Theory of Completeness for Logical Spaces

被引：0
作者：
Gomi, Kensaku [1 ]
机构：
[1] Univ Tokyo, Grad Sch Math Sci, 3-8-1 Komaba, Tokyo 1538914, Japan
来源：
LOGICA UNIVERSALIS | 2009年 / 3卷 / 02期
关键词：
universal logic; abstract logic; semantics; deduction; completeness;
D O I：
10.1007/s11787-009-0008-z
中图分类号：
B81 [逻辑学（论理学）];
学科分类号：
010104 ; 010105 ;
摘要：
A logical space is a pair (A, B) of a non-empty set A and a subset B of PA. Since PA is identified with {0, 1} A and {0, 1} is a typical lattice, a pair (A, F) of a non-empty set A and a subset F of BA for a certain lattice B is also called a B-valued functional logical space. A deduction system on A is a pair (R, D) of a subset D of A and a relation R between A* and A. In terms of these simplest concepts, a general framework for studying the logical completeness is constructed.
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收藏
页码：243 / 291
页数：49
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