, Volume 2, Issue 2, pp 121–131 | Cite as

Human-oriented and machine-oriented reasoning: Remarks on some problems in the history of Automated Theorem Proving

  • Furio Di Paola


Examples in the history of Automated Theorem Proving are given, in order to show that even a seemingly ‘mechanical’ activity, such as deductive inference drawing, involves special cultural features and tacit knowledge. Mechanisation of reasoning is thus regarded as a complex undertaking in ‘cultural pruning’ of human-oriented reasoning. Sociological counterparts of this passage from human- to machine-oriented reasoning are discussed, by focusing on problems of man-machine interaction in the area of computer-assisted proof processing.


human-machine interaction automated theorem proving mathematical proofs reasoning sociology of knowledge tacit knowledge 


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  1. [1]
    Bernardi, C. and P. Pagli (1985) Modelli naturali, assiomatizzazione, incompletezza, in C. Mangione (ed.)Scienza e Filosofia. Garzanti, Milan.Google Scholar
  2. [2]
    Bledsoe, W.W. (1979). Non-resolution Theorem Proving,Artificial Intelligence. 9.Google Scholar
  3. [3]
    Bledsoe, W.W. and P. Bruell (1973). A Man-machine Theorem Proving System. Rep. TEX 39, Dept. of AI, Edinburgh.Google Scholar
  4. [4]
    Bledsoe, W.W. and D.W. Loveland (eds) (1983). Automated Theorem Proving: After 25 Years.Contemporary Mathematics. 29. AMS, Providence-Rhode Island.Google Scholar
  5. [5]
    Boyer, R.S. and J.S. Moore (1983). Proof-Checking, Theorem Proving and Program Verification, in [4].Google Scholar
  6. [6]
    Bowen, K.A. (1982) Programming with Full First-order Logic, in Hayes-Michie-Pao (eds)Machine Intelligence 10. Ellis Horwood, Chichester.Google Scholar
  7. [7]
    Bundy, A. (1983).The Computer Modelling of Mathematical Reasoning. Academic Press, London.Google Scholar
  8. [8]
    Bundy, A. (1985). Discovery and Reasoning in Mathematics.Proceedings of the 9th IJCAI. Morgan Kaufman, Los Altos.Google Scholar
  9. [9]
    Cellucci, C. (1985). Proof Theory and Complexity.Synthese. 62.Google Scholar
  10. [10]
    Cellucci, C. (1986). Using Full First-order Logic as a Programming Language, workshopLogic and Computer Science: New Trends and Applications. Turin.Google Scholar
  11. [11]
    Cellucci, C. (1987). La Logica e l'intelligenza artificiale, in Riuniti (ed.)Ulisse. Rome.Google Scholar
  12. [12]
    Davis, M. (1983). The Prehistory and Early History of Automated Deduction, in [25], 1.Google Scholar
  13. [13]
    Di Paola, F. (1988). Matematici, computer-assisted proof e teorema dei quattro colori, forthcoming in Cannarò (ed.)Studi sociali della scienza. Angeli, Milan.Google Scholar
  14. [14]
    Feigenbaum, E.A. (1984). Knowledge Engineering: The Applied Side, in [18].Google Scholar
  15. [15]
    Genesereth, M.R. and N.J. Nilsson (1987).Logical Foundations of Artificial Intelligence. Kaufmann, Los Altos.Google Scholar
  16. [16]
    Gödel, K. (1959). Uber eine bisher noch nicht benützte Erweiterung des finiten Standpunktes.Logica, Studia Paul Bernays Dedicata. Griffon, Neuchâtel.Google Scholar
  17. [17]
    Groner, M., R. Groner and W.F. Bischof (eds) (1983).Methods of Heuristics. Erlbaum, Hillsdale, New Jersey.Google Scholar
  18. [18]
    Hayes, J.E. and D. Michie (eds) (1984).Intelligent Systems: The Unprecedented Opportunity. Ellis Horwood, Chichester.Google Scholar
  19. [19]
    Kreisel, G. (1977). On the Kind of Data Needed for a Theory of Proofs, in Barwise et al. (eds)Logic Colloquium. Amsterdam.Google Scholar
  20. [20]
    Kreisel, G. (1970). Hilbert's Programme and the Search for Automatic Proof Procedures, inSymposium on Automatic Demonstration, Lecture Notes in Mathematics. Springer.Google Scholar
  21. [21]
    Loveland, D.W. (1983). (1983). Automated Theorem Proving: A Quarter Century Review, in [4].Google Scholar
  22. [22]
    Reichgel, T.H. (1987). A Review of McDermott'sCritique of Pure Reason. InAI Communications. 1.Google Scholar
  23. [23]
    Robinson, J.A. (1984). Logical Reasoning in Machines, in [18].Google Scholar
  24. [24]
    Shepherdson, J.C. (1984). The Calculus of Reasoning, in [18].Google Scholar
  25. [25]
    Siekmann, J. and B. Wrightson (eds) (1983).Automation of Reasoning, 1–2. Springer, Berlin.Google Scholar
  26. [26]
    Wang, H. (1960). Towards Mechanical Mathematics.IBM Journal of Research and Development. 4.Google Scholar
  27. [27]
    Wang, H. (1981).Popular Lectures on Mathematical Logic. Van Nostrand, New York.Google Scholar
  28. [28]
    Wang, H. (1983). Computer Theorem Proving and Artificial Intelligence, in [4].Google Scholar
  29. [29]
    Wilder, R. (1981).Mathematics as a Cultural System. Pergamon, Oxford.Google Scholar
  30. [30]
    Wos. L. and L. Henschen (1983). Automated Theorem Proving 1965–1970, in [25], 2.Google Scholar
  31. [31]
    Wos, L. (1987). Some Obstacles to the Automation of Reasoning, and the Problem of Redundant Information.Journal of Automated Reasoning. 3.Google Scholar

Copyright information

© Springer-Verlag London Limited 1988

Authors and Affiliations

  • Furio Di Paola
    • 1
  1. 1.Department of SociologyUniversity of RomeItaly

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