What Is Negation in a System 2020?

Dov M. Gabbay

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


The notion of negation is basic to any formal or informal logical system. When any such system is presented to us, it is presented either as a system without negation or as a system with some form of negation. In both cases, we are supposed to know intuitively whether there is no negation in the system or whether the form of negation presented in the system is indeed as claimed. To be more specific, suppose Robinson Crusoe writes a logical system with Hilbert-type axioms and rules, which includes a unary connective ∗ A. He puts the document in a bottle and lets it lose at sea. We find it and take a look. We ask: is the connective “ ∗ ” a negation in the system? Yet the notion of what is negation in a formal system is not clear.

Original languageEnglish
Title of host publicationOutstanding Contributions to Logic
PublisherSpringer Science and Business Media B.V.
Number of pages29
StatePublished - 2021
Externally publishedYes

Publication series

NameOutstanding Contributions to Logic
ISSN (Print)2211-2758
ISSN (Electronic)2211-2766

Bibliographical note

Publisher Copyright:
© 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.


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