Empirical Negation, Co-Negation and the Contraposition Rule II: Proof-Theoretical Investigations

Satoru Niki

doi:10.18778/0138-0680.2020.13

Authors

Satoru Niki Japan Advanced Institute of Science and Technology School of Information Science 923-1292, 1-1 Asahidai, Nomi Ishikawa, Japan http://orcid.org/0000-0002-0882-806X

DOI:

https://doi.org/10.18778/0138-0680.2020.13

Keywords:

empirical negation, co-negation, labelled sequent calculus, intuitionism

Abstract

We continue the investigation of the first paper where we studied logics with various negations including empirical negation and co-negation. We established how such logics can be treated uniformly with R. Sylvan's CC_ωas the basis. In this paper we use this result to obtain cut-free labelled sequent calculi for the logics.

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