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We investigate a subsystem of minimal logic related to D. Vakarelov’s logic \, using the framework of subminimal logics by A. Colacito, D. de Jongh and A. L. Vargas. In the course of it, the relationship between the two semantics in the respective frameworks is clarified. In addition, we introduce a sequent calculus for the investigated subsystem, and some prooftheoretic properties are established. Lastly, we formulate a new infinite class of subsystems of minimal logics. 

In this paper, a family of paraconsistent propositional logics with constructive negation, constructive implication, and constructive coimplication is introduced. Although some fragments of these logics are known from the literature and although these logics emerge quite naturally, it seems that none of them has been considered so far. A relational possible worlds semantics as well as sound and complete display sequent calculi for the logics under consideration are presented. 

The goal of this twopart series of papers is to show that constructive logic with strong negation N is definitionally equivalent to a certain axiomatic extension NFL ew of the substructural logic FL ew. The main result of Part I of this series [41] shows that the equivalent variety semantics of N and the equivalent variety semantics of NFL ew are term equivalent. In this paper, the term equivalence result of Part I [41] is lifted to the setting of deductive (...) 

The paper is devoted to the contributions of Helena Rasiowa to the theory of nonclassical negation. The main results of Rasiowa in this area concerns–constructive logic with strong (Nelson) negation. 

We introduce a novel expansion of the fourvalued Belnap–Dunn logic by a unary operator representing reductio ad contradictionem and study its algebraic semantics. This expansion thus contains both the direct, noninferential negation of the Belnap–Dunn logic and an inferential negation akin to the negation of Johansson’s minimal logic. We formulate a sequent calculus for this logic and introduce the variety of reductio algebras as an algebraic semantics for this calculus. We then investigate some basic algebraic properties of this variety, in (...) 