Conditional language = PROB or TEMP. We used to consider BCMG as a conditional term but no more apparently (not sure if that's just us, or the FAA).
You can go if:
1. DEST VIS Cond. Lang. >= 1/2 of that required for the approach. Also CIG >= 1/2 required only if CIG is a published requirement in the approach (not the norm).
AND
2. 1ST ALT VIS & CIG Cond. Lang. >= 1/2 of that required for the approach. Required CIG in this case, if not published, would be the MDA/DH.
AND
3. 2ND ALT VIS & CIG >= normal minimums (2ND ALT is always required for 3585 at least for us).
In all cases main body language must meet mins.