On the translation from quantified modal logic into the counterpart theory

被引：0

作者：

Shen, Yu-Ming ^{[1
]}

Wang, Ju ^{[1
]}

Tang, Su-Qin ^{[1
]}

Jiang, Yun-Cheng ^{[2
]}

机构：

[1] School of Mathematics, Guangxi Normal University, Guilin 541004, China

[2] School of Computer Science, South China Normal University, Guangzhou 510631, China

来源：

Ruan Jian Xue Bao/Journal of Software | 2012年 / 23卷 / 09期

关键词：

Counterpart theories - Faithful and full translations - First order logic - Quantified modal logic - Satisfiability - Sound and complete;

D O I：

10.3724/SP.J.1001.2012.04163

中图分类号：

学科分类号：

摘要：

The counterpart theory is a theory of first-order logic. Lewis interprets modal claims by using a translation from quantified modal logic into the counterpart theory. However, Lewis's translation does not preserve the unsatisfiability of formulas. In this paper, an extended semantics for quantified modal logic is introduced, and the corresponding connection between models of the quantified modal logic and models of the counterpart theory is given. Based on the semantics, a faithful and full translation from quantified modal logic to the counterpart theory, which preserves the satisfiability and the unsatisfiability of formulas, is also established. Furthermore, since the counterpart theory is sound and complete, and the soundness and the completeness are preserved by the faithful and full translation, the quantified modal logic is also sound and complete. © 2012 ISCAS.

引用

页码：2323 / 2335

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