Source: Notre Dame J. Formal Logic
Volume 43, Number 4
The paper discusses several first-order modal
logics that extend the classical predicate calculus. The model theory
involves possible worlds with world-variable domains. The logics rely
on the philosophical tenet known as serious actualism in that within modal
contexts they allow existential generalization from atomic formulas. The
language may or may not have a sign of identity, includes no primitive
existence predicate, and has individual constants. Some logics correspond to various standard constraints on the accessibility relation, whereas others correspond to various constraints on the domains of the worlds. Soundness and strong
completeness are proved in every case; a novel method is used for proving completeness.
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