First-Order Modal Logic

lt;b>Melvin Fitting was a student of Raymond Smullyan. His dissertation became his first book, Intuitionistic Logic, Model Theory, and Forcing (1969). Since then he has authored or co-authored eleven books and served as editor for another three, as well as writing over 130 papers and book chapters. Among the areas he has worked in are intensional logic, semantics for logic programming, fixpoint theories of truth, and justification logic. A significant part of his work has involved developing tableau systems for non-classical logics, thus generalizing the classical systems of his mentor Smullyan. In 2012 he received the Herbrand Award from the Conference on Automated Deduction, largely for this tableau work, and in 2019 he received an honorary PhD from the University of Bucharest. He was on the faculty of the City University of New York from 1969 to his retirement in 2013. At CUNY he was at the undergraduate Lehman College, and at the City University Graduate Center, where he was in the Departments of Mathematics, Computer Science, and Philosophy. He is now an emeritus Professor, but very much active.
Richard L. Mendelsohn studied philosophy, logic and linguistics while a graduate student at M.I.T. Among the areas he has worked in are modal logic, philosophical logic, philosophy of language, history of early  modern analytic philosophy, and the philosophy of Gottlob Frege. He has authored or coauthored 3 books, and many articles and reviews. He was on the faculty of the City University of New York from 1968 until his retirement in 2014. He continues now as an emeritus Professor at CUNY. In addition, after visiting for many years, he has, since 2014, been an Adjunct Professor of Logic and the Philosophy of Science at the University of California, Irvine and a member of the Center for the Advancement of Logic there. At CUNY he taught at the undergraduate Lehman College and at the City University Graduate Center, where he was a member of the Department of Philosophy, serving as chair from 1993 to 1998, as well as a member of the Department of Linguistics.

Preface.- Acknowledgments.- Part I. Background: Propositional Classical Logic. 1. Background: Propositional Language.- 2. Background: Propositional Axiomatics.- 3. Background: Propositional Tableaus.- Part II. Propositional Modal Logic. 4. Modal Logic, an Introduction.- 5. Propositional Modal Logic.- 6. Propositional Modal Axiom Systems.- 7. Propositional Modal Tableaus.- Part III. First-Order Modal Logic. 8. Quantified Modal Logic.- 9. First-Order Modal Tableaus.- 10. First-Order Modal Axiomatics.- Part IV. Equality and Existence. 11. Equality.- 12. Existence.- Part V. Predicate Abstraction and Scope. 13. Predicate Abstraction, Informally.- 14. Predicate Abstraction, Formally.- 15. Tableaus for Predicate Abstraction.- 16. Tableau Soundness and Completeness. Part VI. Applications. 17. Equality and Predicate Abstraction.- 18. Designation.- 19. Rigidity.- 20. Definite Descriptions.- Afterward.