As cpast's answer mentioned, the Department of State has an administrative presumption that you don't intend to relinquish citizenship, in the case of several (but not all) of the potentially expatriating acts.
Furthermore, the statute (INA 349, codified as 8 USC 1481), in subsection (b), provides that claims of loss of US nationality need to be established by the party claiming loss of nationality to the standard of "a preponderance of the evidence". This standard applies to all the potentially expatriating acts (including those included and not included in the Department of State's administrative presumption, and would apply even if the Department of State eliminated their administrative presumption).
(b) Whenever the loss of United States nationality is put in issue in
any action or proceeding commenced on or after September 26, 1961
under, or by virtue of, the provisions of this chapter or any other
Act, the burden shall be upon the person or party claiming that such
loss occurred, to establish such claim by a preponderance of the
evidence. Any person who commits or performs, or who has committed or
performed, any act of expatriation under the provisions of this
chapter or any other Act shall be presumed to have done so
voluntarily, but such presumption may be rebutted upon a showing, by a
preponderance of the evidence, that the act or acts committed or
performed were not done voluntarily.
Here, the potentially expatriating act is presumed to have been committed voluntarily, but the intent to relinquish nationality is not presumed and must still be separately proven by the party claiming loss of nationality by "a preponderance of the evidence", as the US Supreme Court explained in Vance v. Terrazas (1980):
- In establishing loss of citizenship, the Government must prove an intent to surrender United States citizenship, not just the voluntary
commission of an expatriating act such as swearing allegiance to a
foreign nation. Congress does not have any general power to take away
an American citizen's citizenship without his "assent," which means an
intent to relinquish citizenship, whether the intent is expressed in
words or is found as a fair inference from his conduct. The
expatriating acts specified in § 349(a) cannot be treated as
conclusive evidence of the indispensable voluntary assent of the
citizen. The trier of fact must, in the end, conclude that the citizen
not only voluntarily committed the expatriating act prescribed in the
statute, but also intended to relinquish his citizenship.
- Nor is the presumption of voluntariness provided in § 349(c) constitutionally infirm. While the statute provides that any of the
statutory expatriating acts, if proved, is presumed to have been
committed voluntarily, it does not also direct a presumption that the
act has been performed with the intent to relinquish United States
citizenship, which matter remains the burden of the party claiming
expatriation to prove by a preponderance of the evidence. [...]