4 citations · 8 across the 11 of their papers we have counts for
12 papers
Proper varieties of distributive l-pregroups are periodic
Nikolaos Galatos, Simon Santschi
We show that every proper variety of distributive -pregroups is periodic; as a result, the subvariety lattice of the variety of distributive -pregroups decomposes into…
The logic of bunched implications is undecidable
Nick Galatos, Peter Jipsen, Søren Brinck Knudstorp +1
The logic of bunched implications (BI), introduced by O'Hearn and Pym (1999), has attracted significant attention due to its elegant proof calculus, varied semantics, and close con…
Complexities of Well-Quasi-Ordered Substructural Logics
Nikolaos Galatos, Vitor Greati, Revantha Ramanayake +1
Substructural logics are formal logical systems that omit familiar structural rules of classical and intuitionistic logic such as contraction, weakening, exchange (commutativity),…
Axiomatizing small varieties of periodic l-pregroups
Nikolaos Galatos, Simon Santschi
We provide an axiomatization for the variety generated by the -periodic l-pregroup , for every , as well as for all possible joins…
Generation and decidability for periodic l-pregroups
Nikolaos Galatos, Isis A. Gallardo
In [11] it is shown that the variety of distributive l-pregroups is generated by a single algebra, the functional algebra over the integers. Here, we…
Decidability of distributive l-pregroups
Nikolaos Galatos, Isis A. Gallardo
We show that every distributive lattice-ordered pregroup can be embedded into a functional algebra over an integral chain, thus improving the existing Cayley/Holland-style embeddin…
Gluing residuated lattices
Nick Galatos, Sara Ugolini
We introduce and characterize various gluing constructions for residuated lattices that intersect on a common subreduct, and which are subalgebras, or appropriate subreducts, of th…
Unilinear residuated lattices: axiomatization, varieties and FEP
Nick Galatos, Xiao Zhuang
We characterize all residuated lattices that have height equal to and show that the variety they generate has continuum-many subvarieties. More generally, we study unilinear re…
Twist structures and Nelson conuclei
Manuela Busaniche, Nikolaos Galatos, Miguel Andrés Marcos
Motivated by Kalman residuated lattices, Nelson residuated lattices and Nelson paraconsistent residuated lattices, we provide a natural common generalization of them. Nelson conucl…
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…
Most simple extensions of are undecidable
Nikolaos Galatos, Gavin St. John
All known structural extensions of the substructural logic , Full Lambek calculus with exchange/commutativity, (corresponding to subvarieties of commutative residuat…
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…