let C1 = f[1; 4); (6; 8)g and C2 = f(0; 1]; (3; 5); [6; 7]g.”
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“Allen (1983) gives an example of such a graph.”
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“Julia Allen Jones, Assistant Professor at the University of California, Santa Barbara received her B. A. (1977) in Economic Development from Hampshire College. She was awarded her M. A. in International Relations (1979) and her Ph.D. in Geography and Environmental Engineering (1983) from the Johns Hopkins University.”
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“In particular, in the framework introduced by Allen [1], nodes of the network stand for intervals in time, and the arcs are labeled by disjunctions of the basic 13 symbolic relations (Allen’s relations) between two intervals.”
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“For example, a temporal constraint specialist could keep track of constraints among temporal intervals using Allen’s temporal constraint propagation algorithm [47], while an object location specialist could keep track of object locations using an evidence grid.”
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“two objects in lD space is 13. These 13 relations correspond to the relations between time intervals introduced in ( Allen, 1983 ).”
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“Following Allen (1983), I denote these relations as , , , m, mi, o, oi, s, si, f, fi, d, and di and refer to them collectively as Allen relations throughout the paper.”
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“In [2], Allen developed a calculus of temporal intervals, in which the underlying structure of time is linear and a time interval is a connected temporal duration, such as between 3.”
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“For instance f, g in time-point algebra Vilain et al., 1989, fm, m i g in interval algebra Allen, 1983, 10,20030,400 in Quantitative TCNs it can be noticed here that the search tree is such that each leaf is a STP whose satissability is then solved by local consistency enforcement Schwalb and…”
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“…top-level formal ontologies included within SUMO are: (1) the top-level ontology of Sowa (1995) and Russell and Norvig (1995), (2) temporal axioms (Allen 1983, Allen and Hayes 1985), (3) the formal theory of holes (Casati and Varzi 1994), (4) ontology of boundaries (Smith and Varzi 1997), and (5)…”
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“These relations are shown in Figure 2 (compare Allen [1983], Figure 2).”
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Dubois, D., & Prade, H. (1989) · IEEE Transactions on Systems, Man and Cybernetics · doi:10.1109/21.35337 · Cited by 308
Qualitative Spatial Reasoning Using Constraint Calculi
Renz, J., & Nebel, B. (2007) · Handbook of Spatial Logics · doi:10.1007/978-1-4020-5587-4_4 · Cited by 307
Survey of the State of the Art in Human Language Technology
Cohen, K., Varile, G., Zampolli, A., Cole, R., Mariani, J., Uszkoreit, H., Zaenen, A., & Zue, V. (2010) · Language · doi:10.2307/417436 · Cited by 305 · see citing works
Probabilistic Argumentation Frameworks
Li, H., Oren, N., & Norman, T. (2011) · International Workshop on Theorie and Applications of Formal Argumentation · doi:10.1007/978-3-642-29184-5_1 · Cited by 300
Detecting composite events in active database systems using Petri nets
Gatziu, S., & Dittrich, K. (1994) · Proceedings of IEEE International Workshop on Research Issues in Data Engineering: Active Databases Systems · doi:10.1109/ride.1994.282859 · Cited by 300
Constraint-based workflow management systems : shifting control to users
Pesic, M. (2008) · doi:10.6100/ir638413 · Cited by 295
“The authors use thirteen temporal intervals defined by Allen [50] (e.”
BackgroundMethodWerthner, U.-D. D.-I. D. H. (1994) · Springer Vienna · doi:10.1007/978-3-7091-6624-6 · Cited by 292
Semiotic schemas: A framework for grounding language in action and perception
Roy, D. K. (2005) · Artificial Intelligence · doi:10.1016/j.artint.2005.04.007 · Cited by 218 · see citing works
“Categorical beliefs can be used to represent relative temporal and spatial relationships such as Allen’s temporal relations [1] or topological spatial relations [55].”
MethodKnowledge Representation as the Basis for Requirements Specifications
Borgida, Greenspan, & Mylopoulos (1985) · Computer · doi:10.1109/mc.1985.1662870 · Cited by 289
Temporal Annotation in the Clinical Domain
Styler, W., Bethard, S., Finan, S., Palmer, M., Pradhan, S., de Groen, P. D., Erickson, B., Miller, T., Lin, C., Savova, G., et al. (2014) · Transactions of the Association for Computational Linguistics · doi:10.1162/tacl_a_00172 · Cited by 285 · see citing works
Auditing Business Process Compliance
Ghose, A., & Koliadis, G. (2007) · International Conference on Service Oriented Computing · doi:10.1007/978-3-540-74974-5_14 · Cited by 285
“Interval algebra [14] is also applicable.”
Ni, Q., García, A. B., & Pau, I. (2015) · Sensors · doi:10.3390/s150511312 · Cited by 264 · see citing works
“In terms of time interval, the so-called Allen relations [67] are commonly used to describe temporal links between activities: (1) Sequential activities are described by associating their time intervals using the before/after and meet/meetby relations.”
