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- Title
Losing connection: the modal logic of definable link deletion.
- Authors
Li, Dazhu
- Abstract
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 that 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.
- Subjects
MODAL logic; FIRST-order logic; COMMUNICATION models; HYBRID power; DEFINITIONS; NONCOOPERATIVE games (Mathematics)
- Publication
Journal of Logic & Computation, 2020, Vol 30, Issue 3, p715
- ISSN
0955-792X
- Publication type
Article
- DOI
10.1093/logcom/exz036