Title: Semantic and proof-theoretic aspects of subminimal negation

Abstract:
The legitimacy of /ex falso quodlibet/ as one of the properties of
intuitionistic negation has been controversial. Johansson’s
/Minimalkalkül/ was introduced in 1937 as a possible solution to this
problem, and is obtained from the positive fragment of intuitionistic
propositional calculus by adding a unary negation operator satisfying
the principle of contradiction. The aim of this talk is to give an
overview of some recent developments in the study of subsystems of
Johansson's logic—obtained by extending the positive fragment of
intuitionistic logic with weaker unary negations—with special emphasis
on the latest proof-theoretic developments. If time allows, we are
also going to present the matter from a different angle, by
interpreting the weak negations as non-normal modal operators.

This talk is based on joint work with Marta Bilkova.