We extend the theory of unified correspondence to a broad class of logics with algebraic
semantics given by varieties of normal lattice expansions (LEs), also known as 'lattices with …

We introduce a generalisation of Nelson algebras having a not necessarily involutive
negation. We suggest dubbing this class quasi-Nelson algebras, in analogy with quasi-De …

We introduce a generalization of Nelson algebras having a not-necessarily involutive
negation; we suggest to dub this class quasi-Nelson algebras in analogy with quasi-De …

We introduce the logic LRC, designed to describe and reason about agents' abilities and
capabilities in using resources. The proposed framework bridges two—up to now—mutually …

A recent strand of research in structural proof theory aims at exploring the notion of analytic
calculi (ie, those calculi that support general and modular proof-strategies for cut …

Twist-structure representation theorems are established for De Morgan and Kleene lattices.
While the former result relies essentially on the quasivariety of De Morgan lattices being …

Taking an algebraic perspective on the basic structures of Rough Concept Analysis as the
starting point, in this paper we introduce some varieties of lattices expanded with normal …

We introduce a proper display calculus for (non-distributive) Lattice Logic which is sound,
complete, conservative, and enjoys cut-elimination and subformula property. Properness (ie …

We introduce a proper multi-type display calculus for bilattice logic (with conflation) for which
we prove soundness, completeness, conservativity, standard subformula property and cut …

In this article, we extend the research programme in algebraic proof theory from axiomatic
extensions of the full Lambek calculus to logics algebraically captured by certain varieties of …