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/*******************************************************************************
* Copyright (c) University of Toronto and others. All rights reserved.
* The content of this file is licensed under the Creative Commons Attribution-
* ShareAlike 4.0 Unported license. The legal text of this license can be
* found at http://creativecommons.org/licenses/by-sa/4.0/legalcode.
*
* Contributors:
* Michael Gruninger - initial implementation
*******************************************************************************/
(cl-text http://colore.oor.net/time_interval_incidence/hayes_point_continuum.clif
(cl-imports http://colore.oor.net/timepoints/linear_point.clif)
(forall (x y)
(if (in x y)
(and (timepoint x)
(timeinterval y))))
(forall (i)
(if (timeinterval i)
(or (and (open i)
(not (closed i))
(forall (p)
(iff (in p i)
(and (before (beginof i) p)
(before p (endof i))))))
(and (closed i)
(not (open i))
(forall (p)
(iff (in p i)
(and (bbefore (beginof i) p)
(bbefore p (endof i)))))))))
(forall (p q)
(if (and (timepoint p)
(timepoint q))
(or (before q p)
(exists (i)
(and (timeinterval i)
(closed i)
(= (beginof i) p)
(= (endof i) q))))))
(forall (p q)
(if (and (timepoint p)
(timepoint q))
(iff (before p q)
(exists (i)
(and (timeinterval i)
(open i)
(= (beginof i) p)
(= (endof i) q))))))
(forall (p q)
(if (and (timepoint p)
(timepoint q))
(iff (bbefore p q)
(and (timeinterval (between p q))
(= p (beginof (between p q)))
(= q (endof (between p q)))))))
(forall (i)
(if (timeinterval i)
(and (timeinterval (closure i))
(closed (closure i))
(= (beginof i) (beginof (closure i)))
(= (endof i) (endof (closure i))))))
)
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