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Bibliography
W. Ackermann.:Uber die Erfüllbarkeit gewisser Zählausdrücke. Mathematische Annalen, 100:638–649, 1928.
O. Arieli and A. Avron. The value of four values. Artificial Intelligence, 102:97–141, 1998.
F. Baader and W. Snyder. Unification theory. In A. Robinson and A. Voronkov, editors, Handbook of Automated Reasoning, volume I, chapter 8, pages 445–532. Elsevier Science, 2001.
M. Baaz and C.G. Fermüller. Resolution-based theorem proving for many-valued logics. Journal of Symbolic Computation, 19(4):353–391, April 1995.
M. Baaz and A. Leitsch. Complexity of resolution proofs and function introduction. Annals of Pure and Applied Logic, 57:181–215, 1992.
M. Baaz and A. Leitsch. On skolemization and proof complexity. Fundamenta Informaticae, 20:353–379, 1994.
M. Baaz and A. Leitsch. Cut normal forms and proof complexity. Annals of Pure and Applied Logic, 97:127–177, 1999.
M. Baaz and A. Leitsch. Cut-elimination and redundancy-elimination by resolution. J. Symbolic Computation, 29:149–176, 2000.
[Baaz et al., 1994]_M. Baaz, C.G. Fermüller, and A. Leitsch. A non-elementary speed-up in proof length by structural clause form transformation. In Proc. LICS, pages 213–219, 1994.
[Baaz et al., 1996]_M. Baaz, C.G. Fermüller, G. Salzer, and R. Zach. MUltlog 1.0: Towards an expert system for many-valued logics. In 13th Int. Conf. on Automated Deduction (CADE’96), volume 1104 of Lecture Notes in Artificial Intelligence, pages 226–230. Springer, 1996.
[Baaz et al., 1998]_M. Baaz, C.G. Fermüller, G. Salzer, and R. Zach. Labeled calculi and finite-valued logics. Studia Logica, 61(1):7–13, 1998.
[Baaz et al., 2001a]_M. Baaz, U. Egly, and A. Leitsch. Normal form transformations. In A. Robinson and A. Voronkov, editors, Handbook of Automated Reasoning, volume I, chapter 5, pages 273–333. Elsevier Science, 2001.
[Baaz et al., 2001b]_M. Baaz, C.G. Fermüller, and G. Salzer. Automated deduction for many-valued logics. In A. Robinson and A. Voronkov, editors, Handbook of Automated Reasoning, volume II, chapter 20, pages 1355–1402. Elsevier Science, 2001.
[Baaz et al., 2001c]_M. Baaz, C.G. Fermüller, and G. Salzer. Automated deduction for many-valued logics. In John Alan Robinson and Andrei Voronkov, editors, Handbook of Automated Reasoning (in 2 volumes), volume 2, pages 1356–1402. Elsevier and MIT Press, 2001.
L. Bachmair and H. Ganzinger. Rewrite-based equational theorem proving with selection and simplification. Journal of Logic and Computation, 4:1–31, 1994.
L. Bachmair and H. Ganzinger. Resolution theorem proving. In A. Robinson and A. Voronkov, editors, Handbook of Automated Reasoning, volume I, chapter 2, pages 19–99. Elsevier Science, 2001.
N.D. Belnap Jr. A useful four-valued logic. In J. Micheal Dunn and George Epstein, editors, Modern uses of multiple-valued logic, pages 8–37. Reidel, Dordrecht, 1977.
W. Bernays and M. Schönfinkel. Zum Entscheidungsproblem der mathematischen Logik. Mathematische Annalen, 99:342–372, 1928.
G. Boole. An investigation on the laws of thought. Dover Publications, 1958.
[Börger et al., 1997]_E. Börger, E. Grädel, and Y. Gurevich. The Classical Decision Problem. Perspectives in Mathematical Logic. Springer, 1997.
