  Coordinating activities at different sites of a multi-agent system typically
imposes epistemic constraints on the participants. Specifying explicit bounds
on the relative times at which actions are performed induces combined temporal
and epistemic constraints on when agents can perform their actions. This paper
characterises the interactive epistemic state that arises when actions must
meet particular temporal constraints. The new state, called timely common
knowledge, generalizes common knowledge, as well as other variants of common
knowledge. While known variants of common knowledge are defined in terms of a
fixed point of an epistemic formula, timely common knowledge is defined in
terms of a vectorial fixed point of temporal-epistemic formulae. A general
class of coordination tasks with timing constraints is defined, and timely
common knowledge is used to characterise both solvability and optimal solutions
of such tasks. Moreover, it is shown that under natural conditions, timely
common knowledge is equivalent to an infinite conjunction of temporal-epistemic
formulae, in analogy to the popular definition of common knowledge.
