Efficiently supporting temporal granularities

Granularity is an integral feature of temporal data. For instance, a person's age is commonly given to the granularity of years and the time of their next airline flight to the granularity of minutes. A granularity creates a discrete image, in terms of granules, of a (possibly continuous) time-line. We present a formal model for granularity in temporal operations that is integrated with temporal indeterminacy, or “don't know when” information. We also minimally extend the syntax and semantics of SQL-92 to support mixed granularities. This support rests on two operations, scale and cast, that move times between granularities, e.g., from days to months. We demonstrate that our solution is practical by showing how granularities can be specified in a modular fashion, and by outlining a time- and space-efficient implementation. The implementation uses several optimization strategies to mitigate the expense of accommodating multiple granularities     

Augmenting a conceptual model with geospatiotemporal annotations

While many real-world applications need to organize data based on space (e.g., geology, geomarketing, environmental modeling) and/or time (e.g., accounting, inventory management, personnel management), existing conventional conceptual models do not provide a straightforward mechanism to explicitly capture the associated spatial and temporal semantics. As a result, it is left to database designers to discover, design, and implement - on an ad hoc basis - the temporal and spatial concepts that they need. We propose an annotation-based approach that allows a database designer to focus first on nontemporal and nongeospatial aspects (i.e., "what") of the application and, subsequently, augment the conceptual schema with geospatiotemporal annotations (i.e., "when" and "where"). Via annotations, we enable a supplementary level of abstraction that succinctly encapsulates the geospatiotemporal data semantics and naturally extends the semantics of a conventional conceptual model. An overarching assumption in conceptual modeling has always been that expressiveness and formality need to be balanced with simplicity. We posit that our formally defined annotation-based approach is net only expressive, but also straightforward to understand and implement.     

Indeterminacy and Spatiotemporal Data: Basic Definitions and Case Study

For some spatiotemporal applications, it can be assumed that the modeled world is precise and bounded, and that also our record of it is precise. While these simplifying assumptions are sufficient in applications like a land information system, they are unnecessarily crude for many other applications that manage data with spatial and/or temporal extents, such as navigational applications. This work explores fuzziness and uncertainty, subsumed under the term indeterminacy, in the spatiotemporal context. To better illustrate the basic spatiotemporal concepts of change or evolution, it is shown how the fundamental modeling concepts of spatial objects, attributes, and relationships and time points and periods are influenced by indeterminacy and how they can be combined. In particular, the focus is on the change of spatial objects and their geometries across time. Four change scenarios are outlined, which concern discrete versus continuous change and asynchronous versus synchronous measurement, and it is shown how to model indeterminacy for each. A case study illustrates the applicability of the paper’s general proposal by describing the uncertainty related to the management of the movements of point objects, such as the management of vehicle positions in a fleet management system.     

HMAP– A temporal data model managing intervals with different granularities and indeterminacy from natural language sentences

The granularity of given temporal information is the level of abstraction at which information is expressed. Different units of measure allow one to represent different granularities. Indeterminacy is often present in temporal information given at different granularities: temporal indeterminacy is related to incomplete knowledge of when the considered fact happened. Focusing on temporal databases, different granularities and indeterminacy have to be considered in expressing valid time, i.e., the time at which the information is true in the modeled reality. In this paper, we propose HMAP (The term is the transliteration of an ancient Greek poetical word meaning “day”.), a temporal data model extending the capability of defining valid times with different granularity and/or with indeterminacy. In HMAP, absolute intervals are explicitly represented by their start,end, and duration: in this way, we can represent valid times as “in December 1998 for five hours”, “from July 1995, for 15 days”, “from March 1997 to October 15, 1997, between 6 and 6:30 p.m.”. HMAP is based on a three-valued logic, for managing uncertainty in temporal relationships. Formulas involving different temporal relationships between intervals, instants, and durations can be defined, allowing one to query the database with different granularities, not necessarily related to that of data. In this paper, we also discuss the complexity of algorithms, allowing us to evaluate HMAP formulas, and show that the formulas can be expressed as constraint networks falling into the class of simple temporal problems, which can be solved in polynomial time. Received 6 August 1998 / Accepted 13 July 2000 Published online: 13 February 2001     

A 1NF temporal relational model and algebra coping with valid-time temporal indeterminacy

In the real world, many phenomena are time related and in the last three decades the database community has devoted much work in dealing with “time of facts” in databases. While many approaches incorporating time in the relational model have been already devised, most of them assume that the exact time of facts is known. However, this assumption does not hold in many practical domains, in which temporal indeterminacy of facts occurs. The treatment of valid-time indeterminacy requires in-depth extensions to the current relational approaches. In this paper, we propose a theoretically grounded approach to cope with this issue, overcoming the limitations of related approaches in the literature. In particular, we present a 1NF temporal relational model and propose a new temporal relational algebra to query it. We also formally study the properties of the new data model and algebra, thus granting that our approach is interoperable with pre-existent temporal and non-temporal relational approaches, and is implementable on top of them. Finally, we consider computational complexity, showing that only a limited overhead is added when moving from determinate to indeterminate time.     

