TITLE: Book on the first-order modal logic
QUESTION [1 upvotes]: Is there a book on the metatheory for the first-order modal logic, or do I just need to take FOL as a base and use the standard translation?

REPLY [1 votes]: D. M. Gabbay & V. B. Shehtman & D. P. Skvortsov. Quantification in Nonclassical Logic (2009) (Series: Studies in Logic and the Foundations of Mathematics, Volume 153. Elsevier)
It covers a lot of material on first-order modal and first-order intuitionistic logic. E.g. Kripke semantics, algebraic semantics, completeness, etc. Don't be misguided with the titles of the Chapters in the book: "Chapter 1. Basic propositional logic" and "Chapter 2. Basic predicate logic" both mean modal and (super-)intuitionistic logics (propositional ones in Ch.1 and predicate ones in Ch.2).
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