Journal ArticleDOI
Multimo dal Logics of Products of Topologies
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TLDR
In this paper, the authors introduce the horizontal and vertical topologies on the product of topological spaces and study their relationship with the standard product topology, and prove that both of these logics are complete for rational numbers with the appropriate topologies.Abstract:
We introduce the horizontal and vertical topologies on the product of topological spaces, and study their relationship with the standard product topology. We show that the modal logic of products of topological spaces with horizontal and vertical topologies is the fusion S4 ⊕ S4. We axiomatize the modal logic of products of spaces with horizontal, vertical, and standard product topologies.We prove that both of these logics are complete for the product of rational numbers ℚ × ℚ with the appropriate topologies.read more
Citations
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Book ChapterDOI
Modal Logics of Space
TL;DR: The interest of Space remains intriguing – both for mathematical reasons, and given the amount of work in CS and AI on visual reasoning and image processing, which involves logic of spatial structures.
Combining modal logics
TL;DR: In this article, a survey of modal logics can be found and the consequences of combining them are discussed. But the authors focus mainly on fusions and products of Kripke frames.
Book ChapterDOI
Topology and Epistemic Logic
TL;DR: The main ideas behind a number of logical systems for reasoning about points and sets that incorporate knowledge-theoretic ideas, and also the main results about them are presented.
Journal ArticleDOI
Some Results on Modal Axiomatization and Definability for Topological Spaces
TL;DR: It is demonstrated that the d-semantics is more expressive than the C-semantic, and it is shown that the D-logics of the six classes of spaces considered in the paper are pairwise distinct, while the C's of some of them coincide.
References
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Book
Many-Dimensional Modal Logics: Theory and Applications
TL;DR: In this paper, the authors introduce modal axiomatic systems, including first-order modal logics, and demonstrate the decidability of these models with respect to the finite model property.
Book
Exploring Logical Dynamics
TL;DR: This chapter discusses the development of dynamic styles of inference in two-level static-dynamic architecture and its applications in process simulation and definability.