3 citations · 5 across the 14 of their papers we have counts for
16 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 space of preorders on a commutative monoid
Jan Draisma, George Metcalfe, Simon Santschi
For a finitely generated commutative monoid , we present a constructive description of all (total) preorders on that are compatible with the monoid structure. Equipped with…
Logics Containing wK4: Selection à la Fine
Simon Santschi, Niels C. Vooijs
We generalize Fine's Iterative Selection Method to the weakly transitive setting. In particular, this provides a transparent frame-theoretic proof of the finite model property for…
Interpolation above S4
Simon Santschi, Niels C. Vooijs
We complete Maksimova's classification of the normal extensions of S4 with interpolation. In particular, we prove Craig interpolation for the six extensions of S4 for which Craig i…
Residuated lattices do not have the amalgamation property
Peter Jipsen, Simon Santschi
We show that the variety of residuated lattices does not have the amalgamation property, thereby settling a long-standing open problem. In addition, we show that the amalgamation p…
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…
Algebraic Proof Theory for Infinitary Action Logic
Wesley Fussner, Simon Santschi, Borja Sierra Miranda
We exhibit a uniform method for obtaining (wellfounded and non-wellfounded) cut-free sequent-style proof systems that are sound and complete for various classes of action algebras,…
Amalgamation in Semilinear Residuated Lattices
Wesley Fussner, Simon Santschi
We survey the state of the art on amalgamation in varieties of semilinear residuated lattices. Our discussion emphasizes two prominent cases from which much insight into the genera…
Interpolation in Hájek's Basic Logic
Wesley Fussner, Simon Santschi
We exhaustively classify varieties of BL-algebras with the amalgamation property, showing that there are only countably many of them and solving an open problem of Montagna. As a c…
Equational theories of idempotent semifields
George Metcalfe, Simon Santschi
This paper provides answers to several open problems about equational theories of idempotent semifields. In particular, it is proved that (i) no equational theory of a non-trivial…
Interpolation and the Exchange Rule
Wesley Fussner, George Metcalfe, Simon Santschi
It was proved by Maksimova in 1977 that exactly eight varieties of Heyting algebras have the amalgamation property, and hence exactly eight axiomatic extensions of intuitionistic p…
Interpolation in Linear Logic and Related Systems
Wesley Fussner, Simon Santschi
We prove that there are continuum-many axiomatic extensions of the full Lambek calculus with exchange that have the deductive interpolation property. Further, we extend this result…
Deciding Equations in the Time Warp Algebra
Sam van Gool, Adrien Guatto, George Metcalfe +1
Join-preserving maps on the discrete time scale , referred to as time warps, have been proposed as graded modalities that can be used to quantify the growth of information in…
Semilinear idempotent distributive l-monoids
Simon Santschi
We prove a representation theorem for totally ordered idempotent monoids via a nested sum construction. Using this representation theorem we obtain a characterization of the subdir…
Time Warps, from Algebra to Algorithms
Sam van Gool, Adrien Guatto, George Metcalfe +1
Graded modalities have been proposed in recent work on programming languages as a general framework for refining type systems with intensional properties. In particular, continuous…
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…