extends modal logic with time: operators for "always" ($\square$), "eventually" ($\diamond$), "until", "next"
linear temporal logic (LTL) reasons over sequences. computation tree logic (CTL) reasons over branching futures. both are decidable and used for model checking — verifying that systems satisfy specifications.
in the cybergraph: every cyberlink carries an epoch timestamp. temporal queries traverse the link history: "this particle was eventually linked to that one", "this relation held until epoch $n$". the append-only BBG provides a total ordering of state transitions, making temporal reasoning native.