全序时态模块模式的TO_TBCNF分解问题研究

时间粒度是所有时态数据所拥有的共同特点。在许多时态数据库应用中,都涉及多时间粒度约束,但是,具有多时间粒度的时态数据库的设计相当复杂,难以实现。而现实世界中的许多应用涉及到的时态类型集都能满足全序关系,由于具有全序时态类型集的全序时态模块模式有着良好的特性,文章提出了全序时态模块模式、时刻关系模式、全序时态模块投影和全序时态BC范式（TO_TBCNF）等概念,并给出了全序时态BC范式的分解算法,对其正确性、可终止性进行了证明,并对时间复杂度进行了分析。     

Sequenced spatiotemporal aggregation for coarse query granularities

Sequenced spatiotemporal aggregation (SSTA) is an important query for many applications of spatiotemporal databases, such as traffic analysis. Conceptually, an SSTA query returns one aggregate value for each individual spatiotemporal granule. While the data is typically recorded at a fine granularity, at query time a coarser granularity is common. This calls for efficient evaluation strategies that are granularity aware. In this paper, we formally define an SSTA operator that includes a data-to-query granularity conversion. Based on a discrete time model and a discrete 1.5 dimensional space model, we generalize the concept of time constant intervals to constant rectangles, which represent maximal rectangles in the spatiotemporal domain over which an aggregation result is constant. We propose an efficient evaluation algorithm for SSTA queries that takes advantage of a coarse query granularity. The algorithm is based on the plane sweep paradigm, and we propose a granularity aware event point schedule, termed gaEPS, and a granularity aware sweep line status, termed gaSLS. These data structures store space and time points from the input relation in a compressed form using a minimal set of counters. In extensive experiments, we show that for coarse query granularities gaEPS significantly outperforms a basic EPS that is based on an extension of previous work, both in terms of memory usage and runtime.     

Temporal Granularity: Completing the Puzzle

Granularity is an integral feature of both anchored (e.g., 25 October 1995, July 1996) and unanchored (e.g., 3 minutes, 6 hours 20 minutes, 5 days) temporal data. In supporting temporal data that is specified in different granularities, numerous approaches have been proposed to deal with the issues of converting temporal data from one granularity to another. The emphasis, however, has only been on granularity conversions with respect to anchored temporal data. In this paper we provide a novel approach to the treatment of granularity in temporal data. A granularity is modeled as a special kind of unanchored temporal primitive that can be used as a unit of time. That is, a granularity is modeled as a unit unanchored temporal primitive. We show how unanchored temporal data is represented, give procedures for converting the data to a given granularity, provide canonical forms for the data, and describe how operations between the data are performed. We also show how anchored temporal data is represented at different granularities and give the semantics of operations on anchored temporal data.     

基于粒度层次映射转换的时态粒点差运算方法

计算两个时态粒点在任意时态粒度下的差值是时态断言的基础,提出基于时态粒度的层次映射转换方法,将时态粒点映射为各时态粒度下的可列集,差运算可转换为不同粒度映射下的自然数差运算.并论证了时态论域T与自然数集N间的对等关系以及映射的连续性,证明了方法的正确性.克服了弹性时态粒度的影响,适应任何基于非规则时态粒度集或者自定义时态粒度集上的时态粒点差运算.     

Temporal aggregation on user-defined granularities

Time-varying data play a major role in many applications, and, starting from the 80’s, they have been widely studied in temporal databases. In the last two decades, several researchers have shown that, to deal with many application domains, user-defined temporal granularities must be coped with. When data are stored at multiple user-defined temporal granularities, the task of defining proper conversion functions to aggregate data from an origin granularity (e.g., business days) to a task granularity (e.g., months) is of primary importance. However, current temporal database approaches mostly demand such a task to system administrators, or to specific applications, providing no methodology or general guideline to accomplish it. In this paper, we propose a general and application-independent methodology which, on the basis of the temporal relationship between two user-defined granularities, provides users with a set of conversion/aggregation functions between them, consistent with the telic vs. atelic character of the data to be aggregated. The correctness of the approach is also proved.     

An integrated temporal data model incorporating time series concept

Most temporal data models have concentrated on describing temporal data based on versioning of objects, tuples or attributes. The concept of time series, which is often needed in temporal applications, does not fit well within these models. The goal of this paper is to propose a generalized temporal database model that integrates the modeling of both version-based and time-series based temporal data into a single conceptual framework. The concept of calendar is also integrated into our proposed model. We also discuss how a conceptual Extended-ER design in our model can be mapped to an object-oriented or relational database implementation.     

A Logical Formulation of Probabilistic Spatial Databases

There are numerous applications where there: is uncertainty over space and time. Examples of such uncertainty arise in vehicle tracking systems where we are not always sure where a vehicle is now (or may be in the future), and cell and satellite phone applications where we are not sure exactly where a phone may be, and so on. In this paper, we propose the concept of a Spatial Probabilistic Temporal (SPOT) database that contains statements of the form "Object O is in spatial region R at some time / with some probability in the interval [L, U]." We define the syntax and a declarative semantics for SPOT databases based on a mix of logic and linear programming, as well as query algebra. We show alternative implementations of some of these query algebra operators when the SPOT database has a disjoint/less property. Though the declarative semantics of SPOT databases is rooted in linear programming, we have found very efficient algorithms that do not use linear programming methods. We report on experiments we have conducted that show that the system scales to large numbers of SPOT atoms, as well as to fairly fine temporal and spatial granularity.     