A. Church. A note on the Entscheidungsproblem. Journal of Symbolic Logic, 1:40–44, 1936.
M. Davis and H. Putnam. A Computing Procedure for Quantification Theory. Journal of the ACM, 7(3):201–215, July 1960.
N. Dershowitz and D.A. Plaisted. Rewriting. In A. Robinson and A. Voronkov, editors, Handbook of Automated Reasoning, volume I, chapter 9, pages 535–610. Elsevier Science, 2001.
E. Eder. Relative complexities of first-order calculi. Vieweg, 1992.
U. Egly and T. Rath. On the practical value of different definitional translations to normal form. In Proc. of CADE-13, volume 1104 of Lecture Notes in Artificial Intelligence, pages 403–417. Springer, 1996.
C.G. Fermüller and A. Leitsch. Hyperresolution and automated model building. Journal of Logic and Computation, 6(2):173–203, 1996.
[Fermüller et al., 1993]_C.G. Fermüller, A. Leitsch, T. Tammet, and N. Zamov. Resolution Methods for the Decision Problem, volume 679 of Lecture Notes in Artificial Intelligence. Springer, 1993.
[Fermüller et al., 2001]_C.G. Fermüller, A. Leitsch, U. Hustadt, and T. Tammet. Resolution decision procedures. In A. Robinson and A. Voronkov, editors, Handbook of Automated Reasoning, volume II, chapter 25, pages 1791–1849. Elsevier Science, 2001.
G. Frege. Begriffsschrift, eine der arithmetischen nachgebildete Formelsprachedes reinen Denkens. In J. van Heijenoort, editor, From Frege to Gödel: A sourcebook in mathematical logic 1879-1931. Harvard University Press, 1967.
H. Gelernter. Realization of a geometry theorem proving machine. In Proceedings of the International Conference on Information Processing, pages 273–282, June 1959.
G. Gentzen. DeUntersuchungen über das logische Schließen. Mathematische Zeitschrift, 39:405–431, 1934.
G. Gentzen. Untersuchungen über das logische Schließen I-II. Mathematische Zeitschrift, 39:176–210 and 405-431, 1934-35.
P.C. Gilmore. A proof method for quantification theory: its justification and realization. IBM J. Res. Dev., pages 28–35, 1960.
K. Gödel. Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme. Monatshefte für Mathematik und Physik, 38:175–198, 1931.
K. Gödel. Ein Spezialfall des Entscheidungsproblems der theoretischen Logik. Ergebnisse Mathematischer Kolloquien, 2:27–28, 1932.
K. Gödel. Zum intuitionistischen Aussagenkalkül. Anzeiger der Akademie der Wissenschaften in Wien, 69:65–66, 1932.
R. Hähnle. Commodious axiomatization of quantifiers in multiple-valued logic. Studia Logica, 61(1):101–121, 1998.
R. Hähnle. Tableaux and related methods. In A. Robinson and A. Voronkov, editors, Handbook of Automated Reasoning, volume 1, pages 101–178. Elsevier, 2001.
J. Herbrand. Sur le problème fondamental de la logique mathématique. Sprawozdania z posiedzen Towarzysta Naukowego Warszawskiego, Wydzial III, 24:12–56, 1931.
D. Hilbert and W. Ackermann. Grundzüge der theoretischen Logik. Springer, Berlin, 1928.
D. Hilbert and P. Bernays. Grundlagen der Mathematik. Springer, 1970.
W. Joyner. Automated Theorem Proving and the Decision Problem. PhD thesis, Harvard University, 1973.
W.H. Joyner. Resolution strategies as decision procedures. Journal of the ACM, 23: 398–417, 1976.
G.W. Leibniz. Calculus ratiocinator. In Preussische Akademie der Wissenschaften, editor, Sämtliche Schriften und Briefe. Reichel, Darmstadt, 1923.
A. Leitsch. The resolution calculus. Springer. Texts in Theoretical Computer Science, 1997.
D.W. Loveland. A linear format for resolution. In Proc. IRIA Symposium on Automatic Demonstration, volume 125 of Lecture Notes in Mathematics, pages 147–162. Springer, 1970.
