A logical framework for temporal deductive databases S. M. Sripada Departmentof Computing Imperial College of Science& Technology 180 Queen’sGate, London SW7 2BZ Abstract researchers have incorporated time into conventional databasesusing various schemes Temporal deductive databases are deductive providing different capabilities for handling databaseswith an ability to representboth valid temporal information. In particular, work has time and transaction time. The work is basedon been done on adding temporal information to the Event Calculus of Kowalski & Sergot. Event conventionaldatabases to turn them into temporal Calculus is a treatment of time, based on the databases. However, no work is done on notion of events, in first-order classical logic handling both transaction time and valid time in augmentedwith negation as failure. It formalizes deductive databases.In this paper we propose a the semanticsof valid time in deductivedatabases framework for dealing with time in temporal and offers capability for the semantic validation deductivedatabases. of updates and default reasoning. In this paper, the Event Calculus is extended to include the Snodgrass dz Ahn [16,17] describe a concept of transaction time. The resulting classification of databasesdepending on their framework is capable of handling both proactive ability to represent temporal information. They and retroactive updates symmetrically. Error identify three different concepts of time - valid correction is achievedwithout deletionsby means time, transaction time and user-defined time. Of of negation as failure. The semantics of these, user-defined time is temporal transaction time is formalised and the axioms of information of some kind that is of interest to the the Event Calculus are modified to cater for user but does not concern a DBMS. It is just temporal databases. Given a description of treated as any other non-temporal attribute. events, axioms are presented for deducing Valid time is the time for which information relationships and the time periods for which they models reality and correspondsto the actual time hold with respect to any past/presentstate of the for which a relationship holds in the real world. database. Transaction time, on the other hand, is the time at which information is stored in the (1) Introduction database. Databases which represent only the latest snapshotof the world being modelled are Interest in researchconcerning the study of time called snapshot databases. All conventional in databaseshas been growing steadily over the databasescome under this category, for example, past few years. The study of time has attracted INGRES[20]. Databases which represent transaction time alone and therefore treat valid researchersfrom various fields such as artificial time and transaction time as identical are called intelligence, databases, natural language rollback databases since it is possible to processing,logic and concurrent systems.Many rollback to a past state of the databaseand pose a query with respect to that state. The POSTGRES[21] model is a database in this Permission to copy without fee alI or put of this mat&l is category. The problem with representing granted provided tht the copies are not made cr distributed for transaction time alone is that a history of the direct axnmexcial advantage, the VIDB copyright notice and database activities is recorded (since every the title of the publication end its date appca, end notice is given databasestate is stored, in effect), rather than the chat copying is by permission of the Very Large Data Bose history of the world being modelled. Thus it is Endowment. To copy o&wise, or to republish. requires a fee not possibleto make proactive/retroactiveupdates and/or special permission from the Endowmcnt. and errors in a past statecannot be corrected. Proceedingsof the 14thVLDB Conference Los Angeles,California 1988 171 Databases which store the history of the real primitive. Various relationships and the time world as is best known are called historical periods for which they hold are derived from a databases[2,4,5,9,10,12].These databaseshave description of events that occur in the real the concept of valid time alone but it is possible world. The approach is closely related to Lee et to make changes to the history of each tuple. al.