Curtis E. Dyreson and Richard T. Snodgrass. Valid-time Indeterminacy. In Proceedings of the IEEE Intl Conference on Data Engineering (ICDE), 1993.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....by constraints) offers a spatial relation based language, and, integrates geometric types into the data model. Our work is related also to temporal databases where the issues of granularity, scale and partially specified information have received considerable attention (e.g. Kou94a] [DS93], WJS93] in the last few years. To illustrate the expressiveness of the proposed spatial data model, consider the following query examples. 1. Querying Spatial Relations with Granularity. Assume the query: Find if the CS Dept. is inside the scope of V 1. This query may be initially evaluated ....

K. Dyreson and R. Snodgrass. Valid Time Indeterminacy. In Proceedings of the 9th International Conference on Data Engineering, 1993.

.... [1 Jan 1995 beg ; 1 Jan 1996 beg ) 1 Jan 1995 beg 1 Jan 1996 beg ) A formal treatment of determinate intervals and indeterminate time instants and mappings is given in [16] moreover, in handling indeterminacy, we have to consider modality, multiple valued logics, and probabilistic approaches [6, 11, 13, 21] for dealing with uncertainty in relationships. In the rest of this section, since determinate intervals and indeterminate time instants can be mapped to the domain of beginning time instants, we will concentrate on beginning time instants (hereinafter simply time instants) 4.2. Operations on ....

C.E. Dyreson and R.T. Snodgrass. Valid-time Indeterminacy. In Proc. 9th Int'l. Conf. on Data Engineering, IEEE Computer Society Press, Los Alamitos, 335-343, 1993.

....time domain, another temporal primitive exists. For any temporal primitive in a discrete time domain, there is a unique successor and predecessor. Similarly, in handling temporal indeterminacy, some researchers assume a dense temporal domain [12] while others assume a discrete temporal domain [8, 6]. Therefore, selecting the appropriate temporal domain is an integral part of defining a temporal model. Most of the research in the context of temporal databases has assumed that the temporal domain is discrete. Several arguments in favor of using a discrete temporal domain are made by Snodgrass ....

....described above, we are now able to represent determinate and indeterminate calendric instants and intervals and map them to indeterminate time sets that form a uniform, consistent, and sound settheoretical basis of our framework. This is in contrast to other works on temporal indeterminacy [8, 12, 6]. In [8, 6] the underlying temporal domain is assumed to be discrete, while the work of [12] is carried out in the context of a dense temporal domain. 6 Discussion The formalism developed in this paper gives us a framework in which granularities, calendars, calendric instants, and discrete ....

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C.E. Dyreson and R.T. Snodgrass. Valid-time Indeterminacy. In Proc. 9th Int'l. Conf. on Data Engineering, pages 335--343, April 1993.

....the granularity of the timestamps should be suitable for specific applications and hence postpone the choice of granularity to the logical design phase. C7 Support for Temporal (Im ) Precision The temporal variability of different objects in the mini world may be known with different precisions [18, 4, 7, 5]. Although some imprecision may be captured using multiple granularities, granularities are not a general solution. For example, the variability of an attribute may be recorded using timestamps with the granularity of a second, but the varying values may only be known to the precision of 5 ....

C. E. Dyreson and R. T. Snodgrass. Valid-time Indeterminacy. In Proceedings of the 9th International Conference on Data Engineering, pp. 335--343, 1993.

....A happened before event B and after January 23, 1992 ) GNP92] allows two kinds of indefinite information: i) the existence of a tuple in a relation over some interval of time can be uncertain, and (ii) attribute values can be unknown during the period of existence of a tuple in a relation. DS93] extend the model of [Sno87] by allowing the beginning and ending points of the validity interval of a tuple to be indefinite. There are also some other proposals (notably [KSW90] which deal successfully with infinite periodic data (e.g. the commitee meets every Monday ) On the other hand, ....

....interval [c; d] Gamma [a; b] The second kind of indefinite information allows attribute values to be unknown during the period of (possible or certain) existence of the tuple they belong. This kind of indefinite information is not expressible in our model. The possible chronons data model of [DS93] is similar to our proposal. DS93] extends the temporal database model of [Sno87] by allowing indeterminate events and intervals. An indeterminate event is one whose time of occurence cannot be precisely determined. In [DS93] s terminology, an indeterminate event is a set of possible chronons ....