MethodA Survey on Temporal Reasoning in Artificial Intelligence
Vila, L. (1994) · AI Communications · doi:10.3233/aic-1994-7102 · Cited by 275 · see citing works
“1 Qualitative Relations Allen develops an algebra of intervals [3] based on the 13 relations that correspond to the simple de nite mutually exclusive relations that may exist between two intervals (see gure 3).”
InfluentialCognitive models of geographical space
Mark, D., Freksa, C., Hirtle, S. C., Lloyd, R., & Tversky, B. (1999) · International Journal of Geographical Information Science · doi:10.1080/136588199241003 · Cited by 274 · see citing works
“Most of them are strongly related to Allen's work on qualitative temporal reasoning (Allen 1983, Freksa 1992).”
BackgroundQualitative Spatial Reasoning: The Clock Project
Forbus, K. D., Nielsen, P. E., & Faltings, B. (1991) · Artificial Intelligence · doi:10.1016/0004-3702(91)90116-2 · Cited by 270 · see citing works
Modeling multistep cyber attacks for scenario recognition
Cheung, S., Lindqvist, U., & Fong, M. W. (2003) · Proceedings DARPA Information Survivability Conference and Exposition · doi:10.1109/discex.2003.1194892 · Cited by 269 · see citing works
“Temporal Relationships between two time intervals, based on Allen’s work on temporal intervals [1] IsBefore(r1,r2) indicates time interval r1 ends strictly before the start of time interval r2”
MethodSurvey of Temporal Information Retrieval and Related Applications
Campos, R., Dias, G. H., Jorge, A., & Jatowt, A. (2014) · ACM Computing Surveys · doi:10.1145/2619088 · Cited by 244 · see citing works
“Another formal approach is the work of [Allen 1983], which introduces the notion of time intervals rather than fixed time points and describes a set of thirteen possible temporal relationships between two time intervals.”
BackgroundThe temporal query language TQuel
Snodgrass, R. (1987) · ACM Transactions on Database Systems · doi:10.1145/22952.22956 · Cited by 264 · see citing works
“b (3+4) ] (Ba)(3b)(S)(A(a) A B(b) A C(c) A u[l] = a[l] A u[2] = b[l] A u[3] = c[l] A u[4] = Last(a[3], b[3]) A u[5] = First(a[4], b[4]) A Before(u[4], u[5]) A u[6] = 12346 A u[7] = 0 Aa[2]=b[2]Ab[2]=c[2] A UWore(h~(aM, bPl), cL31) V JWore(cWl, at31)) A Before(1009, a[6]) A Before(a[5], 1019) A Before(1009, b[6]) A Bef…”
E-connections of abstract description systems
Kutz, O., Lutz, C., Wolter, F., & Zakharyaschev, M. (2004) · Artificial Intelligence · doi:10.1016/j.artint.2004.02.002 · Cited by 263
Survey of Spatio-Temporal Databases
Abraham, T., & Roddick, J. (1999) · GeoInformatica · doi:10.1023/a:1009800916313 · Cited by 263
“Using simple arithmetics on tesseral addresses and utilizing Allen's temporal logic [4], 34 different relationships can be constructed between events and intervals, representing powerful temporal reasoning capabilities, cf.”
BackgroundMethodInfluentialA taxonomy for task allocation problems with temporal and ordering constraints
Nunes, E., Manner, M., Mitiche, H., & Gini, M. (2017) · Robotics and Autonomous Systems · doi:10.1016/j.robot.2016.10.008 · Cited by 252 · see citing works
“In general terms, time can be modeled using points or intervals [Allen, 1983].”
InfluentialMarks, M., & Hammond, K. J. (1993) · SGAR · doi:10.1145/152941.1064726 · Cited by 256
O'Sullivan, J., Edmond, D., & ter Hofstede, A. T. (2002) · Distributed and parallel databases · doi:10.1023/a:1016547000822 · Cited by 254
“finer-than, groups-into) have previously been offered [1, 7].”
- Authors
- Allen, J. F.
- Affiliations
- University of Rochester (US)
- Corresponding author
- Allen, James F.
- ORCID
- Allen, James F.
- Venue
- Communications of the ACM
- Published
- 1983-11
- Volume
- 26
- Issue
- 11
- Pages
- 832-843
- ISSN
- 0001-0782 (ISSN-L)
- 1557-7317
- OpenAlex
- W2161484642
- Cited by
- 7,593
- References
- 0
- Citations by year
- 2026: 79 · 2025: 88 · 2024: 133 · 2023: 126 · 2022: 115 · 2021: 159 · 2020: 194 · 2019: 175 · 2018: 212 · 2017: 246 · 2016: 291 · 2015: 267 · 2014: 279 · 2013: 326 · 2012: 322
- FWCI
- 27.16
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Communications of the ACM (publishedVersion)
- Funders
- National Science Foundation (8210564)
- Office of Naval Research (N00014)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Logic, Reasoning, and Knowledge
- Physical Sciences › Computer Science › Computer Networks and Communications › Constraint Satisfaction and Optimization
- Physical Sciences › Computer Science › Artificial Intelligence › AI-based Problem Solving and Planning
- Keywords
- temporal reasoning, time intervals, interval arithmetic, knowledge representation, temporal logic, Allen's interval algebra
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
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