关于厄克特的C逻辑

Proceedings 30th IEEE International Symposium on Multiple-Valued Logic (ISMVL 2000) Pub Date : 2000-05-23 DOI:10.1109/ISMVL.2000.848608

A. Ciabattoni

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引用次数: 8

摘要

在本文中，我们研究了Urquhart(1986)引入的基本多值逻辑，这里分别称为C和C/sub new/。我们定义了C/sub - new/的无切超序演算，并给出了以下结果:(1)C和C/sub - new/是哥德尔逻辑的不同版本，没有收缩。(2) C/sub / new/ is determined。(3)在C/sub new/中，公理族((A/sup k//spl rarr/C)/spl rarr和/(B/sup k//spl rarr/C)/spl rarr/((AVB)/sup k//spl rarr/C)与k/spl ges/2实际上是冗余的。

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On Urquhart's C logic

In this paper we investigate the basic many-valued logics introduced by Urquhart (1986), here referred to as C and C/sub new/, respectively. We define a cut-free hyper-sequent calculus for C/sub new/ and show the following results: (1) C and C/sub new/ are distinct versions of Godel logic without contraction. (2) C/sub new/ is decidable. (3) In C/sub new/ the family of axioms ((A/sup k//spl rarr/C)/spl and/(B/sup k//spl rarr/C))/spl rarr/((AVB)/sup k//spl rarr/C), with k/spl ges/2, is in fact redundant.

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Proceedings 30th IEEE International Symposium on Multiple-Valued Logic (ISMVL 2000)

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