6 citations · 42 across the 18 of their papers we have counts for
8 papers · 1 filter
Difference-restriction algebras with operators
Célia Borlido, Ganna Kudryavtseva, Brett McLean
We exhibit an adjunction between a category of abstract algebras of partial functions that we call difference-restriction algebras and a category of Hausdorff étale spaces. Differe…
Complete representation by partial functions for signatures containing antidomain restriction
Brett McLean
We investigate notions of complete representation by partial functions, where the operations in the signature include antidomain restriction and may include composition, intersecti…
EXPTIME-hardness of higher-dimensional Minkowski spacetime
Robin Hirsch, Brett McLean
We prove the EXPTIME-hardness of the validity problem for the basic temporal logic on Minkowski spacetime with more than one space dimension. We prove this result for both the ligh…
Difference-restriction algebras of partial functions with operators: discrete duality and completion
Célia Borlido, Brett McLean
We exhibit an adjunction between a category of abstract algebras of partial functions and a category of set quotients. The algebras are those atomic algebras representable as a col…
Difference-restriction algebras of partial functions: axiomatisations and representations
Célia Borlido, Brett McLean
We investigate the representation and complete representation classes for algebras of partial functions with the signature of relative complement and domain restriction. We provide…
Temporal Logic of Minkowski Spacetime
Robin Hirsch, Brett McLean
We present the proof that the temporal logic of two-dimensional Minkowski spacetime is decidable, PSPACE-complete. The proof is based on a type of two-dimensional mosaic. Then we p…
Free Kleene algebras with domain
Brett McLean
First we identify the free algebras of the class of algebras of binary relations equipped with the composition and domain operations. Elements of the free algebras are pointed labe…
The temporal logic of two-dimensional Minkowski spacetime with slower-than-light accessibility is decidable
Robin Hirsch, Brett McLean
We work primarily with the Kripke frame consisting of two-dimensional Minkowski spacetime with the irreflexive accessibility relation 'can reach with a slower-than-light signal'. W…