ON THREE-VALUED PRESENTATIONS OF CLASSICAL LOGIC

被引：2

作者：

Da Re, Bruno ^{[1
,2
]}

Szmuc, Damian ^{[1
,2
]}

Chemla, Emmanuel ^{[3
]}

Egre, Paul ^{[4
]}

机构：

[1] IIF CONICET SADAF, Buenos Aires, DF, Argentina

[2] Univ Buenos Aires, Dept Philosophy, Buenos Aires, DF, Argentina

[3] EHESS, LSCP CNRS, ENS PSL, Paris, France

[4] EHESS, Inst Jean Nicod CNRS, ENS PSL, Paris, France

来源：

REVIEW OF SYMBOLIC LOGIC | 2024年 / 17卷 / 03期

关键词：

classical logic; strict-tolerant logics; three-valued logics; logical consequence; CONSEQUENCE; TRUTH;

D O I：

10.1017/S1755020323000114

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Given a three-valued definition of validity, which choice of three-valued truth tables for the connectives can ensure that the resulting logic coincides exactly with classical logic? We give an answer to this question for the five monotonic consequence relations st , ss , tt , ss n tt , and ts , when the connectives are negation, conjunction, and disjunction. For ts and ss n tt the answer is trivial (no scheme works), and for ss and tt it is straightforward (they are the collapsible schemes, in which the middle value acts like one of the classical values). For st , the schemes in question are the Boolean normal schemes that are either monotonic or collapsible.

引用

页码：682 / 704

页数：23

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