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C. Dyreson and R. Snodgrass. Valid-time Indeterminacy. In Proceedings of the 9th International Conference on Data Engineering, pages 335--343, 1993.

....happened before event B and after January 23, 1992 ) 22] studied two kinds of indefinite temporal information: i) the existence of a tuple in a relation over some interval of time can be uncertain, and (ii) attribute values can be unknown during the period of existence of a tuple in a relation. [19] extended the model of [57] by allowing the beginning and ending points of the validity interval of a tuple to be indefinite. Finally, this author has proposed the model of temporal tables which exploits temporal constraints for the representation of indefinite and infinite temporal information ....

....As an example, consider the two statements The explosion occured after John left the scene and The explosion occured 5 to 10 minutes after John left the scene . ffl The granularity of the system time line does not match the precision to which the time associated with an event or fact is known [19]. As an example, consider storing the information John was hired on January 25, 1993 in a system with time stamps in the granularity of a second. Since this paper does not consider a TUS, we will not be able to give more examples of this kind of indefinite information. ffl Dating techniques can ....

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C. Dyreson and R. Snodgrass. Valid-time Indeterminacy. In Proceedings of the 9th International Conference on Data Engineering, pages 335--343, 1993.

....functions to some extent) In contrast, here we assume that dynamic attributes change continuously, and consequently the temporal data model is different than the data model presented in this paper. Thus, it is also not clear if and how temporal extensions to deal with imcomplete information (see [4, 7] are applicable to our context. Additionally, temporal languages other than FTL can be used to query MOST databases, but any other processing algorithm will have to be modified to handle dynamic attributes. Another relevant area is constraint databases (see [5] for a survey) In this sense, our ....

C. Dyreson and R. Snodgrass. Valid-time indeterminacy. International Conf. on Data Eng., Apr. 1993.

....ffl Is infinite or indefinite temporal information allowed in the new model Until very recently these kinds of temporal data had been ignored by database researchers. CI88, CI89, Cho90b, Cho90a, KSW90, BNW91, BCW93] have studied infinitely periodic temporal data while [Cha88, MBJK90, GNP92, DS93, vdM92, Kou93a] have concentrated on indefinite temporal data. ffl What is the expressive power of the new model and its query language What is the complexity of query processing in the new model Up to this point these questions have not received the attention they deserve from the database ....

....in various ways: 26 ffl The time associated with an event or fact might be specified via a qualitative relationship (different than equality) to some absolute time. As an example, consider the sentence John became manager after March, 1993 . 26 A similar discussion appears in [Sno92] and [DS93] In these papers the term indeterminate temporal information characterizes a strict subclass of indefinite temporal information. ffl The time associated with an event or fact might be specified via a relationship to the time associated with another event or fact. In this case, the two times ....

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C. Dyreson and R. Snodgrass. Valid-time Indeterminacy. In Proceedings of the 9th International Conference on Data Engineering, pages 335--343, 1993.

....second kind of information can be handled in our model using the difference between the universal relation and the union of the positive and negative components of a paraconsistent relation. A probabilistic approach to modelling indeterminate events and intervals is given in Dyreson and Snodgrass [8]. In this model, an indeterminate event is one whose time of occurrence cannot be precisely determined. However, none of the models discussed above supports inconsistent information. Our paraconsistent temporal algebra is an example of an abstract query language [5] Time is not explicitly ....

C. E. Dyreson and R. T. Snodgrass. Valid-time indeterminacy. In Proceedings of the 9th International Conference on Data Engineering, pages 335--344, Los Angeles, Calif., 1993. IEEE Computer Society Press.

....points and rectilinear regions, but as we show bellow, the integration of lines and polygons is straight forward. Our work is related also to temporal databases where the issues of granularity, scale and partially specified information have received considerable attention (e.g. Kou94a] DS93] WJS93] in the last few years. Work on undetermined boundaries [Had95] and multiple representations of space [PD95] RS95] are also related to this work. In fact, our model agrees with the proposal of [Had95] which suggests that undetermined boundaries can be founded on stochastic space, ....

K. Dyreson and R. Snodgrass. Valid Time Indeterminacy. In Proceedings of the 9th International Conference on Data Engineering, 1993.

....Rather, we focus on modeling temporal indeterminacy at the time primitives level namely, spans, instants, and intervals. Furthermore, we uniformly accommodate temporal indeterminacy arising from the representation of multiple granularities. Our work is closest to that of Dyreson Snodgrass [DS93] in that they support multiple granularities and deal with temporal indeterminacy. However, there are some differences between our approach and theirs: ffl We consistently represent discrete time information with different granularities and continuous time information in the same framework and ....

