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 automated generation ofâ€¦ (More)

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 lattices. Weâ€¦ (More)

Cancellative residuated lattices are natural generalizations of lattice-ordered groups ( -groups). Although cancellative monoids are defined by quasi-equations, the class CanRL of cancellativeâ€¦ (More)

We generalize the notion of an MV-algebra in the context of residuated lattices to include commutative and unbounded structures. We investigate a number of their properties and pr they can beâ€¦ (More)

Equivalences and translations between consequence relations abound in logic. The notion of equivalence can be defined syntactically, in terms of translations of formulas, and order-theoretically, inâ€¦ (More)

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 (associative)â€¦ (More)

An odd Sugihara monoid is a residuated distributive latticeordered commutative idempotent monoid with an order-reversing involution that fixes the monoid identity. The main theorem of this paperâ€¦ (More)

We extend the lattice embedding of the axiomatic extensions of the positive fragment of intuitionistic logic into the axiomatic extensions of intuitionistic logic to the setting of substructuralâ€¦ (More)