Relation Equals

• Defined in ontology: Simple-time
• Source pathname: /tmp_mnt/vol/q/htw/cms/ontolingua/examples/foundation-ontologies/simple-time.lisp

Instance-Of: Binary-Relation, Relation, Set

Arity: 2

Documentation:

a time point ?time-point-1 is equal to a time point ?time-point-2.

a time range ?time-range-1 is identical to a time range ?time-range-2.

Implication Axioms for Equals:

(=> (And (Time-Range ?Time-Range-1) (Time-Range ?Time-Range-2))
    (<=> (Equals ?Time-Range-1 ?Time-Range-2)
         (And (Equals (Start-Time-Of ?Time-Range-1)
                      (Start-Time-Of ?Time-Range-2))
              (Equals (End-Time-Of ?Time-Range-1)
                      (End-Time-Of ?Time-Range-2)))))

(=> (Equals ?Time-Point-1 ?Time-Point-2)
    (=> (And (Time-Point ?Time-Point-1) (Time-Point ?Time-Point-2))
        (<=> (Equals ?Time-Point-1 ?Time-Point-2)
             (And (= (Year-Of ?Time-Point-1) (Year-Of ?Time-Point-2))
                  (= (Month-Of ?Time-Point-1)
                     (Month-Of ?Time-Point-2))
                  (= (Day-Of ?Time-Point-1) (Day-Of ?Time-Point-2))
                  (= (Hour-Of ?Time-Point-1) (Hour-Of ?Time-Point-2))
                  (= (Minute-Of ?Time-Point-1)
                     (Minute-Of ?Time-Point-2))
                  (= (Second-Of ?Time-Point-1)
                     (Second-Of ?Time-Point-2))))))

Implication Axioms mentioning Equals:

(=> (Time-Range ?Time-Range)
    (Equals (+ (Start-Time-Of ?Time-Range) (Duration-Of ?Time-Range))
            (End-Time-Of ?Time-Range)))

(=> (Starts ?Time-Range-1 ?Time-Range-2)
    (Equals (Start-Time-Of ?Time-Range-1)
            (Start-Time-Of ?Time-Range-2)))

(=> (Finishes ?Time-Range-1 ?Time-Range-2)
    (Equals (End-Time-Of ?Time-Range-1) (End-Time-Of ?Time-Range-2)))

Equivalence Axioms mentioning Equals:

(<=> (Meets ?Time-Range-1 ?Time-Range-2)
     (Equals (End-Time-Of ?Time-Range-1)
             (Start-Time-Of ?Time-Range-2)))

(<=> (Starts ?Time-Range-1 ?Time-Range-2)
     (And (Equals (Start-Time-Of ?Time-Range-1)
                  (Start-Time-Of ?Time-Range-2))
          (< (End-Time-Of ?Time-Range-1) (End-Time-Of ?Time-Range-2))))

(<=> (Finishes ?Time-Range-1 ?Time-Range-2)
     (And (> (Start-Time-Of ?Time-Range-1)
             (Start-Time-Of ?Time-Range-2))
          (Equals (End-Time-Of ?Time-Range-1)
                  (End-Time-Of ?Time-Range-2))))

(<=> (During= ?Time-Range-1 ?Time-Range-2)
     (Or (During ?Time-Range-1 ?Time-Range-2)
         (Starts ?Time-Range-1 ?Time-Range-2)
         (Finishes ?Time-Range-1 ?Time-Range-2)
         (Equals ?Time-Range-1 ?Time-Range-2)))

(<=> (Start= ?Time-Range-1 ?Time-Range-2)
     (Or (Starts ?Time-Range-1 ?Time-Range-2)
         (Equals ?Time-Range-1 ?Time-Range-2)))