时态查询语言的并发Lambek演算及范畴语法

Concurrence Lambek calculus and its categorical grammar in temporal querying languages

时态逻辑不可递归公理化的性质,造成它的公理化系统和证明论方法不适于时态查询语言的建模.这使得时态逻辑无法利用公理化系统的良好性质及相关证明论方法对时态数据库的推理和查询做更为严谨和细致地刻画.因此寻找时态逻辑的替代者,以公理化的方式对时态查询语言做句法和语义的分析是必要的.考虑的2个主要工具是作为句法分析工具的以Lambek演算为核心的范畴语法系统,和作为语义分析工具的类型演算λ-演算.这主要是基于类型论的演算特点、SQL语句与陈述句的相似性、Lambek演算和λ-演算的公理化与证明论方法,及它们作为句法和语义分析工具之间的密切联系与对应性决定的.据此从Lambek演算出发,结合时态的处理,构建了并发的Lambek演算(LCTQ)及相应的范畴语法,对以公理化系统为基础的时态查询语言的句法分析做相关研究,并从证明论性质上保障了计算性资源,使得系统更为严谨和完善.

Axiomatic systems and proof methods for temporal logic have so far found relatively few applications in querying language modeling of temporal databases because the standard temporal logic is not recursively axiomatizable. As a result, temporal logic can not use axiomatic systems and proof methods to religiously depict inference and querying of a temporal database. Thus it is necessary to find a replacement for temporal logic which, by axiomatic methods, can become the implement of a syntactic and semantic analysis of temporal querying languages. The Lambek calculus and its categorical grammar as the former and k-calculus as the latter have become those substitutes in this paper, because of the properties of type theory, the comparability between SQL and state sentence, the axiomatic and proof methods of Lambek calculus and k-calculus, and their correspondence by Curry-Howard Isomorphism. So, according to the operations of temporality, we built a new axiomatic system used in syntactic analysis which is called concurrence Lambek calculus （ LCTQ ） , and use its categorial grammar to deal with the temporal querying language. Prof theory shows that for protection of computable resources, LCTQ is more regorous and ideal.