L. Löwenheim. Über Möglichkeiten im Relativkalkül. Mathematische Annalen, 68:169–207, 1915.
J. Lukasiewicz. Philosophische Bemerkungen zu mehrwertigen Systemen des Aussagenkalküls. Comptes rendus des séances de la Société des Sciences et des Lettres de Varsovie Cl. III, 23:51–77, 1930.
A. Martelli and U. Montanari. Unification in linear time and space: a structured presentation. Technical Report B76-16, Istituto di elaborazione della informazione, 1976.
S.Y. Maslov. The inverse method for establishing deducibility for logical calculi. Proc. Steklov Inst. Math., 98:25–96, 1968.
W. McCune. Solution of the Robbins problem. Journal of Automated Reasoning, 19(3): 263–276, 1997.
G. Mints. Gentzen-type systems and resolution rule, part I: Propositional logic. In P. Martin-Löf and G. Mints, editors, Proceedings Int. Conf. on Computer Logic, COLOG’88, Tallinn, USSR, 12-16 Dec 1988, volume 417 of Lecture Notes in Computer Science, pages 198–231. Springer-Verlag, Berlin, 1990.
G. Mints. Gentzen-type systems and resolution rule, part II: Predicate logic. In J. Oikkonen and J. Väänänen, editors, Proceedings ASL Summer Meeting, Logic Colloquium’ 90, Helsinki, Finland, 15-22 July 1990, volume 2 of Lecture Notes in Logic, pages 163–190. Springer-Verlag, Berlin, 1993.
[Ohlbach et al., 2001]_H.J. Ohlbach, A. Nonnengart, M. de Rijke, and D. Gabbay. Encoding two-valued nonclassical logics in classical logic. In A. Robinson and A. Voronkov, editors, Handbook of Automated Reasoning, volume II, chapter 21, pages 1403–1486. Elsevier Science, 2001.
V.P. Orevkov. Lower bounds for increasing complexity of derivations after cut elimination. Journal of Soviet Mathematics, 20:2337–2350, 1982.
R. Pichler. Algorithms on atomic representations of Herbrand models. In Proc. of JELIA’98, pages 199–215. Springer, LNAI 1489, 1998.
J.A. Robinson. Automatic deduction with hyperresolution. Intern. Journal of Computer Math., 1:227–234, 1965.
J.A. Robinson. A machine-oriented logic based on the resolution principle. J. Assoc. Comput. Mach., 12:23–41, 1965.
G. Rousseau. Sequents in many valued logic I. Fundamenta Mathematicæ, LX: 23–33, 1967.
G. Salzer. Optimal axiomatizations for multiple-valued operators and quantifiers based on semilattices. In Michael McRobbie and John Slaney, editors, Proc. 13th Conference on Automated Deduction, New Brunswick/NJ, USA, volume 1104 of LNCS, pages 688–702. Springer-Verlag, 1996.
J.R. Slagle. Automatic theorem proving with renamable and semantic resolution. Journal of the ACM, 14(4):687–697, October 1967.
V. Sofronie-Stokkermans. Resolution-based theorem proving for SHn-logics. In Ricardo Caferra and Gernot Salzer, editors, Int. Workshop on First-Order Theorem Proving (FTP’ 98), Technical Report E1852-GS-981, pages 224–233. Technische Universitat Wien, Austria, 1998.
R. Statman. Lower bounds on Herbrand’s theorem. Proc. of the Amer. Math. Soc., 75:104–107, 1979.
M. Takahashi. Many-valued logics of extended Gentzen style I. Science Reports of the Tokyo Kyoiku Daigaku, Section A, 9(231):95–116, 1967.
G. Takeuti. Proof Theory. North-Holland, second edition, 1987.
A. Turing. On computable numbers with an application to the Entscheidungsproblem. Proc. of the London Math. Soc., Ser. 2(42):230–265, 1936/37.
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Leitsch, A., Fermüller, C. (2005). The Resolution Principle. In: Gabbay, D., Guenthner, F. (eds) Handbook of Philosophical Logic. Handbook of Philosophical Logic, vol 12. Springer, Dordrecht. https://doi.org/10.1007/1-4020-3092-4_2
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