Abstract A natural deduction system of quantified modal logic (S5) with an actuality operator and "rigid " quantifiers (ranging, at every world, over the domain of the actual world) is described and proved to be complete. Its motivation and relation to other systems are discussed. / The language Predicates. One logical predicate: E! , "exists". Individual constants if you want, though for simplicity I'll ignore them (constants thought of as formalizing names or other "rigid designators " ought to behave like the free variables). Individual "parameters " (free variables): u,υ9.... Individual bound variables: x9y,... (I follow the conventions of Thomason [16] here). Truth func-tional connectives: &, v, D, ~. Modal operators: D (necessity), 0 (possibility),

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