7 papers
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 wit…
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,…