C.E. Dyreson and R.T. Snodgrass. Valid-time Indeterminacy. In Proc. 9th Int'l. Conf. on Data Engineering, pages 335--343, April 1993.

....we have in mind seem not to require any further complications. It is, however, conceivable that dealing with several dimensions of linear orderings and uncertainty is needed in two or three dimensional geographic applications. One of the few remarkable papers dealing with time uncertainty is [26]. Parts of these ideas also went in the TSQL2 language definition [32] The former paper discusses how to deal with time uncertainty (called time indeterminacy) However, the paper does not provide a solution to deal with time and uncertainty. If an event occurred but we don t know when, although ....

C. E. Dyreson and R. T. Snodgrass. Valid-time Indeterminacy. In Int Conf on Data Engineering, pages 335--343, 1993.

....and manipulation language extensions necessary to manipulate SQL i relations and data. Section 1. Introduction The need to represent indeterminate temporal information in TRDBMSs has been presented in [14] and a system to accommodate such information has been proposed using probabilistic methods [4]. Other researchers have proposed general constraint satisfaction methods to limit the occurrence time of events [9] methods utilising fuzzy set theory [12] and systems which use temporal rules in order to deduce further information [11] We utilise some of the general constraint satisfaction ....

Dyreson, C. and Snodgrass, R.: Valid-time Indeterminacy. Proc. of the 9th Int. Conf. on Data Engineering, pp. 335 - 343, 1993.

....State : Employee Theta T Theta ftrue,falseg B(SnapshotEmp Theta [0,1] Salary : SnapshotEmp B(Integer) Department : SnapshotEmp B(String) where B(X) denotes the set of all possible bags or multisets built from type X. One of the few remarkable papers dealing with time uncertainty is [19]. Parts of these ideas also went in the TSQL2 language definition [24] The former paper discusses how to deal with time uncertainty (called time indeterminacy) The paper does, however, not provide a solution to deal with time and uncertainty. If an event occurred but we don t know when although ....

C. E. Dyreson and R. T. Snodgrass. Valid-time Indeterminacy. In Int Conf on Data Engineering, pages 335--343, 1993.

....time domain, another temporal primitive exists. For any temporal primitive in a discrete time domain, there is a unique successor and predecessor. Similarly, in handling temporal indeterminacy, some researchers assume a dense temporal domain [12] while others assume a discrete temporal domain [8, 6]. Therefore, selecting the appropriate temporal domain is an integral part of defining a temporal model. Most of the research in the context of temporal databases has assumed that the temporal domain is discrete. Several arguments in favor of using a discrete temporal domain are made by Snodgrass ....

....described above, we are now able to represent determinate and indeterminate calendric instants and intervals and map them to indeterminate time sets that form a uniform, consistent, and sound settheoretical basis of our framework. This is in contrast to other works on temporal indeterminacy [8, 12, 6]. In [8, 6] the underlying temporal domain is assumed to be discrete, while the work of [12] is carried out in the context of a dense temporal domain. 6 Discussion The formalism developed in this paper gives us a framework in which granularities, calendars, calendric instants, and discrete ....

[Article contains additional citation context not shown here]

C.E. Dyreson and R.T. Snodgrass. Valid-time Indeterminacy. In Proc. 9th Int'l. Conf. on Data Engineering, pages 335--343, April 1993.

....procedures. Consequently, each alternative above must be adjusted to reflect the margin of error, e. Thus, if sensors predict alternative A is true with probability p, then the actual estimate is adjusted to be [max(0; p Gamma e) min(1; p e) 3. Temporal Indeterminacy: Dyreson and Snodgrass[10] have noted that in many cases, when a tuple in a relation is time stamped (this is called valid time) the stamp is in fact a temporal interval T I . For example, if a tuple t in such a relation is time stamped with the interval TI 0 , then this is interpreted as tuple t holds at some point ....

C.E. Dyreson and R.T. Snodgrass. (1993) Valid-time Indeterminacy, Proceedings of the International Conference on Data Engineering, Vienna, April, 1993, pp. 335--343.