‘s[10,14] treatment of time in deductive Thus changescould be made to reflect the past as databasesand Allen’s interval temporal logic[ 11. is best known. Finally, databaseswhich store all In his paper, Kowalski[9] deals with database the past history as is best known at every stateof updates using the Event Calculus and compares the databaseare called temporal databases[191. this approach with updates in a conventional These databasesinvolve a representationof both relational databaseand the use of modal temporal valid time and transactiontime for each tuple. An logic, situation calculus and case semantics for extensive bibliography of research concerning storing and updating information in a database.It time in databasesis given in [13,18]. is argued that the Event Calculus combines the expressive power of both case semantics and Temporal databasesare especially useful when situation calculus, derives the computational updates have retrospective effect. For example, power of logic programming and overcomesthe in [ 151, Sergot et al. discuss the representation frame problem of the situation calculus. Schemes of the British Nationality Act as a logic program. for specializing the Event Calculus so as to make A databasemight be used to record the details of it comparable in efficiency to that of relational a person. The logic program can then be used to databaseswith destructive assignment are also deduce whether or not that person is, according presented in Kowalski[9]. In the following, we to the act, a British citizen. As the person’s give an outline of the treatment of time in the details change, their status can change Event Calculus. accordingly. It is possible for a personto become a British citizen and for this statusto have effect In the Event Calculus, event descriptions are from the date of their birth. A temporal database used to deduce the existence as well as the preserves the distinction between what was initiation and termination of time periods. Each previously considered to be their status at the time period is uniquely identified by a time of their birth and what is now considered combination of the relationship that holds during to be their status at that time. This capability is the time period and the event which initiates or achieved by an explicit storage of the time at terminates the period. This is so, because,each which information becomesavailable. In the case eventmay initiate or terminatemore than one time of databases, this time is referred to as the period and there may be several different time transactiontime. periods in which the same relationship holds. The term[7,11] after(e r) is used to denote a In this paper, we extend the Event Calculus of time period started by an event e in which the Kowalski & Sergot[8] to formalize the semantics relationship r holds. Similarly, the term of time for temporal deductive databases.In the before(e r) is used to denote a time period following section, we outline the treatment of terminated by the event e in which the time in the Event Calculus. In section 3, we relationship r holds. The atom[7,11] outline the framework, in section 4 we formalize Holds(after(e r)) is a shorthand version for the the semantics of transaction time in temporal atom Holds(r after(e r)) and means that the databases and, in section 5, we modify the relationship r holds in the time period after(e r). axioms of the Event Calculusto accommodatethe Similarly, the atom Holds(before(e r)) asserts concept of transaction time thereby forming a the fact that the relationship r holds in the period theory of time for temporal deductivedatabases. before(e r). For example, let El be an event in which John (2) Event Calculus gave a book to Mary and E2 be an event in which Mary gave the book to Bob. Assume that The Event Calculus of Kowalski & Sergot[8] is a E2 occurred after El. Then, given these event treatment of time formalized in first-order descriptions, we could deduce that there is a classical logic augmented with negation as period started by the event El in which Mary failure[3]. It is basedon the notion of an event as possessesthe book and that there is a period 172 terminated by El in which John possessesthe Start(after(e r) e) EC3 book. This is representedpictorially in Fig 1. End(before(e r) e) EC4 Start(before(e’ r) e) if 1” after(e r) = before(e’ r) EC5 End(after(e r) e’) if after(e r) = before(e’ r) EC6 Theseaxioms allow us to deducethat Fig 1 (i)the period after(E1 possesses(Mary Book)) is started by the event E 1 (using axiom EC3 ) (ii)the period before(E1 possesses(John The axioms of the Event Calculus for deducing Book)) is terminated by the event El (axiom such time periods are as follows: EC4) (iii)the period before(E2 possesses(Mary Holds(before(e r)) if Terminates(e r) EC1 Book)) is startedby the event El if the periods afer(EI possesses(Mary Book)) and Holds(after(e r)) if Initiates(e r) EC2 before(E2 possesses(Mary Book)) are identical (axiom EC5) and These axioms are used along with application (iv)the period after(E1 possesses(Mary Book)) specific rules such as is terminated by the event E2 if the periods ajler(El possesses(Mary Book)) and Initiates(e possesses(xy)) if before(E2 possesses(Mary Book)) are identical Act(e give) and (axiom EC6). Recipient(e x) and Object(e y) However, deducing that two time periods are and identical involves some default reasoningsince it dependson the assumption that there is no event Terminates(e possesses(xy)) if in between which initiates or terminates a Act(e give) and conflicting time period.