Abstract
Kapsner strong logics, originally studied in the context of connexive logics, are those in which all formulas of the form Arightarrow lnot A or lnot Arightarrow A are unsatisfiable, and in any model at most one of Arightarrow B, Arightarrow lnot 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 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.
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