Wansing's bi-intuitionistic logic: semantics, extension and unilateralisation

Abstract

ABSTRACT The well-known algebraic semantics and topological semantics for intuitionistic logic ( Int ) is here extended to Wansing's bi-intuitionistic logic ( 2 Int ). The logic 2 Int is also characterised by a quasi-twist structure semantics, which leads to an alternative topological characterisation of 2 Int . Later, notions of Fregean negation and of unilateralisation are proposed. The logic 2 Int is extended with a ‘Fregean negation’ connective ∼ , obtaining 2 In t ∼ , and it is showed that the logic N 4 ⋆ (an extension of Nelson's paraconsistent logic) results to be the unilateralisation of 2 In t ∼ via ∼ . The logic 2 In t ∼ is also characterised by a Kripke-style semantics, a twist structure semantics and a topological semantics.