Non-monotonic base-extension semantics (nB-eS), a kind of non-monotonic proof-theoretic semantics (nPTS), is known to validate classical logic when its meta-logic is classical. Schroeder-Heister has remarked that classical ...

In this paper we give a constructive proof that the variety of Boolean algebras has the strong amalgamation property by describing constructively the strong amalgams in the variety. Then, capitalizing on this construction, ...

This work studies the proof theory and ternary relational semantics of left (right) skew monoidal closed categories and skew monoidal bi-closed categories, both symmetric and non-symmetric, from the perspective of ...

The Nonassociative Lambek Calculus (NL) represents a logic devoid of the structural rules of exchange, weakening, and contraction, and it does not presume the associativity of its connectives. Its finitary consequence ...

We introduce the concepts of dually balanced lattices and \(M\)-lattices and provide some basic properties of these classes of lattices. Both classes can be viewed as generalizations of the well-known class of modular ...

One of the most important questions in the area of the equivalential calculus (EC) currently is the issue of the single shortest axiom. We show some new a single organic and inorganic axioms for EC which are either D-complete ...

We analyze the relationship between logics around intuitionistic logic and minimal logic. We characterize the intersection of minimal logic and co-minimal logic introduced by Vakarelov, and reformulate logics given in the ...

Gentzen-style sequent calculi and Gentzen-style natural deduction systems are introduced for a family (C-family) of connexive logics over Wansing’s basic constructive connexive logic C. The C-family is derived from C by ...