Appendix C: Events with Duration - Commonsense Reasoning [Book]

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APPENDIX C

Events with Duration

In most versions of the event calculus, event occurrences are instantaneous. This appendix presents a revised version of EC that allows event occurrences with duration. A three-argument Happens predicate Happens3(e, t₁, t₂) is introduced, representing that event e occurs between t₁ and t₂. EC is revised as follows.

DEFINITION EC1′

Clipped(t₁, f, t₄)

∃e, t₂, t₃ (Happens3(e, t₂, t₃) ∧ t₁ ≤ t₃ ∧ t₂ < t₄ ∧ Terminates(e, f, t₂))

DEFINITION EC2′

Declipped(t₁, f, t₄)

∃e, t₂, t₃ (Happens3(e, t₂, t₃) ∧ t₁ ≤

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