Temporal Specialization

In temporal specialization, the database designer restricts the relationship between the valid t ime-stamp (recording when something is true in the reality being modeled) and the transaction t ime-stamp (recording when a fact is stored in the database). An example is a retroactive temporal event relation, where the event must have occurred before it was stored, i.e., the valid t ime-stamp is restricted to be less than the transaction t ime-stamp. We discuss many useful restrictions, defining a large number of specialized types of temporal relations, and indicate some of their applications. We present a detailed taxonomy of specialized temporal relations. This taxonomy may be employed during database design to specify the particular time semantics of temporal relations. 1 I n t r o d u c t i o n The time of validity of a fact in a temporal relation and the time the fact was recorded in the relation are ostensibly independent. Yet, in many applications of temporal relations, the two times interact in restricted ways. For example, in the monitoring of temperatures during a chemical experiment, temperature measurements are recorded in the temporal relation after they are valid, due to transmission delays. The resulting relation is termed retroactive. Alternatively, salary payments recorded in the temporal relation of a bank are recorded be]ore the time the funds become accessible to employees, resulting in a predictive relation. We explore a variety of temporal relations with specialized relationships between transaction and valid time. Such specialized temporal relations occur in many practical applications, and the framework presented here is a means of capturing more of the semantics of temporal relations, with two primary benefits. Used by designers and researchers, the framework conveys a more detailed understanding of temporal relations. The additional semantics, when captured by an appropriately extended database system, may be used for selecting appropriate storage structures, indexing techniques, and query processing strategies. The paper extends a previously presented taxonomy on time in databases [SA85, SA86]. The previous taxonomy defined three kinds of time that could be associated with facts: userdefined time (with no database system-interpreted semantics), ~alid time (when a fact is true in reality), and transaction time (when a fact is stored in the database). A fact in a temporal relation has bo th a valid and a transaction time. A temporal relation records both the previous states of the relation and the history of reality. Temporal relations support three kinds of queries: (1) current queries, queries on the current state of the database; indeed, conventional database systems support only this kind of query; (2) historical queries, which extract facts about the history of objects from the modeled reality; and (3) rollback queries which extract facts as stored in the database at some point in the past. Though we use relational terminology throughout this paper, most of the analysis applies analogously to other data models. The original taxonomy falls short in its characterization of temporal relations in three ways. First, the taxonomy falls to give an aztequate understanding of some t ime-extended relations. Many proposals for adding time to databases advocate storing a single t ime-stamp per fact (e.g., [JMR91, SR85, SS87]), yet it appears that both rollback and historical queries are possible in these schemes. However, the taxonomy explicitly forbids both kinds of queries on a relation with only one times tamp per tuple. Second, because the taxonomy focuses on the orthogonality of the three kinds of time, it ignores restricted interrelationships between the valid and transaction times of facts in temporal relations. In many practical applications, valid and transaction times of facts exhibit interrelationships. Third, the taxonomy assumes that each fact has at most one transaction time and one valid time t ime-stamp (interval or event). (From now on, we use the shorter, but not quite precise, terms 'valid t ime-stamp' and ' transaction t ime-stamp' .) However, in application systems with multiple, interconnected temporal relations, multiple time dimensions may be associated with facts as they flow from one temporal relation to another. In order to address the first and second of the shortcomings, we explore the space of restricted interrelat ions--in-between the extremes of identity and no interrelation at a l l tha t axe possible between the valid and transaction times of facts. While we have focused primarily on comprehensiveness, we have not considered types of restricted interrelations that are of doubtful use. Addressing the third shortcoming, by providing the means for specifying the application system contexts of temporal relations, is the subject of a later paper. We will not be concerned here with the semantics of timevarying attributes, i.e., how to use t ime-stamp values and stored attr ibute values to derive the value of a time-varying attr ibute. For example, we will not address the issues of how to derive the temperature of a chemical reaction at an arbitrary point in time from time-stamped and stored temperature measurements. We are interested only in the semantics of the t ime-stamps themselves. In Section 2, we present a general definition and description of a temporal relation. In the following section, we examine the kinds of restrictions one might impose on temporal relations, considering in turn restrictions on isolated events, on collections of events, on isolated intervals, and on collections of intervals. The final section summarizes our work and points to future research. 