We define formal notions of temporal domain and temporal database, and use them to survey a wide spectrum of temporal query languages. We distinguish between an abstract temporal database and its concrete representations, and accordingly between abstract and concrete temporal query languages. We also address the issue of incomplete temporal information. 1 Introduction A temporal database is a repository of temporal information. A temporal query language is any query language for temporal databases. In this paper we propose a formal notion of temporal database and use this notion in surveying a wide spectrum of temporal query languages. The need to store temporal information arises in many computer applications. Consider, for example, records of various kinds: financial [37], personnel, medical [98], or judicial. Also, monitoring data, e.g., in telecommunications network management [4] or process control, has often a temporal dimension. There has been a lot of research in temporal dat...

In valid-time indeterminacy it is known that an event stored in a database did in fact occur, but it is not known exactly when. In this paper we extend the SQL data model and query language to support valid-time indeterminacy. We represent the occurrence time of an event with a set of possible instants, delimiting when the event might have occurred, and a probability distribution over that set. We also describe query language constructs to retrieve information in the presence of indeterminacy. These constructs enable users to specify their credibility in the underlying data and their plausibility in the relationships among that data. A denotational semantics for SQL’s select statement with optional credibility and plausibility constructs is given. We show that this semantics is reliable, in that it never produces incorrect information, is maximal, in that if it were extended to be more informative, the results may not be reliable, and reduces to the previous semantics when there is no indeterminacy. Although the extended data model and query language provide needed modeling capabilities, these extensions appear initially to carry a significant execution cost. A contribution of this paper is to demonstrate that our approach is useful and practical. An efficient representation of valid-time indeterminacy and efficient query processing algorithms are provided. The cost of

This proposal represents the first phase of an on-going project to add temporal support to a conventional relational query language. We augment the Structured Query Language (SQL) with time values, i.e., temporal constants. The version of SQL we consider is SQL2, the most recent ANSI developed standardization of the language. Our approach is distinct in that we allow many different calendars to be used in the database management system, and we incorporate only calendar-independent constructs into the language. The proposal motivates and defines three new temporal data types. New language features are defined for temporal built-in functions, special time values, arithmetic expressions involving time, temporal predicates, and aggregate functions over time. Semantics and Backus-Naur-Form syntax are provided for all defined constructs. To illustrate the material, we present a comprehensive example of how the particular SQL2 calendar can be implemented within our proposal.

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Temporal Databases 9 Basic Building Blocks 10 The Snapshot Model 11 Snapshots: Example 12 Histories 13 The Timestamp Model 14 Timestamp Example 15 Query Languages 16 First-order Temporal Connectives 17 Examples of Temporal Connectives 18 Propositional Temporal Logic 19 First-order Temporal Logic: syntax 20 FOTL: semantics 21 Examples 22 Temporal Relational Calculus: syntax 23 Temporal RC: Semantics 24 Examples 25 Examples (cont.) 26 Expressive Power 27 Expressive Power (cont.) 28 How do we prove it? 29 Scope of Temporal Variables 30 Ehrenfeucht-Frass e Games 31 Ehrenfeucht-Frass e Games (cont.) 32 Ehrenfeucht-Frass e Games (cont.) 33 Ehrenfeucht-Frass e Games (cont.) 34 EF Games and Temporal Logic 35 Compatibility of Variables in FOTL 36 Databases not distinguishable by FOTL 37 Communication Complexity 38 Consequences for Temporal Queries 39 Temporal Relational Algebra 40 TRA: example 41 Temporal Logic TL(FO) 42 Plan 43 Concrete Temporal Databases 44 Finite Encoding using Constraints 4...

Temporal Databases 9 Basic Building Blocks 10 The Snapshot Model 11 Snapshots: Example 12 Histories 13 The Timestamp Model 14 Timestamp Example 15 Query Languages 16 First-order Temporal Connectives 17 Examples of Temporal Connectives 18 Propositional Temporal Logic 19 First-order Temporal Logic: syntax 20 FOTL: semantics 21 Examples 22 Temporal Relational Calculus: syntax 23 Temporal RC: Semantics 24 Examples 25 Examples (cont.) 26 Expressive Power 27 Expressive Power (cont.) 28 How do we prove it? 29 Scope of Temporal Variables 30 Ehrenfeucht-Frassb Games 31 Ehrenfeucht-Frassb Games (cont.) 32 Ehrenfeucht-Frassb Games (cont.) 33 Ehrenfeucht-Frassb Games (cont.) 34 EF Games and Temporal Logic 35 Compatibility of Variables in FOTL 36 Databases not distinguishable by FOTL 37 Communication Complexity 38 Consequences for Temporal Queries 39 Temporal Relational Algebra 40 TRA: example 41 Temporal Logic TL(FO) 42 Plan 43 Concrete Temporal Databases 44 Finite Encoding using Constraints 45 Interval Encoding 46 Interval Encoding (cont.) 47 Example 48 Why Intervals? 49 Interval Queries 50 Genericity 51 TSQL2 [Snodgrass, 1995] 52 Duplicate Semantics 53 TSQL2's Successors 54 Example 55 Coalescing 56 Example (cont,) 57 Failure of Coalescing 58 Folding and Unfolding 59 Other Proposals 60 Intervalsvs, True Intervals 61 Temporal Connectives in ,z 62 Translations 63 Closure for Intervals 64 SQL/TP [Toman, 1997] 65 SQL/TP: syntax 66 SQL/TP: encoding of time 67 SQL/TP: Query Evaluation 68 Data Definition Language 69 How do we compile Queries? 70 Closure for SQL/TP 71 Conditional Queries 72 Select Block: Join and Selection 73 Select Block: Duplicate Elimination 74 Time-compatible Queries 75 Normalization 76 Set Operations 77 Set Operations (cont,) 78 Set Operations (cont,) 79 Size of the ...