Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have
published seminal works by leading logicians. Many of the original books in the series have …

We introduce a systematic procedure to transform large classes of (Hilbert) axioms into
equivalent inference rules in sequent and hypersequent calculi. This allows for the …

Residuated frames provide relational semantics for substructural logics and are a natural
generalization of Kripke frames in intuitionistic and modal logic, and of phase spaces in …

Ordered algebras such as Boolean algebras, Heyting algebras, lattice-ordered groups, and
MV-algebras have long played a decisive role in logic, although perhaps only in recent …

We carry out a unified investigation of two prominent topics in proof theory and order
algebra: cut-elimination and completion, in the setting of substructural logics and residuated …

We discuss an ongoing line of research in the relational (non topological) semantics of non-
distributive logics. The developments we consider are technically rooted in dual …

Substructural logics have received a lot of attention in recent years from the communities of
both logic and algebra. We discuss the algebraization of substructural logics over the full …

Pratt (1991, Proceedings of JELIA'90, Volume 478, pp. 97–120) defines action algebras as
Kleene algebras with residuals and action logic as the equational theory of action algebras …

We develop a general algebraic and proof-theoretic study of substructural logics that may
lack associativity, along with other structural rules. Our study extends existing work on …

A residuated algebra (RA) is a generalization of a residuated groupoid; instead of one basic
binary operation with residual operations\,/, it admits finitely many basic operations, and …