Simplifying proofs in fitch-style natural deduction systems

Journal of Automated Reasoning

Volumn 34, Issue 3, 2005, Pages 239-294

  Arkoudas, Konstantine ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Assumption bases; Denotational proof languages; Detours; Fitch style; Natural deduction; NDL; Proof simplification

Indexed keywords

COMPUTATIONAL COMPLEXITY; COMPUTER PROGRAMMING LANGUAGES; FORMAL LOGIC; SEMANTICS;

ASSUMPTION BASES; DETONATION PROOF LANGUAGES; DETOURS; FITCH STYLE; NATURAL DEDUCTION; NDL; PROOF SIMPLIFICATION;

AUTOMATIC PROGRAMMING;

EID: 33746050366     PISSN: 01687433     EISSN: 15730670     Source Type: Journal    
DOI: 10.1007/s10817-005-9000-3     Document Type: Article

References (37)

1. Arkoudas, K.: Athena, http://www.pac.csail.mit.edu/athena.
2. Arkoudas, K.: Denotational Proof Languages. PhD dissertation, MIT, 2000.
3. Arkoudas, K.: Type-α DPLs. MIT AI Memo 2001-25.
4. Arkoudas, K.: Type-ω DPLs. MIT AI Memo 2001-27.
5. Arkoudas, K., Khurshid, S., Marinov, D. and Rinard, M.: Integrating model checking and theorem proving for relational reasoning, in Proceedings of the 7th International Seminar on Relational Methods in Computer Science (RelMiCS 7), Malente, Germany, May 2003.
6. Arkoudas, K. and Rinard, M.: Deductive runtime certification, in Proceedings of the 2004 Workshop on Runtime Verification, Barcelona, Spain, April 2004.
7. Barwise, J. and Etchemendy, J.: Hyperproof: for Macintosh, CSLI Publications, 1995.
8. Bergmann, M., Moor, J. and Nelson, J.: The Logic Book, Random House, New York, 1980.
9. Bonevac, D.: Deduction, Blackwell Publishing, 2003.
10. Boolos, G.: Don't eliminate cut, J. Philos. Logic 13 (1984), 373-378.
11. Copi, I. M.: Symbolic Logic, 5th edn., Macmillan Publishing Co., New York, 1979.
12. Dalen, D. V.: Logic and Structure, Springer Verlag, 1983.
13. Dragalin, A. G.: Mathematical Intuitionism. Introduction to Proof Theory, volume 67 of Translations of Mathematical Monographs, American Mathematical Society, Providence, RI, 1988.
14. Ebbinghaus, H.-D., Flum, J. and Thomas, W.: Mathematical Logic, 2nd edn., Springer-Verlag, 1994.
15. Fitch, F. B.: Symbolic Logic: An Introduction, The Ronald Press Co., New York, 1952.
16. Gentzen, G.: The Collected Papers of Gerhard Gentzen, North-Holland, Amsterdam, Holland, 1969, English translations of Gentzen's papers, edited and introduced by M. E. Szabo.
17. Girard, J.-Y., Lafont, Y. and Taylor, P.: Proofs and Types, volume 7 of Cambridge Tracts in Theoretical Computer Science, Cambridge University Press, 1989.
18. Gordon, M. J. C. and Melham, T. F.: Introduction to HOL, A Theorem Proving Environment for Higher-Order Logic, Cambridge University Press, Cambridge, England, 1993.
19. Harper, R., Honsell, F. and Plotkin, G.; A framework for defining logics, J. Assoc. Comput. Mach. 40(1) (1993), 143-184, January.
20. Howard, W. A.: The formulae-as-types notion of construction, in J. Hindley and J. R. Seldin (eds.), To H. B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalisms, Academic Press, 1980, pp. 479-490.
21. Kahn, G.: Natural semantics, in Proceedings of Theoretical Aspects of Computer Science, Passau, Germany, February 1987.
22. Kalish, D. and Montague, R.: Logic: Techniques of Formal Reasoning, Harcourt Brace Jovanovich, Inc., New York, 1964, 2nd edn in 1980, with G. Mar.
23. Lemmon, E. J.: Beginning Logic, Hackett Publishing Company, 1978.
24. Necula, G. and Lee, P.: Proof-carrying code. Computer Science Technical Report CMU-CS-96-165, CMU, September 1996.
25. Necula, G. and Lee, P.: Efficient representation and validation of logical proofs. Computer Science Technical Report CMU-CS-97-172, CMU, October 1997.
26. Paulson, L.: Isabelle, A Generic Theorem Prover, Lecture Notes in Computer Science. Springer-Verlag, 1994.
27. Pelletier, F. J.: A brief history of natural deduction, Hist. Philos. Logic 20 (1999), 1-31.
28. Pelletier, J.: Automated natural deduction in thinker, Stud. Log. 60(1) (1998), 3-43.
29. Plotkin, G. D.: A structural approach to operational semantics. Research Report DAIMI FN-19, Computer Science Department, Aarhus University, Aarhus, Denmark, September 1981.
30. Pollock, J. L.: Rational cognition in OSCAR, in Agent Theories, Architectures, and Languages, 1999, pp. 71-90.
31. Prawitz, D : Natural Deduction, Almqvist & Wiksell, Stockholm, Sweden, 1965.
32. Rescher, N.: Introduction to Logic, St. Martin's Press, 1964.
33. Reynolds, J. C.: Theories of Programming Languages, Cambridge University Press, 1998.
34. Troelstra, A. S. and Schwichtenberg, H.: Basic Proof Theory, Cambridge University Press, Cambridge, England, 1996.
35. Voronkov, A.; The anatomy of Vampire: implementing bottom-up procedures with code trees, J. Autom. Reason. 15(2) 1995.
36. Wechler, W.: Universal Algebra for Computer Scientists, Springer-Verlag, 1992.
37. Weidenbach, C.: Combining superposition, sorts, and splitting, in A. Robinson and A. Voronkov (eds.), Handbook of Automated Reasoning, volume 2, North-Holland, 2001.