....definitions from training examples. function is defined procedurally. For instance, given some numbers, the built in function Sum computes the sum of these numbers. Finally, derived functions are defined in a declarative way. One of the few remarkable papers dealing with time uncertainty is [6]. Part of these ideas also went in the TSQL2 language definition [7] The former paper discusses how to deal with time uncertainty (called time indeterminacy) The paper does not, however, provide a solution to deal with time and uncertainty. If an event occurred but we don t know when although it ....

....in example 2 is to replace all time points by time intervals. It might seem that we can then avoid the problems arising when modeling the application using time points. For example, instead of storing Valuation(F1,6 4 88,true) f10 000g, the information could also be stored as Valuation(F1,[6 4 88,6 10 88]) f10 000g, saying that Valuation(F1) f10 000g during the period [6 4 88,6 10 88] This has two drawbacks. Firstly, we need to know in advance when the information Valuation(F1,6 4 88,true) f10 000g will be replaced by fresh information (in our example this takes place at 6 10 88) ....

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C. E. Dyreson and R. T. Snodgrass. Valid-time Indeterminacy. In Int Conf on Data Engineering, pages 335--343, 1993.

....true even if we consider indefinite relational databases vs. indefinite temporal constraint databases. In future research we would like to use this work as a basis to study the complexity of query evaluation in other temporal database models particularly the ones allowing indefinite information [DS93, BCPT95]. Indefinite temporal information is important in many applications and has been included in TSQL2. Yet, in most cases, the presence of indefinite information makes query evaluation intractable. Therefore it is important to know what are the interesting cases where indefinite information can be ....

C. Dyreson and R. Snodgrass. Valid-time Indeterminacy. In Proceedings of the 9th International Conference on Data Engineering, pages 335--343, 1993.

....the granularity of the timestamps should be suitable for specific applications and hence postpone the choice of granularity to the logical design phase. C7 Support for Temporal (Im ) Precision The temporal variability of different objects in the mini world may be known with different precisions [17, 4, 7, 5]. Although some imprecision may be captured using multiple granularities, granularities are not a general solution. For example, the variability of an attribute may be recorded using timestamps with the granularity of a second, but the varying values may only be known to the precision of Sigma5 ....

C. E. Dyreson and R. T. Snodgrass. Valid-time Indeterminacy. In Proceedings of the 9th International Conference on Data Engineering, pages 335--343, Vienna, Austria, 1993.

....in [0; 1] State : Employee Theta T Theta ftrue,falseg B(SnapshotEmp Theta [0,1] Salary : SnapshotEmp B(Integer) Department : SnapshotEmp B(String) where B(X) denotes the set of all possible bags or multisets built from type X. One of the few papers dealing with time uncertainty is [7]. This paper discusses how to deal with time uncertainty (called time indeterminacy) but it does not provide solutions to deal with time and uncertainty. If an event occurred but we don t know when although it is clear that the event occurred in the period [t 1 ; t 2 ] then this is a case of ....

....uncertainty about the value alone. We present here the very first query language handling uncertainties also thorough intensional data definitions (intensional data definitions are views in the relational model, and derived function definitions in our object oriented model) Furthermore, whereas [7] is restricted to time points, we clearly and elegantly manage time points and intervals. We can provide function and attribute time stamping (see [5] for a comprehensive discussion) whereas this seems impossible in the mentioned study. Our language is able to deal with recursion (whereas the fine ....

C. E. Dyreson and R. T. Snodgrass. Valid-time Indeterminacy. In Int Conf on Data Engineering, pages 335--343, 1993.

....exactly when (i.e. what minute or hour) the decision occurred, then it is inappropriate to store that fact with a timestamp at a minute granularity. The reason is that a particular minute must be chosen, and that minute is probably incorrect, with the implication that the model is incorrect [DS93b] This property of time varying attributes is important for database design because temporal relational data models and query languages are frequently based on the (sometimes implicit) assumption that all time varying attributes of a relation may be recorded with the same precision. For example, ....

C. E. Dyreson and R. T. Snodgrass. Valid-time Indeterminacy. In Proceedings of the International Conference on Data Engineering, pages 335--343, Vienna, Austria, April 1993.

....Sometimes, the time when an event occurred is known only imprecisely. For instance, we may know that an event happened sometime in June 1993, which is an imprecise period of 30 days. An indeterminate instant is the time of an event, which is known to have occurred, but exactly when is unknown [Dyreson and Snodgrass 1993b, Dyreson 1994] The times when the event might have occurred is called the period of indeterminacy and is delimited by a lower and an upper bound (e.g. the event occurred sometime between June 1 and June 30) An indeterminate instant could have an associated probability distribution that gives ....

