Augmentation of Relation <

• Defined in ontology: Simple-time
• Source pathname: /tmp_mnt/vol/q/htw/cms/ontolingua/examples/foundation-ontologies/simple-time.lisp
• Also defined in: Kif-numbers, Physical-quantities, Unary-scalar-functions

Instance-Of:

Binary-Relation, Binary-Relation, Relation, Relation, Relation ...

Inverse: >

Arity: 2

Documentation:

a time point ?time-point-1 preceeds a time point ?time-point-2.

and also:

The sentence {tt (< $tau_1$ $tau_2$)} is true if and only if the number denoted by $tau_1$ is less than the number denoted by $tau_2$.

Implication Axioms for <:

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

Implication Axioms mentioning <:

(=> (> ?Time-Point-1 ?Time-Point-2)
    (=> (And (Time-Point ?Time-Point-1) (Time-Point ?Time-Point-2))
        (<=> (> ?Time-Point-1 ?Time-Point-2)
             (< ?Time-Point-2 ?Time-Point-1))))

(=> (During ?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)
    (< (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 mentioning <:

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

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

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

(<=> (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))))

(<=> (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))))