COMPLETENESS OF SECOND-ORDER PROPOSITIONAL S4 AND H IN TOPOLOGICAL SEMANTICS

被引：3
|
作者：
Kremer, Philip [1 ]
机构：
[1] Univ Toronto, Dept Philosophy, Toronto, ON M5S 3H7, Canada
来源：
REVIEW OF SYMBOLIC LOGIC | 2018年 / 11卷 / 03期
关键词：
second-order propositional logic; modal logic; intuitionistic logic; topological semantics; MODAL LOGIC; QUANTIFIERS;
D O I：
10.1017/S1755020318000229
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We add propositional quantifiers to the propositional modal logic S4 and to the propositional intuitionistic logic H, introducing axiom schemes that are the natural analogs to axiom schemes typically used for first-order quantifiers in classical and intuitionistic logic. We show that the resulting logics are sound and complete for a topological semantics extending, in a natural way, the topological semantics for S4 and for H.
引用
收藏
页码：507 / 518
页数：12
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