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Automated Natural Deduction in Thinker

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References

  • Andrews, P. (1991), 'More on the problem of finding a mapping between clause representation and natural-deduction representation', Journal of Automated Reasoning 7, 285-286.

    Google Scholar 

  • Bergmann, M., J. Moor, J. Nelson (1990), The Logic Book, 2nd Ed, NY: McGraw-Hill.

    Google Scholar 

  • Beth, F. (1958), 'On machines which prove theorems', in Siekmann & Wrightson, 79-90.

  • Bledsoe, W. (1971), 'Splitting and reduction heuristics in automatic theorem proving', Artificial Intelligence 2, 55-78.

    Google Scholar 

  • Bledsoe, W. (1977), 'Non-resolution theorem proving', Artificial Intelligence 9, 1-35.

    Google Scholar 

  • Bledsoe, W. (1983), The UT Natural-Deduction Prover, Technical Report, Dept. Computer Science, Univ. Texas.

  • Edgar, A. & F. J. Pelletier (1993), 'Natural language generation from natural deduction proofs', Proceedings of PACLING, Vancouver: Simon Fraser Univ., 269-278.

    Google Scholar 

  • De Haven, S. (1994), The Logic Course, Pigeon Enterprises: Calgary.

    Google Scholar 

  • Kalish, D. (1974), 'Review of I. Copi Symbolic Logic', Journal of Symbolic Logic, 177-178.

  • Kalish, D. & R. Montague (1964), Logic, Hartcourt, Brace, Janovich.

    Google Scholar 

  • Kalish, D., R. Montague, and G. Mar (1980), Logic, Hartcourt, Brace, Janovich.

    Google Scholar 

  • Li Dafa (1997), 'Unification algorithms for eliminating and introducing quantifiers in natural deduction automated theorem proving', Journal of Automated Reasoning 18, 105-134.

    Google Scholar 

  • Newell, A., J. Shaw, H. Simon (1957), 'Empirical explorations with the logic theory machine', in Siekmann & Wrightson, 49-73.

  • Pelletier, F. J. (1982), Completely Non-Clausal, Completely Heuristic-Driven, Automatic Theorem Proving, Tech. Report TR82-7, Dept. Computing Science, Univ. Alberta.

  • Pelletier, F. J. (1986/7), '75 graduated problems for testing automated theorem provers', Journal of Automated Reasoning 3, 191-216, and 'Errata for 75 problems', Journal of Automated Reasoning 4, 235–236.

    Google Scholar 

  • Pelletier, F. J. (1987), Further Developments in THINKER, an Automated Theorem Prover, Tech. Report TR-ARP-16/87 Automated Reasoning Project, Australia National University.

  • Pelletier, F. J. (1991), 'The philosophy of automated theorem proving', Proceedings of IJCAI-91, Morgan Kaufmann, 1039-1045.

  • Pelletier, F. J. (1993a), 'Automated modal logic theorem proving in Thinker', Technical Report TR 93-14, Dept. Computing Science, Univ. Alberta.

  • Pelletier, F. J. (1993b), 'Identity in modal logic theorem proving', Studia Logica 52, 291-308.

  • Pelletier, F. J. & P. Rudnicki (1986), 'Non-obviousness', Newsletter of the Association for Automated Reasoning, No. 6, 4-6.

    Google Scholar 

  • Pollock, J. (1992a), 'Interest-driven suppositional reasoning', Journal of Automated Reasoning 6, 419-462.

    Google Scholar 

  • Pollock, J. (1992b), 'How to reason defeasibly', Artificial Intelligence 57, 1-42.

    Google Scholar 

  • Pollock, J. (1997), 'Skolemization and unification in natural deduction', unpublished paper available at http://www.u.arizona.edu/~pollock/.

  • Portoraro, F. & R. Tully (1994), Logic with SYMLOG, Prentice Hall: Englewood Cliffs.

    Google Scholar 

  • Prawitz, D., H. Prawitz & N. Voghera (1960), 'A mechanical proof procedure and its realization in an electronic computer' in Siekmann & Wrightson, 202-228.

  • Sieg, W. & J. Byrnes (1996), 'Normal natural deduction proofs (in classical logic)', Technical Report PHIL-74, Dept. Philosophy, Carnegie Mellon Univ.

  • Sieg, W. & B. Kauffmann (1993), 'Unification for quantified formulae', Technical Report PHIL-46, Dept. Philosophy, Carnegie Mellon Univ.

  • Sieg, W. & R. Scheines (1992), 'Searching for proofs (in sentential logic)', in L. Burkholder (ed.), Philosophy and the Computer, Westview: Boulder, 137-159.

    Google Scholar 

  • Siekmann, J. & G. Wrightson (1983), The Automation of Reasoning, Vol. 1, Springer-Verlag.

  • Smullyan, R. (1968), First Order Logic, Springer-Verlag.

  • Suppes, P. (1981), University-Level Computer-Assisted Instruction at Stanford, 1968–1981, Institute for Mathematical Studies in the Social Sciences: Stanford Univ.

  • Wang, H. (1960), 'Toward mechanical mathematics', reprinted in Siekmann & Wrightson 1983, 244–264.

  • Whitehead, A. & B. Russell (1910), Principia Mathematica, Vol. I. Cambridge Univ. Press.

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Pelletier, F.J. Automated Natural Deduction in Thinker. Studia Logica 60, 3–43 (1998). https://doi.org/10.1023/A:1005035316026

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