Temporal Relational Calculus
Temporal Relational Calculus
复制标题
时间关系演算
DOI：
10.1007/978-0-387-39940-9_1531
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
David Toman
中科院分区：
文献类型：
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作者：
J. Chomicki;David Toman
正文关系演算的自然时间扩展允许在给定的时间域上显式变量和量化，以及在未解释的常量的数据域上的变量和量词。该语言只是数据域D和时间域T上的一阶逻辑的两个分类版本(变量和常量是临时的或非临时的)。数据库模式ρ={r1，.。。，Rk}由语法规则定义：Q：：=R(ti，xi1，.。。，xik)|ti<；tj|xi=xj|q∧q|q|∃xi.q|∃ti.q在语法中，ti‘s用于表示时间变量，xi’s用于表示数据(非时间)变量。原子式ti<；tj提供了引用时间域的基本排序的手段。请注意，模式ρ包含带时间戳的时态关系的模式(请参阅带入口点戳的时态模型)。给定点时间戳数据库DB和两个排序的赋值θ，以标准方式(类似于关系演算的语义)使用满足关系DB，θ|=Q：Db，θ|=Rj(ti，xi1，.。。，xik)如果Rj∈ρ和(θ(Ti)，θ(Xi1)，.。。，θ(Xik))∈R j Db，θ|=ti<；tj ifθ(Ti)<；θ(Tj)DB，θ|=xi=xj ifθ(Xi)=θ(Xj)DB，θ|=q1∧q2 if DB，θ|=q1 and DB，θ|=q1 if Not DB，θ|=q1 if Not DB，θ|=Q1 ifθ|=∃∈T使得DB，θ[ti 7→S]|=q1 DB，θ|=∃xi.Q1如果存在∈D使得DB，θ[xi 7→a]|=q1其中Rj是数据库DB中谓词符号RJ的解释。查询Q over DB的答案是使Q在DB中为真的赋值集合Q(DB)。即Q(Db)：={θ|Fv(Q)：Db，θ|=Q}其中θ|Fv(Q)是估值θ对Q的自由变量的限制。
MAIN TEXT A natural temporal extension of the relational calculus allows explicit variables and quantification over a given time domain, in addition to the variables and quantifiers over a data domain of uninterpreted constants. The language is simply the two-sorted version (variables and constants are temporal or non-temporal) of first-order logic over a data domain D and a time domain T . The syntax of the two-sorted first-order language over a database schema ρ = {R1, . . . , Rk} is defined by the grammar rule: Q ::= R(ti, xi1 , . . . , xik) | ti < tj | xi = xj | Q ∧Q | ¬Q | ∃xi.Q | ∃ti.Q In the grammar, ti’s are used to denote temporal variables and xi’s to denote data (non-temporal) variables. The atomic formulae ti < tj provide means to refer to the underlying ordering of the time domain. Note that the schema ρ contains schemas of timestamped temporal relations (see the entry Point-stamped Temporal Models). Given a point-timestamped database DB and a two-sorted valuation θ, the semantics of a TRC query Q is defined in the standard way (similarly to the semantics of relational calculus) using the satisfaction relation DB, θ |= Q: DB, θ |= Rj(ti, xi1 , . . . , xik) if Rj ∈ ρ and (θ(ti), θ(xi1), . . . , θ(xik)) ∈ R j DB, θ |= ti < tj if θ(ti) < θ(tj) DB, θ |= xi = xj if θ(xi) = θ(xj) DB, θ |= Q1 ∧Q2 if DB, θ |= Q1 and DB, θ |= Q2 DB, θ |= ¬Q1 if not DB, θ |= Q1 DB, θ |= ∃ti.Q1 if there is s ∈ T such that DB, θ[ti 7→ s] |= Q1 DB, θ |= ∃xi.Q1 if there is a ∈ D such that DB, θ[xi 7→ a] |= Q1 where R j is the interpretation of the predicate symbol Rj in the database DB. The answer to a query Q over DB is the set Q(DB) of valuations that make Q true in DB. Namely, Q(DB) := {θ|FV (Q) : DB, θ |= Q} where θ|FV (Q) is the restriction of the valuation θ to the free variables of Q.