A 1NF temporal relational model and algebra coping with valid-time temporal indeterminacy

Abstract

In the real world, many phenomena are time related and in the last three decades the database community has devoted much work in dealing with "time of facts" in databases. While many approaches incorporating time in the relational model have been already devised, most of them assume that the exact time of facts is known. However, this assumption does not hold in many practical domains, in which temporal indeterminacy of facts occurs. The treatment of valid-time indeterminacy requires in-depth extensions to the current relational approaches. In this paper, we propose a theoretically grounded approach to cope with this issue, overcoming the limitations of related approaches in the literature. In particular, we present a 1NF temporal relational model and propose a new temporal relational algebra to query it. We also formally study the properties of the new data model and algebra, thus granting that our approach is interoperable with pre-existent temporal and nontemporal relational approaches, and is implementable on top of them. Finally, we consider computational complexity, showing that only a limited overhead is added when moving from determinate to indeterminate time.

Temporal Reasoning with Layered Preferences

“…For instance, the resume operation applied to the two following "compact" PyP_STP constraints, concerning RT and NA1 and concerning NA1 and NA2 respectively, produces as a result a new PyP_STP constraint concerning RT and NA2 ƒ , 1, …⟨ [5,24], ⟩, ⟨ [6,24], ⟩, ⟨ [6,24], ℎ ℎ⟩ ‡ˆ⊙ / ⟨ 1, 2, ⟨⟨ [10,15], ⟩, ⟨ [11,13], ⟩, ⟨ [12,12], ℎ ℎ⟩⟩⟩⟩ = ⟨ , 2, …⟨ [15,39], ⟩, ⟨ [17,37], ⟩, ⟨ [18,36], ℎ ℎ⟩ ‡⟩ Complexity of the ⊕ and ⊙ operators. Since the intersection and the sum of two intervals can be computed in constant time and they are computed for each preference value, both the ⊕ 7 and ⊙ 7 operators can operate in time Θ( ), where r is the number of preference values in Sr, thus ⊕ = ⊙ = Θ( ).…”

“…Although our approach is domain-and task-independent, we aim at applying it mainly within our GLARE project [12], to support physicians in the treatment of comorbid patients [13], by integrating medical preferences in the reasoning process. Moreover, we also wish to investigate its integration in temporal relational databases for dealing with temporal indeterminacy [14][15][16][17][18].…”

Relational model of temporal data based on 6th normal form

“…Four categories of temporal database have been identified with respect to valid and transaction times: snapshot, historical, rollback and bitemporal [2]. Snapshot databases store the single state of the real world (usually the most recent state), historical databases store data with respect to valid time, rollback databases store data with respect to transaction time and bitemporal databases store data with respect to both valid and transaction time [28].…”

“…A denormalized model and therefore an opposite approach, proposed by Anselma [2], presents a temporal relational model in the first normal form, together with new relational algebra to query it. In accordance with the relational theory, only efficient structures, achieved by high normalization, can prevent redundancy of the temporal data.…”

“…The temporal approach introduces additional complexities, such as dealing with model design and keys. It is difficult if not impossible to identify a substantial computer application that does not evolve over time [2]. This means that time-varying data is usually involved.…”