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Modal definability in topology Master's thesis Acknowledgments During the year spent in Amsterdam at ILLC I have been lucky to be supported by many. The proper acknowledgment of everyone would have resulted in a separate book. I will only name a few, with the hope that the others will find my gratitude in between the lines. I am greatly indebted to Dr. Yde… (More)
We show that—unlike products of 'transitive' modal logics which are usually undecidable— their 'expanding domain' relativisations can be decidable, though not in primitive recursive time. In particular, we prove the decidability and the finite expanding product model property of bimodal logics interpreted in two-dimensional structures where one… (More)
We consider two topological interpretations of the modal diamond—as the closure operator (C-semantics) and as the derived set operator (d-semantics). We call the logics arising from these interpretations C-logics and d-logics, respectively. We axiomatize a number of subclasses of the class of nodec spaces with respect to both semantics, and characterize… (More)
We introduce pairwise Stone spaces as a bitopological generalisation of Stone spaces – the duals of Boolean algebras – and show that they are exactly the bitopological duals of bounded distributive lattices. The category PStone of pairwise Stone spaces is isomorphic to the category Spec of spectral spaces and to the category Pries of Priestley spaces. In… (More)
In this paper, we construct and investigate a hierarchy of spatio-temporal formalisms that result from various combinations of propositional spatial and temporal logics such as the propositional temporal logic PT L, the spatial logics RCC-8, BRCC-8, S4 u and their fragments. The obtained results give a clear picture of the trade-off between expressiveness… (More)
Recently, a hierarchy of spatio-temporal languages based on the propositional temporal logic PTL and the spatial languages RCC-8, BRCC-8 and S4u has been introduced. Although a number of results on their computational properties were obtained, the most important questions were left open. In this paper, we solve these problems and provide a clear picture of… (More)
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 .