C. E. Dyreson and R. T. Snodgrass. Valid-time Indeterminacy. In Proceedings of the International Conference on Data Engineering, pp. 335--343, Vienna, Austria, April 1993.

....exactly when (i.e. what minute or hour) the decision occurred, then it is inappropriate to store that fact with a timestamp at a minute granularity. The reason is that a particular minute must be chosen, and that minute is probably 40 incorrect, with the implication that the model is incorrect [DS93b] This property of time varying attributes is important for database design because temporal relational data models and query languages are frequently based on the (sometimes implicit) assumption that all time varying attributes of a relation may be recorded with the same precision. For example, ....

C. E. Dyreson and R. T. Snodgrass. Valid-time Indeterminacy. In Proceedings of the International Conference on Data Engineering, pages 335--343, Vienna, Austria, April 1993.

....Sometimes, the time when an event occurred is known only imprecisely. For instance, we may know that an event happened sometime in June 1993, which is an imprecise period of 30 days. An indeterminate instant is the time of an event, which is known to have occurred, but exactly when is unknown [19, 21]. The times when the event might have occurred is called the period of indeterminacy and is delimited by a lower and an upper bound (e.g. the event occurred sometime between June 1 and June 30) An indeterminate instant could have an associated probability distribution that gives the ....

C. E. Dyreson and R. T. Snodgrass. Valid-time Indeterminacy. In Proceedings of the International Conference on Data Engineering, pp. 335--343, Vienna, Austria, April 1993.

....set or range of chronons. We call such an instant an indeterminate instant. The indeterminacy refers to the location of the instant, rather than to the existence of the instant. An indeterminate instant is described by a lower support , an upper support , and a probability mass function (p.m.f. [Dyreson and Snodgrass 1993]. The supports are chronons that delimit when the instant is located; the instant is no earlier than during the lower support and no later than during the upper support. Between the supports lies a period of indeterminacy . The period of indeterminacy is a contiguous set of possible chronons. The ....

....credibility is at a minimum when the indeterminacy is at a maximum. The credibility phrase is optional and has an initial default value of INDETERMINATE. The default value can be changed using a SET DEFAULT CREDIBILITY statement. This support for credibility simplifies that described elsewhere [Dyreson and Snodgrass 1993; Dyreson 1994; Dyreson and Snodgrass 1995b] The third syntactic extension concerns the ordering plausibility. The ordering plausibility is the plausibility in the where predicate among the instants, periods, and intervals that participate in the predicate. The default ordering plausibility is ....

Dyreson, C. E. and Snodgrass, R. T. 1993. Valid-Time Indeterminacy. In Proceedings of the International Conference on Data Engineering (Vienna, Austria, April 1993), pp. 335--343.

....between two determinate instants 3 . In our model of time, it is represented by a sequence of chronons, denoted by the starting and terminating chronons in the sequence. A period bounded by indeterminate instants (called the starting and terminating instants) is termed an indeterminate period [Dyreson 1994]. An indeterminate period could start during any member of the set of possible chronons of the starting instant. Likewise, the indeterminate period could end during any member of the set of possible chronons of the terminating instant. Since the location of the starting and terminating instants ....

....when the indeterminacy is at a maximum. The credibility phrase is optional and has an initial default value of INDETERMINATE. The default value can be changed using a SET DEFAULT CREDIBILITY statement. This support for credibility simplifies that described elsewhere [Dyreson and Snodgrass 1993; Dyreson 1994; Dyreson and Snodgrass 1995b] The third syntactic extension concerns the ordering plausibility. The ordering plausibility is the plausibility in the where predicate among the instants, periods, and intervals that participate in the predicate. The default ordering plausibility is specified using ....

Dyreson, C. E. 1994. Valid-time Indeterminacy. Ph. D. thesis, Computer Science Department, The University of Arizona.

....can be easily and efficiently used to support multiple calendars [Soo et al. 1992] In future, we will need to more thoroughly explore the issue of compact interval timestamps. New formats may also have to be developed for incomplete or imprecisely specified events, spans, and intervals [Dyreson Snodgrass 1993B, Gadia et al. 1991] Since not all the format types have been utilized, our design accommodates the addition of new timestamp formats. 25 Acknowledgements This work was supported in part by NSF grant ISI 8902707 and in part by IBM contract #1124. We would also like to thank Alan Condit, who ....

