When pulling a mob such as a pig with a lead, they will not automatically walk up a bottom half slab if they are on a path block. However, they will walk up from one path block to another that is 1 meter higher. If they are on a solid block rather than a path block, they have no trouble walking up a bottom half slab or just from one solid block to another solid block 1 meter higher.

Here is a chart to describe the behavior, first block is 1 meter lower than second:

Path -> path: Yes

Path -> solid: Yes

Solid -> path: Yes

Solid -> solid: Yes

Solid -> bottom slab: Yes

Path -> bottom slab: No

bottom slab -> path: Yes (in this case and the following one the two blocks are at the same Y level)

bottom slab -> solid: Yes