X-2019-01: Losing Connection: the Modal Logic of Definable Link Deletion

X-2019-01: Li, Dazhu (2019) Losing Connection: the Modal Logic of Definable Link Deletion. [Report]

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In this article, we start with a two-player game that models communication under adverse circumstances in everyday life and study it from the perspective of a modal logic of graphs, where links can be deleted locally according to definitions available to the adversarial player. We first introduce a new language, semantics, and some typical validities. We then formulate a new type of first-order translation for this modal logic and prove its correctness. Then, a novel notion of bisimulation is proposed which leads to a characterization theorem for the logic as a fragment of first-order logic, and a further investigation is made of its expressive power against hybrid modal languages. Next, we discuss how to axiomatize this logic of link deletion, using dynamic-epistemic logics as a contrast. Finally, we show that our new modal logic lacks both the tree model property and the finite model property, and that its satisfiability problem is undecidable.

Item Type: Report
Report Nr: X-2019-01
Series Name: Technical Notes (X) Series
Year: 2019
Uncontrolled Keywords: Graph Game, Modal Logic, Dynamic Logic, Link Deletion, Undecidability
Subjects: Computation
Depositing User: Dazhu Li
Date Deposited: 24 Feb 2019 13:30
Last Modified: 24 Feb 2019 13:30
URI: https://eprints.illc.uva.nl/id/eprint/1664

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