Logics for Databases and Information Systems by Jan Chomicki, Gunter Saake

By Jan Chomicki, Gunter Saake

Time is ubiquitous in info platforms. virtually each company faces the matter of its facts changing into old-fashioned. even though, such information is frequently valu­ capable, so it's going to be archived and a few ability to entry it's going to be supplied. additionally, a few facts could be inherently historic, e.g., clinical, cadastral, or ju­ dicial documents. Temporal databases supply a uniform and systematic method of facing ancient facts. Many languages were proposed for tem­ poral databases, between others temporal common sense. Temporal good judgment combines ab­ stract, formal semantics with the amenability to effective implementation. This bankruptcy exhibits how temporal common sense can be utilized in temporal database applica­ tions. instead of providing new effects, we record on fresh advancements and survey the sphere in a scientific approach utilizing a unified formal framework [GHR94; Ch094]. The guide [GHR94] is a finished reference on mathematical foundations of temporal common sense. during this bankruptcy we examine how temporal good judgment is used as a question and integrity constraint language. accordingly, model-theoretic notions, fairly for­ mula pride, are of basic curiosity. Axiomatic platforms and facts meth­ ods for temporal good judgment [GHR94] have chanced on to this point really few functions within the context of knowledge platforms. in addition, one must take into account that for a standard linearly-ordered time domain names temporal good judgment isn't re­ cursively axiomatizable [GHR94]' so recursive axiomatizations are via necessity incomplete.

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For simplicity from now on we assume a discrete integer-like structure of time. However, dense time can also be accommodated by introducing open and half-open intervals. All the results in this section carryover to the latter setting. Definition 21 (Interval-based Domain T I ) Let Tp = (T, <) be a discrete linearly ordered point-based temporal domain. We define the set J(T) = {(a, b) : a ~ b, a E T U {-oo}, bET U {oo}} where < is the order over Tp extended with {( -00, a), (a, (0), (-00, (0) : a E T} (similarly for~).

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If there is a negated literal with a predicate symbol p in a rule which we need to derive tuples for a predicate of stratum Si, then all positive facts with that predicate symbol p have already been computed because p belongs to a stratum Sj with j < i. Then we say that a negative literal -'CP cannot be satisfied by a substitution if the corresponding positive literal cp was derived before. , -'Cp is a consequence of the logic program because cp cannot b~ proven. Stratification does not provide semantics for logic programs which are not stratifiable and which cannot be transformed into an equivalent stratifiable logic program.

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