Related papers: Analysing Spatial Properties on Neighbourhood Spac…

Neighbourhood structures are the standard semantic tool used to reason about non-normal modal logics. The logic of all neighbourhood models is called classical modal logic. In coalgebraic terms, a neighbourhood frame is a coalgebra for the…

Our objective is to extend the standard results of preservation and reflection of properties by bisimulations to the coalgebraic setting, as well as to study under what conditions these results hold for simulations. The notion of…

The topological interpretation of modal logics provides descriptive languages and proof systems for reasoning about points of topological spaces. Recent work has been devoted to model checking of spatial logics on discrete spatial…

We define a notion of Lambda-simulation for coalgebraic modal logics, parametric on the choice Lambda of predicate liftings for a functor T. We show this notion is adequate in several ways: i) it preserves truth of positive formulas, ii)…

Closure spaces are a generalisation of topological spaces obtained by removing the idempotence requirement on the closure operator. We adapt the standard notion of bisimilarity for topological models, namely Topo-bisimilarity, to closure…

Graph pattern matching is often defined in terms of subgraph isomorphism, an NP-complete problem. To lower its complexity, various extensions of graph simulation have been considered instead. These extensions allow pattern matching to be…

Closure spaces, a generalisation of topological spaces, have shown to be a convenient theoretical framework for spatial model checking. The closure operator of closure spaces and quasi-discrete closure spaces induces a notion of…

Persistence modules are a central algebraic object arising in topological data analysis. The notion of interleaving provides a natural way to measure distances between persistence modules. We consider various classes of persistence modules,…

We study properties of contiguity distance between simplicial maps. In particular, we show that simplicial versions of $LS$-category and topological complexity are particular cases of this more general notion.

We investigate how various forms of bisimulation can be characterised using the technology of logical relations. The approach taken is that each form of bisimulation corresponds to an algebraic structure derived from a transition system,…

Topological Spatial Model Checking is a recent paradigm where model checking techniques are developed for the topological interpretation of Modal Logic. The Spatial Logic of Closure Spaces, SLCS, extends Modal Logic with reachability…

We introduce a class of neighbourhood frames for graded modal logic embedding Kripke frames into neighbourhood frames. This class of neighbourhood frames is shown to be first-order definable but not modally definable. We also obtain a new…

Collective Adaptive Systems often consist of many heterogeneous components typically organised in groups. These entities interact with each other by adapting their behaviour to pursue individual or collective goals. In these systems, the…

In contrast to classical strongly continuous semigroups, the study of bi-continuous semigroups comes with some freedom in the properties of the associated locally convex topology. This paper aims to give minimal assumptions in order to…

A central question in cognitive science is whether conceptual representations converge onto a shared manifold to support generalization, or diverge into orthogonal subspaces to minimize task interference. While prior work has discovered…

Spectral Clustering (SC) is widely used for clustering data on a nonlinear manifold. SC aims to cluster data by considering the preservation of the local neighborhood structure on the manifold data. This paper extends Spectral Clustering to…

Generalized topological spaces in the sense of Cs\'{a}sz\'{a}r have two main features which distinguish them from typical topologies. First, these families of subsets are not closed under intersections. Second, we allow for the possibility…

In this paper we investigate certain systems of propositional intuitionistic modal logic defined semantically in terms of neighborhood structures. We discuss various restrictions imposed on those frames but our constant approach is to…

In this article we consider PMC surfaces in complex space forms, and we study the interaction between the notions of PMC, totally real and biconservative. We first consider PMC surfaces in non-flat complex space forms and we prove that they…

Model checking large networks of processes is challenging due to state explosion. In many cases, individual processes are isomorphic, but there is insufficient global symmetry to simplify model checking. This work considers the verification…