Kapsner Complementation: An Algebraic Take on Kapsner Strong Logics

Abstract

AbstractKapsner strong logics, originally studied in the context of connexive logics, are those in which all formulas of the form $$A\rightarrow \lnot A$$ A → ¬ A or $$\lnot A\rightarrow A$$ ¬ A → A are unsatisfiable, and in any model at most one of $$A\rightarrow B, A\rightarrow \lnot B$$ A → B , A → ¬ B is satisfied. In this paper, such logics are studied algebraically by means of algebraic structures in which negation is modeled by an operator $$\lnot $$ ¬ s.t. any element a is incomparable with $$\lnot a$$ ¬ a . A range of properties which are (in)compatible with such operators are studied, and examples are given; finally, the question of which further operators can be added to such structures is broached.