Linear temporal sequences and their interpretation using midpoint relationships (original) (raw)

Imprecise Temporal Interval Relations

Lecture Notes in Computer Science, 2006

When the time span of an event is imprecise, it can be represented by a fuzzy set, called a fuzzy time interval. In this paper we propose a representation for 13 relations that can hold between intervals. Since our model is based on fuzzy orderings of time points, it is not only suitable to express precise relationships between imprecise events ("the mid 1930's came before the late 1930's) but also imprecise relationships ("the late 1930's came long before the early 1990's). Furthermore we show that our model preserves many of the properties of the 13 relations Allen introduced for crisp time intervals.

Temporal Relations Between Imprecise Time Intervals: Representation and Reasoning

Lecture Notes in Computer Science, 2019

Temporal data given by users are often imprecise. In this paper, we propose an approach to represent and reason about temporal relations between imprecise time intervals which are classical time intervals characterized by gradual beginnings and/or endings. It is mainly based on extending the Allen's interval algebra. It is not only suitable to express precise temporal interval relations (e.g., "Before") but also imprecise personalized ones (e.g., "Just Before"). Compared to related work, our imprecise relations are personalized, in the sense that they are not limited to a given number and their meanings are determined by a domain expert. For instance, the classic Allen's relation "Before" may be generalized in 5 imprecise relations, where "Before (1) " means "just before" and gradually the time gap between the two intervals increases until "Before (5) " which means "too long before". Our imprecise personalized relations are based on our extension of the Vilain and Kautz's point algebra. We showed that, unlike most related work, our temporal interval relations preserve many of the properties of the Allen's interval algebra. Furthermore, we show how they can be used for temporal reasoning by means of a transitivity table. Finally, our approach is applied to the Semantic Web. We propose a fuzzy ontology-based prototype. Inferences are done via a set of SWRL and fuzzy IF-THEN rules. We illustrate the usefulness of our approach in the context of an ontology-based memory prosthesis for Alzheimer's patients. Keywords: Imprecise time interval Á Temporal interval relation Á Temporal reasoning Á Allen's interval algebra Á Semantic Web Á Fuzzy ontology

Reasoning about qualitative temporal information☆

Artificial Intelligence, 1992

Interval and point algebras have been proposed for representing qualitative temporal information about the relationships between pairs of intervals and pairs of points, respectively. In this paper, we address two related reasoning tasks that arise in these algebras : Given (possibly indefinite) knowledge of the relationships between some intervals or points, (1) find one or more scenarios that are consistent with the information provided, and (2) find all the feasible relations between every pair of intervals or points . Solutions to these problems have applications in natural language processing, planning, and a knowledge representation language . We define computationally efficient procedures for solving these tasks for the point algebra and for a corresponding subset of the interval algebra. Our algorithms are marked improvements over the previously known algorithms . We also show how the results for the point algebra help us to design a backtracking algorithm for the full interval algebra that is useful in practice .

A representation for collections of temporal intervals

1986

Temporal representation and reasoning are necessary components of systems that consider events that occur in the real world. This work explores ways of considering collections of intervals of time. This line of research is motivated by related work being done by our research group on appointment scheduling and time management. Natural language expressions that refer to collections of intervals are used naturally and routinely in these contexts, and an effective means of representing them is essential. Previous studies, which considered intervals primarily in isolation, have difficulties in representing some classes of expressions. This occurs not only with expressions that explicitly refer to collections of intervals, such as “the first of every month, ” but also with expressions that do so only

Knowledge Discovery from Series of Interval Events

Journal of Intelligent Information Systems

Knowledge discovery from data sets can be extensively automated by using data mining software tools. Techniques for mining series of interval events, however, have not been considered. Such time series are common in many applications. In this paper, we propose mining techniques to discover temporal containment relationships in such series. Specifically, an item A is said to contain an item B if an event of type B occurs during the time span of an event of type A, and this is a frequent relationship in the data set. Mining such relationships provides insight about temporal relationships among various items. We implement the technique and analyze trace data collected from a real database application. Experimental results indicate that the proposed mining technique can discover interesting results. We also introduce a quantization technique as a preprocessing step to generalize the method to all time series.

Robust mining of time intervals with semi-interval partial order patterns

Proceedings of the 2010 SIAM International Conference on Data Mining, 2010

We present a new approach to mining patterns from symbolic interval data that extends previous approaches by allowing semi-intervals and partially ordered patterns. The mining algorithm combines and adapts efficient algorithms from sequential pattern and itemset mining for discovery of the new semi-interval patterns. The semi-interval patterns and semi-interval partial order patterns are more flexible than patterns over full intervals, and are empirically demonstrated to be more useful as features in classification settings. We performed an extensive empirical evaluation on seven real life interval databases totalling over 146k intervals from more than 400 classes demonstrating the flexibility and usefulness of the patterns.

Fuzzifying Allen's Temporal Interval Relations

IEEE Transactions on Fuzzy Systems, 2000

When the time span of an event is imprecise, it can be represented by a fuzzy set, called a fuzzy time interval. In this paper, we propose a framework to represent, compute, and reason about temporal relationships between such events. Since our model is based on fuzzy orderings of time points, it is not only suitable to express precise relationships between imprecise events ("Roosevelt died before the beginning of the Cold War") but also imprecise relationships ("Roosevelt died just before the beginning of the Cold War"). We show that, unlike previous models, our model is a generalization that preserves many of the properties of the 13 relations Allen introduced for crisp time intervals. Furthermore, we show how our model can be used for efficient fuzzy temporal reasoning by means of a transitivity table. Finally, we illustrate its use in the context of question answering systems.

Point-versus interval-based temporal data models

Proceedings 14th International Conference on Data Engineering

The association of timestamps with various data items such as tuples or attribute values is fundamental to the management of time-varying information. Using intervals in timestamps, as do most data models, leaves a data model with a variety of choices for giving a meaning to timestamps. Specifically, some such data models claim to be point-based while other data models claim to be interval-based. The meaning chosen for timestamps is important-it has a pervasive effect on most aspects of a data model, including database design, a variety of query language properties, and query processing techniques, e.g., the availability of query optimization opportunities. This paper precisely defines the notions of point-based and interval-based temporal data models, thus providing a new, formal basis for characterizing temporal data models and obtaining new insights into the properties of their query languages. Queries in point-based models treat snapshot equivalent argument relations identically. This renders point-based models insensitive to coalescing. In contrast, queries in interval-based models give significance to the actual intervals used in the timestamps, thus generally treating non-identical, but possibly snapshot equivalent, relations differently. The paper identifies the notion of timefragment preservation as the essential defining property of an interval-based data model.