# Melvin Fitting

**Melvin** "**Mel**" **Fitting** (born January 24, 1942) is a logician with special interests in philosophical logic and tableau proof systems.[lower-alpha 1] He was a Professor at City University of New York, Lehman College and the Graduate Center.[1]^{:723–724} from 1968 to 2013. At the Graduate Center he was in the departments of Computer Science, Philosophy, and Mathematics, and at Lehman College he was in the department of Mathematics and Computer Science. He is now Professor emeritus.

Melvin Fitting | |
---|---|

Born | U.S. | 24 January 1942

Alma mater | |

Awards | Herbrand Award by CADE, June 2012 |

Scientific career | |

Fields | Mathematics, Philosophy, Computer Science |

Institutions | City University of New York |

Doctoral advisor | Raymond Smullyan |

Fitting was born in Troy, New York. His undergraduate degree is from Rensselaer Polytechnic Institute, and his doctorate is from Yeshiva University, both in mathematics. His thesis advisor was Raymond Smullyan.

In June 2012 Melvin Fitting was given the Herbrand Award by CADE, for distinguished contributions to automated deduction.[lower-alpha 2]

A loose motivation for much of Melvin Fitting's work can be formulated succinctly as follows. There are many logics. Our principles of reasoning vary with context and subject matter. Multiplicity is one of the glories of modern formal logic. The common thread tying logics together is a concern for what can be said (syntax), what that means (semantics), and relationships between the two. A philosophical position that can be embodied in a formal logic has been shown to be coherent, not correct. Logic is a tool, not a master, but it is an enjoyable tool to use.

## Selected publications

**Intuitionistic Logic, Model Theory, and Forcing**, North-Holland, Amsterdam, 1969.- Tableau methods of proof for modal logics, Notre Dame Journal of Formal Logic, 13 (2), 237-247 (1972).
- Model existence theorems for modal and intuitionistic logics, Journal of Symbolic Logic, 38, 613-627 (1973).
- Fundamentals of Generalized Recursion Theory, North-Holland, Amsterdam, 1981.
- Proof Methods for Modal and Intuitionistic Logics, D. Reidel, Dordrecht, 1983.
**A Kripke-Kleene Semantics for Logic Programs**, Journal of Logic Programming, 2 (4), 295-312, (1985); North-Holland.- First-Order Modal Tableaux, Journal of Automated Reasoning, 4 (2), 191-213 (1988) Springer.
- Logic Programming on a Topological Bilattice, Fundamenta Informaticae, 1988.
- Bilattices and the theory of truth, Journal of Philosophical Logic, 18 (3), 225-256 (1989) Springer.
**First-Order Logic and Automated Theorem Proving**, Springer-Verlag, 1990, second edition 1996.- Bilattices in Logic Programming, in Proc. of the IEEE Int'l Symposium on Multiple-Valued Logic, pp238–246 (1990).
**Bilattices and the Semantics of Logic Programming**, Journal of Logic (and Algebraic) Programming, 11 (1&2), 91-116 (1991) Elsevier.- Kleene's Logic, Generalized, Journal of Logic and Computation (LOGCOM), 1 (6), 797-810 (1991) Oxford University Press.
- Many-Valued Modal Logics (I), Fundamenta Informaticae, 15 (3-4), 235-254 (1991).
- Many-Valued Model Logics II, Fundamenta Informaticae, 17 (1-2), 55-73 (1992).
- The Family of Stable Models, Journal of Logic (and Algebraic) Programming, 17 (2/3&4), 197-225 (1993) Elsevier.
- Basic modal logic, in Handbook of logic in artificial intelligence and logic...(cut off?), 1993.
- Metric Methods: Three Examples and a Theorem, Journal of Logic and Algebraic Programming, 21 (3), 113-127 (1994).
- Kleene's Three Valued Logics and Their Children, Fundamenta Informaticae, 20 (1/2/3), 113-131 (1994) IOS Press.
**Set Theory and the Continuum Problem**, with Raymond M. Smullyan, 288 pages, Oxford University Press (or Clarendon Press?), 1996. Revised edition, Dover, 2010.[lower-alpha 3]- A theory of truth that prefers falsehood, Journal of Philosophical Logic, 26 (5), 477-500 (1997).
- Bertrand Russell, Herbrand's Theorem, and the assignment statement, in Artificial Intelligence and Symbolic Computation, Springer Lecture Notes in Artificial Intelligence 1476, pp 14–28, 1998.
**First-Order Modal Logic**, with Richard L. Mendelsohn, Verlag: Kluwer Academic Publishers, 1998, paperback, 1999, ISBN 9780792353355.[2][3]- Higher-order modal logic - a sketch, in 1999 volume on First-order Theorem Proving (FTP'98), pages 22–36.[lower-alpha 4]
- First order alethic modal logic, in the Blackwell Companion to Philosophical Logic, Dale Jacquette (ed.), 2000.
- Databases and Higher Types, CL2000 Invited Speakers and Tutorials.[lower-alpha 5]
- Term-Modal Logics, with Lars Thalmann and Andrei Voronkov.[lower-alpha 6]
- Fixpoint semantics for logic programming, Theoretical Computer Science (journal), 278 (1-2), 25-51 (2002) Elsevier.
- AddOns, FLoC'02 HYLO, Invited speaker.[lower-alpha 7]
**Types, Tableaus, and Gödel's God**, Kluwer, 2002; also, in the 2005-12-01 Journal Studia Logica, 81 (3), 425-427 (2005).[lower-alpha 8]- Beyond Two: Theory and Applications of Multiple-Valued Logic, co-edited with Ewa Orlowska, Springer, 2003.
- First-order intensional logic, Annals of Pure and Applied Logic, 127 (1), 171193 (2004).
- The logic of proofs, semantically, Annals of Pure and Applied Logic, 132 (1), 1-25 (2005) Elsevier.
- Bilattices are nice things, in Self-Reference, Center for the Study of Language and Information, Thomas Bolander, Vincent Hendricks, Stig Andur Pedersen editors, 55-77 (2006).
**Incompleteness in the Land of Sets**, College Publications, 2007.[lower-alpha 9]- Modal proof theory, chapter in
*Handbook of Modal Logic*, P. Blackburn, J. Van Benthem, F. Wolter (eds.), pp85–138 (2007) Elsevier.[4] - Explicit Logics of Knowledge and Conservativity, ISAIM 2008.[lower-alpha 10]
- Prefixed tableaus and nested sequents, Annals of Pure and Applied Logic, 163 (3), 291-313 (2012).
- ESSLLI 2012. Evening lecture.[lower-alpha 11]
- Justification Logic, Stanford Encyclopedia of Philosophy, (Fall 2012 Edition), Edward N. Zalta (ed.), co-authored with Sergei N. Artemov.[lower-alpha 12]
- Intensional Logic, Stanford Encyclopedia of Philosophy, (Winter 2012 Edition), Edward N. Zalta (ed.).[lower-alpha 13]

