紧命题哥德尔逻辑

Proceedings. 1998 28th IEEE International Symposium on Multiple- Valued Logic (Cat. No.98CB36138) Pub Date : 1998-05-27 DOI:10.1109/ISMVL.1998.679315

M. Baaz, R. Zach

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引用次数: 44

摘要

命题哥德尔逻辑中的蕴涵可以用一种自然的方式来定义。虽然所有真值的无限集产生相同的重言式集，但蕴涵关系不同。证明了无限值哥德尔逻辑存在丰富的结构，其中只有一个是紧的。并证明了紧无限值哥德尔逻辑是唯一具有插值的逻辑，也是唯一具有正则蕴涵关系的逻辑。

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Compact propositional Godel logics

Entailment in propositional Godel logics can be defined in a natural way. While all infinite sets of truth values yield the same sets of tautologies, the entailment relations differ. It is shown that there is a rich structure of infinite-valued Godel logics, only one of which is compact. It is also shown that the compact infinite-valued Godel logic is the only one which interpolates, and the only one with an r.e. entailment relation.

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Proceedings. 1998 28th IEEE International Symposium on Multiple- Valued Logic (Cat. No.98CB36138)

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