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Our paper studies a new temporal agents’ knowledge logic TLDistKnI,U, which expresses localised agents’ knowledge, operation of knowledge via agents’ interaction, operation of uncertainty and operations responsible for measuring distances. We study problems of satisfiability and decidability for TLDistKnI,U. We _nd an algorithm which recognizes theorems of TLDistKnI,U, this implies that TLDistKnI,U is decidable, and the satisfiability problem for TLDistKnI,U is solvable
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