Relation Overlaps

• 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 range ?time-range-1 and a time range ?time-range-2 overlaps.

Implication Axioms for Overlaps:

(=> (Overlaps ?Time-Range-1 ?Time-Range-2)
    (< (End-Time-Of ?Time-Range-1) (End-Time-Of ?Time-Range-2)))

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

(=> (Overlaps ?Time-Range-1 ?Time-Range-2)
    (< (Start-Time-Of ?Time-Range-1) (Start-Time-Of ?Time-Range-2)))

Equivalence Axioms for Overlaps:

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

Equivalence Axioms mentioning Overlaps:

(<=> (Overlaps= ?Time-Range-1 ?Time-Range-2)
     (Or (Overlaps ?Time-Range-1 ?Time-Range-2)
         (Meets ?Time-Range-1 ?Time-Range-2)))