The dogs are joined together with a red harness.
The dog walker harnesses the dogs together for safety.
first sentence does not say the harness belongs to the dog walker.  Dogs can be harnessed together for other reasons than saftey.
exists e1 s1 s2 x1 x2.(n_dog(x1) & with(e1,x2) & n_harness(x2) & a_red(s2) & Theme(s2,x2) & a_together(s1) & Manner(e1,s1) & Theme(e1,x1) & v_join(e1))
exists e1 s1 x1 x2 x3.(n_dog(x2) & n_dog(x2) & n_walker(x1) & of(x1,x2) & for(e1,x3) & n_safety(x3) & a_together(s1) & Manner(e1,s1) & Theme(e1,x2) & Actor(e1,x1) & v_harness(e1))