11 citations · 43 across the 14 of their papers we have counts for
17 papers
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 corrected strategy for proving no finite variable axiomatisation exists for RRA
Rob Egrot, Robin Hirsch
We show that if for all finite there is a pair of non-isomorphic finite digraphs satisfying some additional conditions, one of which is that they cannot be distinguished in a c…
Demonic Lattices and Semilattices in Relational Semigroups with Ordinary Composition
Robin Hirsch, Jaš Šemrl
Relation algebra and its reducts provide us with a strong tool for reasoning about nondeterministic programs and their partial correctness. Demonic calculus, introduced to model th…
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…
Finite Representability of Semigroups with Demonic Refinement
Robin Hirsch, Jaš Šemrl
Composition and demonic refinement of binary relations are defined by \begin{align*} (x, y)\in (R;S)&\iff \exists z((x, z)\in R\wedge (z, y)\in S) R\sqsubseteq S&\iff…
The algebra of non-deterministic programs: demonic operators, orders and axioms
Robin Hirsch, Szabolcs Mikulás, Tim Stokes
Demonic composition, demonic refinement and demonic union are alternatives to the usual "angelic" composition, angelic refinement (inclusion) and angelic (usual) union defined on b…
Marxism, Logic and the Rate of Profit
Robin Hirsch
It is argued that Marxism, being based on contradictions, is an illogical method. More specifically, we present a rejection of Marx's thesis that the rate of profit has a long-term…
First-order axiomatisations of representable relation algebras need formulas of unbounded quantifier depth
Rob Egrot, Robin Hirsch
Using a variation of the rainbow construction and various pebble and colouring games, we prove that RRA, the class of all representable relation algebras, cannot be axiomatised by…
Seurat games on Stockmeyer graphs
Rob Egrot, Robin Hirsch
We define a family of vertex colouring games played over a pair of graphs or digraphs by players and . These games arise from work on a longstanding open…
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…
Algebraic foundations for qualitative calculi and networks
Robin Hirsch, Marcel Jackson, Tomasz Kowalski
A qualitative representation is like an ordinary representation of a relation algebra, but instead of requiring , as we do for ordinary representations, we…
The Temporal Logic of two dimensional Minkowski spacetime is decidable
Robin Hirsch, Mark Reynolds
We consider Minkowski spacetime, the set of all point-events of spacetime under the relation of causal accessibility. That is, can access if an electromagnetic…
Meet-completions and ordered domain algebras
Rob Egrot, Robin Hirsch
Using the well-known equivalence between meet-completions of posets and standard closure operators we show a general method for constructing meet-completions for isotone poset expa…
The algebra of functions with antidomain and range
Robin Hirsch, Marcel Jackson, Szabolcs Mikulás
We give complete, finite quasiequational axiomatisations for algebras of unary partial functions under the operations of composition, domain, antidomain, range and intersection. Th…
There is no finite-variable equational axiomatization of representable relation algebras over weakly representable relation algebras
Jeremy F. Alm, Robin Hirsch, Roger D. Maddux
We prove that any equational basis that defines RRA over wRRA must contain infinitely many variables. The proof uses a construction of arbitrarily large finite weakly representable…
Completely Representable Lattices
Robert Egrot, Robin Hirsch
It is known that a lattice is representable as a ring of sets iff the lattice is distributive. CRL is the class of bounded distributive lattices (DLs) which have representations pr…