If someone makes a Neder prohibiting foods that are Mevushal the Tana of our Mishnah holds that he is permitted to eat roasted and undercooked foods.
Rebbi Yoshiyah holds that he is prohibited from eating roasted foods. (1)
The interpretation of a Neder is dependent on the normal Lashon that is used during regular conversation.
If someone makes a Neder prohibiting foods that are a Tavshil he may eat watery porridge but not thick porridge.
Anything that is eaten with bread is regarded as a Tavshil.
If someone makes a Neder prohibiting foods that are a Tavshil he may not eat roasted or cooked food or small pumpkins that are eaten by the ill.
According to Rebbi Yosi who holds that a person is judged every day we should Daven for the ill every day. (2)
If a Babylonian makes a Neder prohibiting foods that are a Tavshil he may not eat thick chopped wheat. (3)
A person should travel up to a Parsah (four Mil) to eat cooked wheat and up to three Parsah to eat beef.
Melachah is great because it honors the one who is occupied in it.
A BIT MORE
1. In the place that Rebbi Yoshiyah lived people called roasted foods Mevushal while in the place that the Tana of our Mishnah lived people did not call roasted foods Mevushal.
2.Acording to the opinion that a person is judged on Rosh Hashanah it is a Tefilas Shav (wasted Tefilah) to Daven daily for the ill since his Din has already been decided on Rosh Hashanah.
3. Because the Babylonians eat thick chopped wheat with bread and anything that is eaten with bread is regarded as a Tavshil.
If someone makes a Neder prohibiting foods that are Mevushal he is permitted to eat Shaluk. The Rashba says that Shaluk means food that is not completely cooked. Even though undercooked food is regarded as cooked Min ha'Torah however Nedarim depends on the Lashon of Bnei Adam and people do not regard undercooked food as Mevushal. However food that is overcooked is prohibited because people do regard overcooked food as Mevushal.
COOKED VS. ROASTED
If someone makes a Neder or Shevu'ah prohibiting foods that are Mevushal, if the Derech for that place, language and time is to call roasted and partially cooked foods Mevushal they are forbidden. However if the Derech of that place is to call only fully cooked foods Mevushal, roasted and partially cooked foods are permitted. Similarly with regard to smoked and fried foods it is dependent on the Lashon of the place in which that person lives. (Shulchan Aruch YD 217:1)