Kapsner Complementation: An Algebraic Take on Kapsner Strong Logics
Andrew Tedder · Studia Logica · 2022
Abstract Kapsner 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 elementais 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.