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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…