Independence and Hintikka games

This paper investigates the formalization of independence in logic, in particular between quantifiers. We first illustrate that this form of independence plays a role in many fields. A logic that has the possibility to express such a form of independence is Independence Friendly logic (introduced by Hintikka); its semantics is defined by means of strategies in a sequential game. It will be shown that this logic gives results that are in not in accordance with intuitions on independence. An alternative semantics is presented where the logic is interpreted by means of a strategic game. The semantics exploits one assumption: the players are assumed to be rational (they do not play a strategy if there is a better one available). It is shown that this semantics gives results that are in accordance with intuitions about independence.