How Things Are Elsewhere
Wolfgang Schwarz · Palgrave Macmillan UK eBooks · 2012
When quantifiers and modal operators mingle, all sorts of troubles arise. Legend has it that after some initial confusion about how to make sense of formulas like ∃x◊Fx, the issue was finally settled by Saul Kripke, who put forward what is now known as Kripke semantics for quantified modal logic. Formulas like ∃x◊Fx are interpreted by models consisting of some “possible worlds”, each equipped with a quantifier domain, and an interpretation function that specifies which individuals satisfy which predicates relative to which worlds. Modal operators function as quantifiers over the worlds, restricted by an “accessibility” relation. ∃x◊Fx is true at a world w iff there is an individual in the domain of w that satisfies F relative to some world accessible from w. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.