I did some experimentation on how Wolfram Alpha handles ambiguity in "who is the ruler of $place?" using places with varying degrees of difficulty.

Monarchies

Britain

• Ruler: Elizabeth II (the queen)
• Prime Minister: David Cameron
• President: "Wolfram|Alpha didn't understand your query. Showing instead results for query: president"
• Chancellor: "Using closest Wolfram|Alpha interpretation: chancellor; listed Werner Faymann as Chancellor of Austria and Angela Merkel as Chancellor of Germany; "who is chancellor of the exchequer" yielded the same result

Scottland

• Ruler: no result found; rules of Bahrain listed
• Prime minister: no result found; got statistics on clergy in the US
• First minister: Alex Salmond

Canada * Ruler: Elizabeth II

Spain:

• Ruler: Felipe VI (the king)
• Prime Minister: Mariano Rajoy
• President (the Prime Minister's official title is "Presidente del Gobierno", which I believe can be translated as "President of the Government" or "President of the Cabinet"): no answer

Jordan:

• Ruler: Abdullah II (the king)
• Prime Minister: Abdullah Ensour

Non-monarchies

America

*Ruler: Barack Obama

Germany

• Ruler: Joachim Gauck (the figurehead president)
• Prime Minister: "Wolfram|Alpha doesn't understand your question"; gave statistics about the number of clergy in the United States
• Chancellor: Angela Merkel

Ireland

• Prime Minister (official title is Taoiseach): Enda Kenny
• Ruler: Michael D. Higgins (figurehead president)

France

• Ruler: Francois Hollande

China

• Ruler: Xi Jingping

Republic of China:

• Ruler: Ma Ying-jeou

Korea:

• Ruler: "Wolfram|Alpha doesn't understand your query", with a list of people who have held the title of Bahrain

South Korea:

• Ruler: Park Geun-hye

North Korea:

• Ruler: Kim Jong Il (not Kim Jong Un), along with some rather odd chronology (apparently the position was vacant from 1994 to 1997); his end date is listed as Dec. 17, 2011; no mention of Kim Jong Un Georgia

• Ruler: (none in office); the current Governor, Nathan Deal, is listed as a past governor with and end date of today, as are Senators Johnny Isakson and Saxby Chambliss, neither of whom has ever been governor; former governor Roy Barnes is listed with the correct dates, but his successor Sonny Perdue is not listed; the page also states that it is assuming "Georgia" is referring to the US state and gives a link to look up the country instead

Republic of Georgia

• Ruler: Giorgi Margvelashvili (President)

New Mexico

• Ruler: no information available
• Governor: Susana Martinez

Mexico

• Ruler: Enrique Peña Nieto
• Governor: Wolfram|Alpha didn't understand your query; no results given (exceeded max computation time)

"Who is the prime minister?": exceeded max computation time

General Observations The "ruler" of a place is determined based solely on the title

• If there is both a monarch and a prime minister, the monarch is listed as the ruler, whether the monarch has more power (Jordan) or the prime minister does (Britain, Canada, Spain)
• If there is both a president and a prime minister, the president is listed as the ruler, whether the president is actually in charge (France) or is a figurehead (Germany)

Close matches don't count (prime minister of Germany, president of Spain)

It tries to answer every question but says when it doesn't understand something (president of britain, ruler of korea)

Sometimes it gets the facts blatantly wrong, but almost right (Kim Jong Il still rules North Korea; Georgia has no governor)

It handles both very slightly ambiguous (China vs Republic of China; Mexico vs New Mexico) and moderately ambiguous ("Georgia" as State of Georgia vs Republic of Georgia) reasonably