3 citations · 11 across the 10 of their papers we have counts for
11 papers
Canonicity in power and modal logics of finite achronal width
Robert Goldblatt, Ian Hodkinson
We develop a method for showing that various modal logics that are valid in their countably generated canonical Kripke frames must also be valid in their uncountably generated ones…
Completeness of Pledger's modal logics of one-sorted projective and elliptic planes
Robert Goldblatt
Ken Pledger devised a one-sorted approach to the incidence relation of plane geometries, using structures that also support models of propositional modal logic. He introduced a mod…
Modal Logics of Some Hereditarily Irresolvable Spaces
Robert Goldblatt
A topological space is \emph{hereditarily -irresolvable} if none of its subspaces can be partitioned into dense subsets, We use this notion to provide a topological semantic…
Modal Logics that Bound the Circumference of Transitive Frames
Robert Goldblatt
For each natural number we study the modal logic determined by the class of transitive Kripke frames in which there are no cycles of length greater than and no strictly asc…
Strong completeness of modal logics over 0-dimensional metric spaces
Robert Goldblatt, Ian Hodkinson
We prove strong completeness results for some modal logics with the universal modality, with respect to their topological semantics over 0-dimensional dense-in-themselves metric sp…
Morphisms and Duality for Polarities and Lattices with Operators
Robert Goldblatt
Structures based on polarities have been used to provide relational semantics for propositional logics that are modelled algebraically by non-distributive lattices with additional…
Definable operators on stable set lattices
Robert Goldblatt
A fundamental result from Boolean modal logic states that a first-order definable class of Kripke frames defines a logic that is validated by all of its canonical frames. We genera…
Cover Systems for the Modalities of Linear Logic
Robert Goldblatt
Ono's modal FL-algebras are models of an extension of Full Lambek logic that has the modalities ! and ? of linear logic. Here we define a notion of modal FL-cover system that combi…
Tangled Closure Algebras
Robert Goldblatt, Ian Hodkinson
The tangled closure of a collection of subsets of a topological space is the largest subset in which each member of the collection is dense. This operation models a logical `tangle…
Fine's Theorem on First-Order Complete Modal Logics
Robert Goldblatt
Fine's influential Canonicity Theorem states that if a modal logic is determined by a first-order definable class of Kripke frames, then it is valid in its canonical frames. This a…
Spatial logic of modal mu-calculus and tangled closure operators
Robert Goldblatt, Ian Hodkinson
There has been renewed interest in recent years in McKinsey and Tarski's interpretation of modal logic in topological spaces and their proof that S4 is the logic of any separable d…