premise: A black and white dog jumps up and down in the snow.
hypothesis: A dog plays in the winter.
explanation_1: A dog plays when he jumps up and down.  There is snow during winter.
explanation_2: Black and white dog is a type of dog, and snow implies winter.
explanation_3: The phrase "jumping up and down" suggests playing.  The fact that there is snow on the ground suggests that it is winter.
premise_logic: exists e1 e2 s1 s2 s3 s4 s5 s6 x1 x2 x3 x4.(n_snow(x4) & n_snow(x2) & in(e2,x4) & a_down(s6) & Manner(e2,s6) & Actor(e2,x3) & v_jump(e2) & n_dog(x3) & a_white(s5) & Theme(s5,x3) & a_black(s4) & Theme(s4,x3) & in(e1,x2) & a_up(s3) & Manner(e1,s3) & Actor(e1,x1) & v_jump(e1) & n_dog(x1) & a_white(s2) & Theme(s2,x1) & a_black(s1) & Theme(s1,x1))
hypothesis_logic: exists e1 x1 x2.(n_winter(x2) & in(e1,x2) & Actor(e1,x1) & v_play(e1) & n_dog(x1))