## References

- Jean-Louis Lassez; Gordon Plotkin, eds. (1991).
*Computational Logic — Essays in Honor of Alan Robinson*. Cambridge/MA: MIT Press. ISBN 978-0-262-12156-9. - Review: Melvin Fitting, Richard L. Mendelsohn, First-Order Modal Logic
- Teach yourself logic, #2: Modal logic
- Hakli, Raul and Negri, Sara. "Does the deduction theorem fail for modern logic?

## Notes

- "Google Scholar Citations report for Melvin Fitting".
- Leading Mathematics and Computer Sciences Researcher Wins Prestigious Award
- https://books.google.com/books/about/Set_theory_and_the_continuum_problem.html
- http://logic.at/ftp98/
- http://doc.ic.ac.uk/cl2000/speakers.htm
- http://jstor.org/stable/20016340
- http://floc02.diku.dk/HYLO/
- Girle, Roderic A. (2005). "Melvin Fitting, Types Tableaus and Gödel's God".
*Studia Logica*.**81**(3): 425–427. doi:10.1007/s11225-005-4652-x. - http://www.chronon.org/Science/Incompleteness_in_the_land_of_sets.php , book review
- http://isaim2008.unl.edu/PAPERS/SS1-AI+Logic/MFitting-ss1.pdf
- "ESSLLI 2012 lectures". Also speaking were Jonathan Ginzburg and Adam Przepiorkowski.
- http://plato.stanford.edu/entries/logic-justification
- http://plato.stanford.edu/entries/logic-intensional/

## External links

- Melvin Fitting, official homepage
- The Graduate Center, faculty page at CUNY
- Mathematical Genealogy Project