5 papers · 1 filter
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…
Ordering groups and validity in lattice-ordered groups
Almudena Colacito, George Metcalfe
A characterization is given of the subsets of a group that extend to the positive cone of a right order on the group and used to relate validity of equations in lattice-ordered gro…
Proof Theory and Ordered Groups
Almudena Colacito, George Metcalfe
Ordering theorems, characterizing when partial orders of a group extend to total orders, are used to generate hypersequent calculi for varieties of lattice-ordered groups (l-groups…