量词模态逻辑的代数语义学（Ⅲ）──关于不含Barcan公式的正规模态系统的情形

本文首先讨论嵌套论域语义的相应代数语义并由Ｈｕｇｈｅｓ和Ｃｒｅｓｓｗｅｌｌ在［５］中建立的关于具有嵌套论域的正规量词模态系统的关系语义完全性定理推出其相应的代数语义完全性定理：然后对于具有任意可变论域语义的正规系统，我们用Ｈｅｎｋｉｎ方法给出其关于狭义Ｋｒｉｐｋｅ语义的关系语义完全性定理，由此通过将关系语义转化为代数语义从而亦推得其代数语义完全性定理。

A1gebraic Semantics for Quantifed Modal Logic (III)──The Case of Normal Modal Systems without the Barcan Formula

In this paper we acquaint the reader first with the algebraic semantics which is corre-sponding to the Kripke’s semantic having nested domaius. By an application of the completenesstheorem on relational semantics of the quantified normal modal systems with nested domains proved in Hughes and Cresswell’s method to prove a completeness theorem on relational algebraic semantics of those system. Next for normal systems with semantics which admits arbi-trarily variable domains we use Henkin’s method to prove a completeness theorem on relationalsemantics of them which is concerning with Kripke’s special semantic; then through the con-version of relational semantics to algebraic ones we obtained also the completeness theorem onalgebraic semantics of those systems.