Temp oral Databases Richard T Sno dgrass Department of Computer Science University of Arizona Tucson AZ rtscsarizonaedu Abstract This pap er summarizes the ma jor concepts approaches and implementation strategies that have b een generated over the last f teen years of research into data base management system supp ort for timevarying information We rst examine the time domain its struc ture dimensional i ty indeterminacy and representation We then discuss facts may b e asso ciated with time and consider data mo deling and how representational issues We survey the many temp oral query languages we examine the impact to each of the that have b een prop osed Finally comp onents of a DBMS of adding temp oral supp ort fo cusing on query optimization and evaluation Intro duction Time is an imp ortant asp ect of all realworld phenomena Events o ccur at sp ecic p oints in time ob jects and the relationships among ob jects exist over time The ability to mo del this temp oral dimension of the real wold is essential to many computer applications such as econometrics banking inventory control accounting law medical records land and geographical information systems and airline reservations Con ventional databases represent the state of an enterprise at a single mo ment of time Although the contents of the database continue to change as new information is added these changes are viewed as mo dications to the state with the old outofdate data b eing deleted from the database The current such contents of the database may b e viewed as a shapshot of the enterprise In systems the attributes involving time are manipulated solely by the application programs the database management system DBMS interprets dates as values in the base data typ es No conventional system interprets temp oral domains when deriving new relations Applicationindep endent DBMS supp ort for timevarying information has years with approximately pa b een an active area of research for ab out p ers generated thus far citeBolourmckenzieAstamso o This pap er attempts to capture and summarize the ma jor concepts approaches and imple mentation strategies that have b een generated by that research W e rst examine the time domain its structure dimensionality interest ingly there are several time dimensions and temp oral indeterminacy followed by issues in representing values in this domain We demonstrate that time is actually more complex than the spatial domain as the formers dimensions are nonhomogeneous Section follows a similar organization in examining how facts may b e asso ciated with time Data mo deling issues are rst examined then representational t comparisons with space We briey con alternatives are explored with frequen sider how facts may b e simultaneously asso ciated with b oth space and time a common phenomena in land and geographic information systems We next consider languages for expressing temp oral queries We illustrate the various typ es of queries through examples in the temp oral query language TQuel and briey appraise various standards eorts Temp oral DBMS implementation is the topic of Sec We examine the im pact to each of the comp onents of a DBMS of adding temp oral supp ort dis cussing query optimization and evaluation in some detail We conclude with a summary of the ma jor accomplishments and disapp oint ments of research into temp oral databases We omit one ma jor asp ect that of database design due to lack of space The Time Domain In this section we fo cus on time itself how it is mo deled and how it is repre sented The next section will then combine time with facts to mo del timevarying information Structure We initially assume that there is one dimension of time The distinctions we address here will apply to each of the several dimensions we consider in the next section Early work on temporal logic centered around two structural mo dels of time linear and branching citevanBenthem In the linear mo del time advances from the past to the future in a totally ordered fashion In the branching mo del futures mo del time is linear from the past to now where also termed the possible it then divides into several time lines each representing a p otential sequence of events citeWorb oysA Along any future path additional branches may exist The structure of branching time is a tree ro oted at now The most general mo del of time in a temp oral logic represents time as an arbitrary set with a partial order imp osed on it Additional axioms intro duce other more rened or example linear time can b e sp ecied by adding an axiom mo dels of time F imp osing a total order on this set Recurrent pro cesses may b e asso ciated with a cyclic mo del of time citeChomickiA LorentzosC LorentzosB In spatial mo dels there is much less diversity and a linear mo del is generally adequate Axioms may also b e added to temp oral logics to characterize the density of the time line citevanBenthem Combined with the linear mo del discrete mo dels of time are isomorphic to the natural numb ers implying that each p oint in time has a single successor citeCliord Dense mo dels of time are iso morphic to either the rationals or the reals b etween any two moments of time another moment exists Continuous mo dels of time are isomorphic to the reals ie they are b oth dense and unlike the rationals contain no gaps In the continuous mo del each real numb er corresp onds to a p oint in time in the discrete mo del each natural numb er corresp onds to a nondecomp osable unit of time with an arbitrary duration Such a nondecomp osable unit of time is refered to as a chronon citeAriavACliordB other p erhaps less desir able terms include time quantum citeAnderson moment citeAllenB instant citeGadiaA and time unit citeNavatheTanselE A chronon is the smallest duration of time that can b e represented in this mo del It is not a p oint but a line segment on the time line Although time itself is generally p erceived to b e continuous most prop osals for adding a temp oral dimension to the relational data mo del are based on the discrete time mo del Several practical arguments are given in the literature for this preference for the discrete mo del over the continuous mo del First measures CLIFFORD Clo ck of time are inherently imprecise citeANDERSON ing instruments invariably rep ort the o ccurrence of events in terms of chronons not time p oints Hence events even socalled instantaneous events can at b est b e measured as having o ccurred during a chronon Secondly most natural language references to time are compatible with the discrete time mo del For example when we say that an event o ccurred at pm we usually dont mean that the event o ccurred at the p oint in time asso ciated with pm but at some time in the chronon p erhaps minute asso ciated with pm citeANDERSON CLIFFORDB DyresonD Thirdly the concepts of chronon and interval allow us to naturally mo del events that are not instanta neous but have duration citeANDERSON Finally any implementation of a data mo del with a temp oral dimension will of necessity have to have some discrete enco ding for time Sec Space may similarly b e regarded as discrete dense or continuous Note that in all three of these alternatives two separate spacelling ob jects cannot b e lo cated in the same p oint in space and time they can b e lo cated in the same place at dierent times or at the same time in dierent places Axioms can also b e placed on the boundedness of time Time can b e b ounded orthogonally in the past and in the future The same applies to mo dels of space Mo dels of time may include the concept of distance most temp oral logics do not do so however Both time and space are metrics in that they have a distance function satisfying four prop erties the distance is nonnegative the distance b etween any two nonidentical elements is nonzero the distance from time to time is identical to the distance from to and the distance from to is equal to or greater than the distance from to plus the distance from to the triangle inequality With distance and b oundedness restrictions on range can b e applied The scientic cosmology of the Big Bang p osits that time b egins with the Big Bang billion years ago There is much debate on when it will end dep ending on whether the universe is open or closed Hawking provides a readable intro duction to this controversy citeHawking If the universe is closed then time will have an end when the universe collapses back onto itself in what is called the Big Crunch If it is op en then time will go on forever Similar considerations apply to space In particular an op en universe im plies unb ounded space However many applications assume a b ound as well as a range geographical information systems dont need to contend with values greater than approximately million meters time from absolute time more precise Finally one can dierentiate relative terms are unachored and anchored For example AM Jan uary is an absolute time whereas hours is a relative time This distinction though is not as crisp as one would hop e b ecause absolute time is with resp ect to another time in this example midnight January AD We will show in Sec how to exploit this interaction Relative time diers from distance in that the former has a direction eg one could envision a relative time of hours whereas a distance is unsigned One can also dierentiate b etween relative and absolute space with the same provisos ity Dimensional Time is multidimensional citeSno dgrassA Valid time concerns the time a fact was true in reality The valid time of an