David Gabelaia

Learn 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, S4u and their fragments. The obtained results give a clear picture of the trade-off between expressiveness(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)
This thesis is mainly concerned with the definability issue when modal logic is interpreted on topological spaces. A topological analogon of Goldblatt-Thomason theorem is proved. Some new topological constructions are introduced. One of them, namely the notion of compact extension, is a generalization of the concept of Stone-Čech compactification known in(More)
GURAM BEZHANISHVIL I†‖, N ICK BEZHANISHVIL I‡ ‖ , DAVID GABELAIA§ ‖ and ALEXANDER KURZ¶ †Department of Mathematical Sciences, New Mexico State University, Las Cruces NM 88003-8001, U.S.A. Email: gbezhani@nmsu.edu ‡Department of Computing, Imperial College London, 180 Queen’s Gate, London SW7 2AZ, U.K. Email: nbezhani@doc.ic.ac.uk §Department of Mathematical(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)
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)