Conceptual Data Modeling for Spatiotemporal Applications

Many exciting potential application areas for database technology manage time-varying, spatial information. In contrast, existing database techniques, languages, and associated tools provide little built-in support for the management of such information. The focus of this paper is on enhancing existing conceptual data models with new constructs, improving their ability to conveniently model spatiotemporal aspects of information. The goal is to speed up the data modeling process and to make diagrams easier to comprehend and maintain. Based on explicitly formulated ontological foundations, the paper presents a small set of new, generic modeling constructs that may be introduced into different conceptual data models. The ER model is used as the concrete context for presenting the constructs. The semantics of the resulting spatiotemporal ER model, STER, is given in terms of the underlying ER model. STER is accompanied by a textual counterpart, and a CASE tool based on STER is currently being implemented, using the textual counterpart as its internal representation.     

Modeling Moving Objects over Multiple Granularities

This paper introduces a framework for modeling the movement of objects or individuals over multiple granularities. Granularity refers to selecting the appropriate level of detail for a task. At fine granularities, spatio-temporal information is revealed that was not previously known, such as additional locations that an individual visited or multiple visits to the same location. Conversely, moving to a coarser granularity or simpler view generalizes spatial and temporal aspects of movement allowing for an improved understanding of movement. Movement is modeled as geospatial lifelines, time-stamped records of the locations that an individual has occupied over a period of time. Depending on the desired granularity, lifelines are modeled as lifeline beads, necklaces, or more general approximations of these structures and this paper examines how different aspects of lifelines become relevant at refined or coarse granularities.     

Modeling and formal verification of embedded systems based on a Petri net representation

In this paper we concentrate on aspects related to modeling and formal verification of embedded systems. First, we define a formal model of computation for embedded systems based on Petri nets that can capture important features of such systems and allows their representation at different levels of granularity. Our modeling formalism has a well-defined semantics so that it supports a precise representation of the system, the use of formal methods to verify its correctness, and the automation of different tasks along the design process. Second, we propose an approach to the problem of formal verification of embedded systems represented in our modeling formalism. We make use of model checking to prove whether certain properties, expressed as temporal logic formulas, hold with respect to the system model. We introduce a systematic procedure to translate our model into timed automata so that it is possible to use available model checking tools. We propose two strategies for improving the verification efficiency, the first by applying correctness-preserving transformations and the second by exploring the degree of parallelism characteristic to the system. Some examples, including a realistic industrial case, demonstrate the efficiency of our approach on practical applications.     

A general framework for time granularity and its application to temporal reasoning

This paper presents a general framework to define time granularity systems. We identify the main dimensions along which different systems can be characterized, and investigate the formal relationships among granularities in these systems. The paper also introduces the notion of a network of temporal constraints with (multiple) granularities emphasizing the semantic and computational differences from constraint networks with a single granularity. Consistency of networks with multiple granularities is shown to beNP‐hard in general and approximate solutions for this problem and for the minimal network problem are proposed. This revised version was published online in June 2006 with corrections to the Cover Date.     

Incorporating ontology-based semantics into conceptual modelling

With the increasing complexity of applications and user needs, recent research has shifted from a data-information level to a human semantic level interaction. Research has begun to address the increasing use and development of ontologies in various applications, strongly motivated by the semantic web initiative. However, existing conceptual models are not rich enough to incorporate ontologies in one single conceptual schema. To improve this situation, it is necessary to refine modelling formalisms and make them more expressive while ensuring they remain semantically sound. We argue that conceptual modelling methodologies would be semantically richer if they were able to express the semantics of a domain that arises in concrete application scenarios. This paper investigates the incorporation of ontologies into three popular conceptual modelling methodologies, presenting the Ontological Entity-Relationship (OntoER) model, Ontological Object Role Modelling (OntoORM) and the Ontological Unified Modelling Language (OntoUML) class diagram. An extended conceptual framework for modelling ontologies and a transformation algorithm for mapping ontological constructs to relational schemata are provided so that querying the database through the conceptualisation of the database can be managed.     

具有全序时态类型集时态函数依赖集的研究

好的数据库逻辑设计目标是消除数据冗余以及插入、删除和更新异常.对于时态数据库,可以通过具有多时间粒度的时态函数依赖(TFDs)约束对时态数模式进行规范化.但是由于时间维的引入和多时间粒度的使用而给数据库设计带来巨大的复杂性.一般来说,系统所能处理的和相当多的应用所涉及到的时态类型集满足全序关系,并且具有全序时态类型集的TFD集的推导规则与传统函数依赖(FDs)的Armstrong公理有着紧密的联系.通过分析TFDs与FDs之间存在的联系,利用传统FD集的相应算法,提出了成员籍、有限属性闭包等TFD集的一些重要算法.这些算法是时态数据库进一步规范化的基础.