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I'm studying proof theory and I've seen that linear logic can be used as a way to control resource usage, since by the propositions-as-types it is equivalent to the linear lambda calculus.

Is there a logic that allows resource control (like linear logic) and can express properties that vary over a notion of time like linear time temporal logics (LTL)?

Any reference or point to literature is highly appreciated.

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As time can be a resource, it is a bit unclear to me what you seek.

Nevertheless, you might want to look at weighted extensions of LTL, like Metric Temporal Logic first defined here. (Specifying real-time properties with metric temporal logic)

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    $\begingroup$ Thanks for the reference. I'll check the suggested article. My interest in timed resource control is to ensure that a certain amount of resources satisfies a given property over time. Since temporal logics express properties over time, and linear logic can be used to express resource control, I'm wondering if there's a logic that can express properties about resources over time. $\endgroup$
    – Rodrigo Ribeiro
    Jan 19, 2015 at 18:59

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