1 citations · 1 across the 5 of their papers we have counts for
8 papers
From distributive l-monoids to l-groups, and back again
Almudena Colacito, Nikolaos Galatos, George Metcalfe +1
We prove that an inverse-free equation is valid in the variety LG of lattice-ordered groups (l-groups) if and only if it is valid in the variety DLM of distributive lattice-ordered…
Nilpotency and the Hamiltonian property for cancellative residuated lattices
Almudena Colacito, Constantine Tsinakis
The present article studies nilpotent and Hamiltonian cancellative residuated lattices and their relationship with nilpotent and Hamiltonian lattice-ordered groups. In particular,…
A Study of Subminimal Logics of Negation and their Modal Companions
Nick Bezhanishvili, Almudena Colacito, Dick de Jongh
We study propositional logical systems arising from the language of Johansson's minimal logic and obtained by weakening the requirements for the negation operator. We present their…
Theorems of Alternatives for Substructural Logics
Almudena Colacito, Nikolaos Galatos, George Metcalfe
A theorem of alternatives provides a reduction of validity in a substructural logic to validity in its multiplicative fragment. Notable examples include a theorem of Arnon Avron th…
Proof Theory for Positive Logic with Weak Negation
Marta Bílková, Almudena Colacito
Proof-theoretic methods are developed for subsystems of Johansson's logic obtained by extending the positive fragment of intuitionistic logic with weak negations. These methods are…
Orders on groups, and spectral spaces of lattice-groups
Almudena Colacito, Vincenzo Marra
Extending pioneering work by Weinberg, Conrad, McCleary, and others, we provide a systematic way of relating spaces of right orders on a partially ordered group, on the one hand, a…