Could Ukraine hold a presidential election right now? Will Europe use frozen Russian assets to fund war? How can Ukraine rebuild China ties? 'Ukraine is running out of men, money and time' Russian attacks killed three people, including a 20-year-old woman, and injured 11 others in Ukraine's Kharkiv region, Governor Oleh Syniehubov wrote on Telegram on Sunday. In Ukraine's Kherson region, two people were killed, and one person was injured, as Russian forces launched attacks using drones, air strikes and shelling, Governor Oleksandr Prokudin said on Telegram on Sunday.

What is in the 28-point US plan for Ukraine? 'Ukraine is running out of men, money and time' Can the US get all sides to end the war? Why is Europe opposing Trump's peace plan? IAEA flags damage to Chornobyl nuclear plant's protective shield in Ukraine A drone strike has damaged a protective shield at the Chornobyl nuclear plant in Ukraine, rendering it unable to contain the radioactive material from the 1986 explosion of the plant, the United Nations nuclear watchdog said. The International Atomic Energy Agency (IAEA) said on Friday that the shield can no longer perform its main safety function, following an inspection of the steel structure last week.

At least 51 people were killed and 271 injured when two Russian ballistic missiles hit a military academy and a nearby hospital in Ukraine's central town of Poltava in the deadliest single attack in the war this year. The missiles hit shortly after the air raid alert sounded when many people were on their way to a bomb shelter, the Ministry of Defence said in a statement. A woman and her eight-year-old son were killed after the Zaporizhia region hotel where they were staying was hit in a Russian missile attack. Her husband and daughter were injured, Ukrainian authorities said. Ukraine's Ministry of Energy said three employees were injured in a Russian drone attack on a power facility in the northern region of Chernihiv.

A Ukrainian drone attack has set an oil depot in Russia's southern region of Rostov alight, the authorities said. On Wednesday, regional Governor Vasily Golubev confirmed the overnight strike, saying on the Telegram messaging app that firefighters were extinguishing the blaze at the depot in Rostov's Kamensky district, with no casualties reported. Russia's Ministry of Defence earlier said air defence units destroyed four drones over the region overnight, without mentioning the attack on the oil depot. Three tanks were burning at the oil depot after two drones fell in the area, according to the Baza Telegram channel, which is close to Russian security services. Ukraine's strike marked its latest attack on Russian oil and gas facilities in retaliation for attacks on its energy infrastructure.

Fixpoints play a key role in the mathematical set up of abstract argumentation theory but, we argue, have been relatively underexamined in the literature. The paper studies the logical structure underlying the computation via approximation sequences of the sort of fixpoints relevant in argumentation. Concretely, it presents a number of novel results on the fixed point theory underpinning the main Dung's semantics and, inspired by recent literature on the logical analysis of equilibrium computation in games, it provides a characterization of those semantics in terms of iterated model updates.

The paper addresses how the information state of an agent relates to the arguments that the agent endorses. Information states are modeled in doxastic logic and arguments by recasting abstract argumentation theory in a modal logic format. The two perspectives are combined by an application of the theory of product logics, delivering sound and complete systems in which the interaction of arguments and beliefs is investigated.

The paper develops a formal theory of the degree of justification of arguments, which relies solely on the structure of an argumentation framework. The theory is based on a generalisation of Dung's notion of acceptability, making it sensitive to the numbers of attacks and counter-attacks on arguments. Graded generalisations of argumentation semantics are then obtained and studied. The theory is applied by showing how it can arbitrate between competing preferred extensions and how it captures a specific form of accrual in instantiated argumentation.