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An on-the-fly tableau construction for a real-time temporal logic

An on-the-fly tableau construction for a real-time temporal logic

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4. Real-<strong>time</strong> On-<strong>the</strong>-<strong>fly</strong> Tableaux<br />

TS 1<br />

TS 2<br />

TS 3<br />

'<br />

¦ 1<br />

¥ 1<br />

¦ 2<br />

¥ 2<br />

¦ k<br />

¥ k<br />

© 2<br />

• Normal <strong>for</strong>m<br />

ϕ = (Π1 ∧ Ξ1 ∧ ○Φ1)∨<br />

(Π2 ∧ Ξ2 ∧ ○Φ2) ∨ . . .<br />

• Propositi<strong>on</strong>al part Πi<br />

• Timer C<strong>on</strong>diti<strong>on</strong>s Ξi<br />

• Future part Φi<br />

A 22

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