dthom0425,
The wording of the standard technically require that position and some other controls require that for most practical purposes the feature be defined as a Feature of Size (FOS) - there is some wiggle room for possibly bending these rules with the application of MMC as it does not involve a UAME as Burunduk suggested, but that is a whole other topic. Assuming you are going by ASME Y14.5 the subject of FOS vs nonFOS can bring up significant debate - a search around these forums will bring up a plethora of discussions on the topic.
The main defining feature of a FOS not directly covered by the definition for regular FOS (regular FOS is a fully formed cylinder, opposed parallel planes, etc..) is whether it can be contained or contained by a Unrelated Actual Mating Envelope (UAME). What exactly this means can again be the subject of debate, but for practical purposes in your example your UAME would be a theoretical cylinder expanded within the half cylinder not constrained to any datum features. Imagine using an expanding pin which is not fixed in location/orientation (free floating) which is expanded within the feature for both cases (cylinder having less than 180 deg and cylinder having more than 180 deg) - is there a point at which the feature limits expansion of the pin? I would answer no to the less than 180 degree case and yes to the more than 180 degree case - some others may have differing opinions but I find this to be the most useful interpretation.