This research monograph presents our approach to the general algebraic study of non-
classical logics. More precisely, it offers a systematic study of weakly implicative logics, a …

Hereditary structural completeness is established for a range of substructural logics, mainly
without the weakening rule, including fragments of various relevant or many-valued logics …

Bochvar algebras consist of the quasivariety $\mathsf {BCA} $ playing the role of equivalent
algebraic semantics for Bochvar (external) logic, a logical formalism introduced by Bochvar …

Structural completeness properties are investigated for a range of popular t-norm based
fuzzy logics—including Łukasiewicz Logic, Gödel Logic, Product Logic, and Hájek's Basic …

In this work we study the notions of structural and universal completeness both from the
algebraic and logical point of view. In particular, we provide new algebraic characterizations …

It is proved that in the variety of positive Sugihara monoids, every finite subdirectly
irreducible algebra is a retract of a free algebra. It follows that every quasivariety of positive …

A quasivariety K of algebras has the joint embedding property (JEP) if and only if it is
generated by a single algebra A. It is structurally complete if and only if the free ℵ0 …

In this paper we deal with quasivarieties of residuated structures which form the equivalent
algebraic semantics of a positive fragment of some substructural logic. Our focus is mainly …

A deductive system is structurally complete if all of its admissible inference rules are
derivable. For several important systems, like the modal logic S5, failure of structural …

In this paper we define and study a generalized notion of a logical system that covers on an
equal formal basis sentential, equational and sequential systems. We develop a general …