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Empirical Negation, Co-negation and Contraposition Rule I: Semantical Investigations

Satoru Niki — 2020

Bulletin of the Section of Logic

We investigate the relationship between M. De's empirical negation in Kripke and Beth Semantics. It turns out empirical negation, as well as co-negation, corresponds to different logics under different semantics. We then establish the relationship between logics related to these negations under unified syntax and semantics based on R. Sylvan's CCω.

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

Satoru Niki — 2020

Bulletin of the Section of Logic

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 CCω as the basis. In this paper we use this result to obtain cut-free labelled sequent calculi for the logics.

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