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ON POLY-LOGISTIC NATURAL-DEDUCTION FOR FINITELY-VALUED PROPOSITIONAL LOGICS

被引：0
|
作者：
Francez, Nissim [1 ]
Kaminski, Michael [1 ]
机构：
[1] Technion IIT, Dept Comp Sci, Haifa, Israel
来源：
JOURNAL OF APPLIED LOGICS-IFCOLOG JOURNAL OF LOGICS AND THEIR APPLICATIONS | 2019年 / 6卷 / 02期
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D O I：
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中图分类号：
B81 [逻辑学（论理学）];
学科分类号：
010104 ; 010105 ;
摘要：
The paper presents a systematic construction of natural-deduction proof-systems for multi-valued logics from the truth-tables for the connectives. The construction is based on poly-sequents of the form Gamma(1) vertical bar ... vertical bar Gamma(n) : Delta(1)vertical bar ... vertical bar Delta(n), n >= 2, improving on a previous approach by Baaz et. al. [2] Poly-sequents allow to speak explicitly about the truth-value of a formula, and have in I/E-rules both assumptions and conclusion that have any truth-value. Soundness and strong completeness are proved. The generality of the construction is exemplified by retrieving within the constructed ND-system a host of well-known ND-systems for multi-valued logics.
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页码：255 / 288
页数：34
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