Dyreson, C.E. and R.T. Snodgrass. "Valid-Time Indeterminacy," to appear in Proceedings of the International Conference on Data Engineering. Vienna, Austria: Apr. 1993.

....indeterminate instant. For example, we may know that a plane left sometime on 1994 06 12, but, at the granularity of minutes, we do not know the minute during which that plane departed. An indeterminate instant is described by a lower support , an upper support , and a probability mass function [DS93b] The supports are granules that delimit when the instant is located; the instant is no earlier than the lower support and no later than the upper support. Between the support lies a period of indeterminacy . The period of indeterminacy identifies a set of possible granules . The instant is ....

C. E. Dyreson and R. T. Snodgrass. Valid-Time Indeterminacy. In Proceedings of the International Conference on Data Engineering, pages 335--343, Vienna, Austria, April 1993.

....techniques, uncertainty in planning, and unknown or imprecise event times. There have been several proposals for adding temporal indeterminacy to the time model [55, 65, 117] as well as more specific work on accommodating multiple time granularities [122, 223, 221] The possible chronons model [56] unifies treatment of both aspects [57] In this model, an event is determinate if it is known when (i.e. during which chronon) it occurred. A determinate event cannot overlap two chronons. If it is unknown when an event occurred, but known that it did occur, then the event is temporally ....

Dyreson, C.E., and Snodgrass, R.T., "Valid-time Indeterminacy," in Proceedings of the International Conference on Data Engineering, pp. 335--343, Vienna, Austria, April 1993.

....known exactly when (i.e. what minute or hour) the decision occurred, then it is inappropriate to store that fact with a timestamp at a minute granularity. The reason is that a particular minute must be chosen, and that minute is probably incorrect, with the implication that the model is incorrect [17]. This property of time varying attributes is important for database design because temporal relational data models and query languages are frequently based on the (sometimes implicit) assumption that all time varying attributes of a relation may be recorded with the same precision. For example, ....

C. E. Dyreson and R. T. Snodgrass. Valid-time Indeterminacy. In Proceedings of the International Conference on Data Engineering, pp. 335--343, Vienna, Austria (1993).

....set or range of chronons. We call such an instant an indeterminate instant. The indeterminacy refers to the location of the instant, rather than to the existence of the instant. An indeterminate instant is described by a lower support , an upper support , and a probability mass function (p.m.f. DS93] The supports are chronons that delimit when the instant is located; the instant is no earlier than during the lower support and no later than during the upper support. Between the supports lies a period of indeterminacy . The period of indeterminacy is a contiguous set of possible chronons . ....

.... [ hinstant 1 i OVERLAPS PERIOD( hinstant 2 i, hinstant 3 i) op = Before I ( hinstant 2 i ] SQL ; hinstant 1 i ] SQL ; fl) T Before I ( hinstant 1 i ] SQL ; hinstant 3 i ] SQL ; fl) Elsewhere we show how constructors can be extended in the presence of indeterminacy [DS93] We reiterate that in the probabilistic ordering all instants are assumed to be independent. So in the expression Before I (e 2 ; e 3 ; fl) AND Before I (e 3 ; e 4 ; fl) the two Before I operations operations are separately evaluated, returning a set of boolean values that is subsequently ....

C. E. Dyreson and R. T. Snodgrass. Valid-time Indeterminacy. In Proceedings of the International Conference on Data Engineering, pp. 335--343, Vienna, Austria, April 1993.

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Curtis E. Dyreson and Richard T. Snodgrass. Valid-time Indeterminacy. In Proceedings of the IEEE Intl Conference on Data Engineering (ICDE), 1993.

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C. E. Dyreson and R. T. Snodgrass. Valid-time Indeterminacy. In Proceedings of the IEEE Intl Conference on Data Engineering (ICDE), 1993.

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C.E. Dyreson and R.T. Snodgrass. Valid-time Indeterminacy. In Proc. 9th Int'l. Conf. on Data Engineering, pages 335--343, April 1993.

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# C.E. Dyreson and R.T. Snodgrass, "Valid-Time Indeterminacy," Proc. Ninth Int'l Conf. Data Eng., pp. 335--343, 1993.

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C.E. Dyreson and R.T. Snodgrass. Valid-time Indeterminacy. In Proc. 9th Int'l. Conf. on Data Engineering, pages 335--343, April 1993.

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