Independence-friendly logic

A Simple Logic of Functional Dependence

“…57 In response to an earlier version of this paper, completeness and decidability results for the temporal dependence logic of dynamical systems have been claimed in [56]. 58 It is often said that committing to a strategy makes one's actions independent from those by the other player, since the strategy was chosen beforehand. However, this seems a confusion between pre-game deliberation and in-game play: as the game is played, a strategy does follow the particular moves chosen by the other players.…”

“…Moreover, in contrast with LFD, IF-logic is second-order and non-axiomatizable. For a complete mathematical development of IF-logic, see [58].…”

“…Thus, committing to a choice, or a strategy in general, changes the current dependence model for the game to one where appropriate dependence statements come to hold. 58 Extensive game trees can be associated with dependence models whose variables stand for successive actions by the players. 59 Moreover, the action perspective introduces the dependence dynamics of Section 6.4.…”

Game theoretical semantics for some non-classical logics

“…Additionally, relating GTS to constructivism and intuitionism with some reference to type-theoretical foundations was presented by Ranta (Ranta, 1988). An epistemic, first-order extension of GTS, called "Independence-Friendly" logic, was suggested by Hintikka and Sandu (Hintikka & Sandu, 1989;Mann, Sandu, & Sevenster, 2011). Independence-friendly logics can be viewed as the logics for imperfect information games and they introduce Henkin quantifiers to game theoretical discussions.…”

“…Yet another complication is that such a move involves formula dependency, and the game rules must reflect this fact. For this reason, we have not considered preservationist paraconsistent systems in this work, even if they seem to provide a rich mathematical machinery and interesting applications, especially for IF-logic or dependency logic (Mann et al, 2011;Väänänen, 2007).…”