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President Donald Trump says a new Greenland agreement with Denmark gives the U.S. "permanent control" over the island's security and expands its Arctic military presence.

Tech expert Kurt'CyberGuy' Knutsson joins'Fox & Friends' to discuss the future of AI development in the United States. Vice President JD Vance is poised to kick off a trip to Italy and India on Friday – marking his third international trip with the Trump administration. Vance and the second family are poised to meet with and "discuss shared economic and geopolitical priorities with leaders in each country," according to a statement from Vance's office. When in Rome, Vance is scheduled to meet with Italy's Prime Minister Giorgia Meloni and Vatican Secretary of State Cardinal Pietro Parolin. He will meet with India's Prime Minister Narendra Modi while visiting New Delhi, Jaipur and Agra.

We introduce a framework for reasoning about the security of computer systems using modal logic. This framework is sufficiently expressive to capture a variety of known security properties, while also being intuitive and independent of syntactic details and enforcement mechanisms. We show how to use our formalism to represent various progress- and termination-(in)sensitive variants of confidentiality, integrity, robust declassification and transparent endorsement, and prove equivalence to standard definitions. The intuitive nature and closeness to semantic reality of our approach allows us to make explicit several hidden assumptions of these definitions, and identify potential issues and subtleties with them, while also holding the promise of formulating cleaner versions and future extension to entirely novel properties.