Modal Languages for Topology: Expressivity and Definability

In this paper we study the expressive power and definability for (extended) modal languages interpreted on topological spaces. We provide topological analogues of the van Benthem characterization theorem and the Goldblatt-Thomason definability theorem in terms of the well established first-order topological language $L_t$

Bisimilarity and refinement for hybrid(ised) logics

The complexity of modern software systems entails the need for reconfiguration mechanisms governing the dynamic evolution of their execution configurations in response to both external stimulus or internal performance measures. Formally, such systems may be represented by transition systems whose nodes correspond to the different configurations they may assume. Therefore, each node is endowed with, for example, an algebra, or a first-order structure, to precisely characterise the semantics of the services provided in the corresponding configuration. Hybrid logics, which add to the modal description of transition structures the ability to refer to specific states, offer a generic framework to approach the specification and design of this sort of systems. Therefore, the quest for suitable notions of equivalence and refinement between models of hybrid logic specifications becomes fundamental to any design discipline adopting this perspective. This paper contributes to this effort from a distinctive point of view: instead of focussing on a specific hybrid logic, the paper introduces notions of bisimilarity and refinement for hybridised logics, i.e. standard specification logics (e.g. propositional, equational, fuzzy, etc) to which modal and hybrid features were added in a systematic way.FC

Modal languages for topology: Expressivity and definability

International audienceIn this paper we study the expressive power and definability for (extended) modal languages interpreted on topological spaces. We provide topological analogues of the van Benthem characterization theorem and the Goldblatt-thomason definability theorem in terms of the well-established first-order topological language Lt

Contents

Model theory for extended modal language