6 citations · 42 across the 18 of their papers we have counts for
18 papers
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…
Constructive S4 modal logics with the finite birelational frame property
Philippe Balbiani, Martín Diéguez, David Fernández-Duque +1
The logics and are the two leading intuitionistic variants of the modal logic . Whether the finite model property holds for each of these…
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…
Gödel-Dummett linear temporal logic
Juan Pablo Aguilera, Martín Diéguez, David Fernández-Duque +1
We investigate a version of linear temporal logic whose propositional fragment is Gödel-Dummett logic (which is well known both as a superintuitionistic logic and a t-norm fuzzy lo…
Preservation theorems for Tarski's relation algebra
Bart Bogaerts, Balder ten Cate, Brett McLean +1
We investigate a number of semantically defined fragments of Tarski's algebra of binary relations, including the function-preserving fragment. We address the question whether they…
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…
A Gödel Calculus for Linear Temporal Logic
Juan Pablo Aguilera, Martín Diéguez, David Fernández-Duque +1
We consider Gödel temporal logic (), a variant of linear temporal logic based on Gödel--Dummett propositional logic. In recent work, we have shown this logic to enjoy natu…
Time and Gödel: Fuzzy temporal reasoning in PSPACE
Juan Pablo Aguilera, Martín Diéguez, David Fernández-Duque +1
We investigate a non-classical version of linear temporal logic whose propositional fragment is Gödel--Dummett logic (which is well known both as a superintuitionistic logic and a…
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…
A categorical duality for algebras of partial functions
Brett McLean
We prove a categorical duality between a class of abstract algebras of partial functions and a class of (small) topological categories. The algebras are the isomorphs of collection…
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…
Disjoint-union partial algebras
Robin Hirsch, Brett McLean
Disjoint union is a partial binary operation returning the union of two sets if they are disjoint and undefined otherwise. A disjoint-union partial algebra of sets is a collection…
Algebras of multiplace functions for signatures containing antidomain
Brett McLean
We define antidomain operations for algebras of multiplace partial functions. For all signatures containing composition, the antidomain operations and any subset of intersection, p…
The finite representation property for composition, intersection, domain and range
Brett McLean, Szabolcs Mikulás
We prove that the finite representation property holds for representation by partial functions for the signature consisting of composition, intersection, domain and range and for a…
Complete representation by partial functions for composition, intersection and antidomain
Brett McLean
For representation by partial functions in the signature with intersection, composition and antidomain, we show that a representation is meet complete if and only if it is join com…