Relation TP<

• Defined in theory: Jat-generic
• Source code: job-assignment-generic.lisp

Slots on this relation:

Documentation:

a time point ?tp1 preceeds a time point ?tp2.

Instance-Of: Relation

Arity: 2

Equivalence Axioms:

(<=> (Tp< ?Tp1 ?Tp2)
     (Or (< (Time-Point.Year ?Tp1) (Time-Point.Year ?Tp2))
         (And (= (Time-Point.Year ?Tp1) (Time-Point.Year ?Tp2))
              (Or (< (Time-Point.Month ?Tp1) (Time-Point.Month ?Tp2))
                  (And (= (Time-Point.Month ?Tp1)
                          (Time-Point.Month ?Tp2))
                       (Or (< (Time-Point.Day ?Tp1)
                              (Time-Point.Day ?Tp2))
                           (And (= (Time-Point.Day ?Tp1)
                                   (Time-Point.Day ?Tp2))
                                (Or (< (Time-Point.Hour ?Tp1)
                                       (Time-Point.Hour ?Tp2))
                                    (And (= (Time-Point.Hour ?Tp1)
                                            (Time-Point.Hour ?Tp2))
                                         (Or (< (Time-Point.Minute ?Tp1)
                                                (Time-Point.Minute ?Tp2))
                                             (And (= (Time-Point.Minute ?Tp1)
                                                     (Time-Point.Minute ?Tp2))
                                                  (< (Time-Point.Second ?Tp1)
                                                     (Time-Point.Second ?Tp2)))))))))))))

Other Related Axioms:

(<=> (Before ?Tr1 ?Tr2)
     (Tp< (Time-Range.End-Time ?Tr1) (Time-Range.Start-Time ?Tr2)))

(<=> (After ?Tr1 ?Tr2)
     (Tp< (Time-Range.End-Time ?Tr2) (Time-Range.Start-Time ?Tr1)))

(<=> (During ?Tr1 ?Tr2)
     (And (Tp> (Time-Range.Start-Time ?Tr1)
               (Time-Range.Start-Time ?Tr2))
          (Tp< (Time-Range.End-Time ?Tr1) (Time-Range.End-Time ?Tr2))))

(<=> (Overlaps ?Tr1 ?Tr2)
     (And (Tp< (Time-Range.Start-Time ?Tr1)
               (Time-Range.Start-Time ?Tr2))
          (Tp< (Time-Range.Start-Time ?Tr2)
               (Time-Range.End-Time ?Tr1))
          (Tp< (Time-Range.End-Time ?Tr1) (Time-Range.End-Time ?Tr2))))

(<=> (Starts ?Tr1 ?Tr2)
     (And (Tp= (Time-Range.Start-Time ?Tr1)
               (Time-Range.Start-Time ?Tr2))
          (Tp< (Time-Range.End-Time ?Tr1) (Time-Range.End-Time ?Tr2))))

(<=> (Tp< ?Tp1 ?Tp2)
     (Or (< (Time-Point.Year ?Tp1) (Time-Point.Year ?Tp2))
         (And (= (Time-Point.Year ?Tp1) (Time-Point.Year ?Tp2))
              (Or (< (Time-Point.Month ?Tp1) (Time-Point.Month ?Tp2))
                  (And (= (Time-Point.Month ?Tp1)
                          (Time-Point.Month ?Tp2))
                       (Or (< (Time-Point.Day ?Tp1)
                              (Time-Point.Day ?Tp2))
                           (And (= (Time-Point.Day ?Tp1)
                                   (Time-Point.Day ?Tp2))
                                (Or (< (Time-Point.Hour ?Tp1)
                                       (Time-Point.Hour ?Tp2))
                                    (And (= (Time-Point.Hour ?Tp1)
                                            (Time-Point.Hour ?Tp2))
                                         (Or (< (Time-Point.Minute ?Tp1)
                                                (Time-Point.Minute ?Tp2))
                                             (And (= (Time-Point.Minute ?Tp1)
                                                     (Time-Point.Minute ?Tp2))
                                                  (< (Time-Point.Second ?Tp1)
                                                     (Time-Point.Second ?Tp2)))))))))))))

(<=> (Tp> $Arg1 $Arg2) (Tp< $Arg2 $Arg1))

(Inverse Tp> Tp<)