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Independence-friendly logic (IF logic), proposed by Jaakko Hintikka and Gabriel Sandu, aims at being a more natural and intuitive alternative to classical first-order logic (FOL). IF logic is characterized by branching quantifiers. It is more expressive than FOL because it allows one to express independence relations between quantified variables. For example, the formula ∀a∀b∃c/b∃d/aφ(a,b,c,d) ("x/y" should be read as "x independent of y") cannot be expressed in FOL.
Semantics
Hintikka argues that the standard Tarskian semantics of FOL cannot accommodate IF logic because the principle of compositionality fails in the latter. But Wilfrid Hodges (1997) proposes a counter-example by giving such a semantics for it. Hintikka still objects that it really provides a compositional semantics for all forms of IF logic under all interpretations of compositionality.
The game-theoretic semantics for FOL treats an FOL formula as zero sum games of perfect information, whose players are Verifier and Falsifier. The same holds for the standard semantics for an IF formula, except that a game of imperfect information may be required.
A formula is true if Verifier has a winning strategy and false if Falsifier has one. A winning strategy is defined as a strategy that is guaranteed to win the game, regardless of how the other players play.
Independence relations are expressed by informational independence amongst players.
References
- Wilfred Hodges, 1997, 'Compositional semantics for a language of imperfect information'. Journal of the IGPL 5: 539–563.
- Wilfred Hodges, 2004. 'Logic and Games'. Stanford Encyclopedia of Philosophy.
- Janssen, Theo M. V. "Independent choices and the interpretation of IF logic."
- Dag Westerståhl, 2005. 'Generalized Quantifiers'. Stanford Encyclopedia of Philosophy.
External link
"Independence-friendly logic"