0-8186-2545-7/92 $3.00 © 1992 IEEE 594 ©1992 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder. 2 Temporal Relations We present a conceptual model of a temporal relation as a prelude to the extensions discussed in the remainder of the paper. A temporal relation has two orthogonal time dimensions, valid time and transaction time. Valid time is used for capturing the time-varying nature of the part of reality being modeled by the relation. Transaction time models the update activity of the relation. Thus, a temporal relation may be envisioned as a sequence of historical states indexed by transaction time. A temporal relation consists of a set of temporal elements, each of which records one or more facts about an object (entity or relationship) from the part of reality being modeled by the temporal relation. Temporal elements have the following attribute values: element surrogate, object surrogate, transaction time-stamp, valid t ime-stamp (interval or event), time-invariant at tr ibute values, time-varying at t r ibute values, and user-defined times. We examine each briefly in turn. An element surrogate is a system-generated, unique identifier of an element that can be referenced and compared for equality, but not displayed to the user [Dat85, HOT76]. We will discuss element surrogates in more detail shortly. An object surrogate is a unique identifier of the object being modeled by an element. It is used for identifying all the database representations of individual real-world objects. At any point in time, each real-world object may have, in a single relation, a set of associated elements, all with the same object surrogate (c.f., a "life-line" [Sch77] or a "time sequence" [SK86]). Thus, a relation (c.f., a "time sequence collection" [SK86]) can be parti t ioned into a collection of sets so that elements of distinct sets have distinct object surrogates and elements of any single set have the same object surrogate. This is termed a per surrogate partitioning. Transaction times are generated by the database system itself using monotonically increasing t ime-stamp generators; thus each historical state has an associated unique transaction time. The granularity of transaction time-stamps is arbitrary, as long as uniqueness is ensured. Transaction time models the update activity of the temporal relation, and as such, its semantics are entirely independent of the application and the enterprise being modeled. The transaction time of an element is the time when the facts recorded by the element were stored in the relation. Therefore, no stored transaction time exceeds the current time. The historical state resulting from a transaction remains unchanged from the time of that transaction to the time of the next transaction. Therefore, the semantics of transaction time have been characterized as stepwise constant. We will associate two transaction times, tt~e and tt~, with each element e in a temporal relation. The first, tt~, is the time when the element e is stored in the relation. The second, tt4e, is the time when the element e is logically removed from the relation. The existence interval for e, [tt~e, ttde ), is thus the time between the transaction time of the historical state in which the element first appeared and the transaction time of the historical state succeeding the one in which the element last appeared. The element surrogate identifies the element for the purpose of defining the existence interval (in the database) for the element, ff a particular event or interval is (logically) deleted, then immediately re-inserted, the two resulting elements will have different element surrogates, allowing the deletion (ttde) and insertion (tt~) points to be unambiguously defined. If a modification is made by a transaction executed on the database, the element in the current historical state is (logically) deleted, and a new element, recording the modified information, is stored in the new historical state, indexed by the transaction time of the transaction making the change. The database system uses the transaction times of elements for implementing the rollback operator [BZ82, Sch77]. In general, any domain of elements with an identity relation and a total ordering is suitable for transaction time. Example domains include the natural numbers and regular da te / t ime values. Valid times are usually supplied by the user, but they may be system-generated. The valid t ime-stamp of an element records when the facts represented by the time-varying (and timeinvariant) and user-defined time at t r ibute values are true in reality. Valid times are always drawn from the domain of times and dates. The elements of a relation may represent events, in which case the valid t ime-stamp of an element is a single valid time value. Alternatively, the facts represented by the elements of a relation may be true for a duration of time, in which case the valid t ime-stamp of an element is an interval consisting of two valid time values. The valid t ime-stamps are used by the database system for implementing the time-slice operator [BZ82, JMS791. An element may contain a number of time-invariant attribute values, i.e., values that never change. An important example is the time-invariant key [NA89] which, although it resembles the object surrogate, is still necessary. Social security, account, and membership numbers are important time-invariant keys in many applications. Non-key tlme-invariant at tr ibute values also exist, e.g., race. An element may record several facts about a real-world object, using several time-varying attribute values. For exampie, an element may record both the title and the salary of an employee. Each relation may have an individual valid times tamp granularity, or the database system may impose a fixed granularity on all relations managed by the database system. While different granularities may be ascribed to individual timevarying attributes within an element, it may still be necessary to fix the (overall) element granularity. An element may also have several user-defined times. Such time-stamps are drawn from a domain of dates and times with an identity relation and a total ordering. User-defined times may be manually supplied or computed by an application program. The system gives no special semantics to user-defined times; they are most appropriately thought of as specialized kinds of time-varying at tr ibute values. Note that in this conceptual model we do not assume any particular type system on surrogates, historical states, or attributes. In particular, while an element is associated with a valid time-stamp, the model makes no mention of whether tuple time-stamping or attribute-value t ime-stamping is employed. Neither do we assume a particular data model; elements could be tuples in a relational database [Cod70], records in a network database [Datg0], or events in a time sequence collection [SK86]. Finally, the conceptual model of a sequence of historical states does not imply (nor disallow) a particular physical representation. For example, a temporal relation may be represented as a collection of tuples with an event or interval valid time-stamp and an interval transaction t ime-stamp [Sno87] or with one or two valid t ime-stamps and three transaction timestamps [BZ82], as a backlog relation of insertion, modification, and deletion operations (tuples) with single transaction timestamps [JMRS90] or with time warp at tr ibutes [Tho91], and as tuples containing attributes t ime-stamped with one or more finite unions of intervals ( termed temporal elements [Gad88], distinct from the term element used in this paper).