Title: Subminimal negation based on a class of absurdities
Abstract:
In this talk we will discuss several approaches to add a negation to
the positive part of the intuitionistic propositional logic, like
minimal negation and subminimal negations. One such logic is the
propositional contraposition logic, CoPC, which has as its only axiom
for negation (p -> q)-> (-q -> -p). For this logic two different types
of semantics are known. One is a neighborhood semantics, the other,
surprisingly, a generalization of the semantics for minimal logic,
using, instead of one â€˜absurdumâ€™, a class of absurdities. We will
point out the relationship between the two semantics and briefly
discuss the arithmetic based on contraposition logic.