In casual usage “or” is not well defined. Sometimes it means “exactly one” and sometimes it means “one or more”
Therefore, you cannot assume that the speaker is using the second definition when speaking especially in the middle of a tricky logic puzzle with a speaker who might be an always-liar.
Furthermore, speaking more naturally would be “X thing is true, or I am a liar”—which is a fairly common construction of an Oath even in America—just substitute “so help me god” for the second part, which is the same meaning.
In casual usage “or” is not well defined. Sometimes it means “exactly one” and sometimes it means “one or more”
Therefore, you cannot assume that the speaker is using the second definition when speaking especially in the middle of a tricky logic puzzle with a speaker who might be an always-liar.
Furthermore, speaking more naturally would be “X thing is true, or I am a liar”—which is a fairly common construction of an Oath even in America—just substitute “so help me god” for the second part, which is the same meaning.
In order to make the problem simpler/solvable that assumption is often made. It is one of the cases.