Skip to main content
SpringerLink
Log in

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

  • Published:
AI & SOCIETY Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Article Open access 15 September 2015

Adam Grabowski, Artur Korniłowicz & Adam Naumowicz

References

  1. Bernardi, C. and P. Pagli (1985) Modelli naturali, assiomatizzazione, incompletezza, in C. Mangione (ed.)Scienza e Filosofia. Garzanti, Milan.

    Google Scholar 

  2. Bledsoe, W.W. (1979). Non-resolution Theorem Proving,Artificial Intelligence. 9.

  3. Bledsoe, W.W. and P. Bruell (1973). A Man-machine Theorem Proving System. Rep. TEX 39, Dept. of AI, Edinburgh.

  4. Bledsoe, W.W. and D.W. Loveland (eds) (1983). Automated Theorem Proving: After 25 Years.Contemporary Mathematics. 29. AMS, Providence-Rhode Island.

  5. Boyer, R.S. and J.S. Moore (1983). Proof-Checking, Theorem Proving and Program Verification, in [4].

  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. Bundy, A. (1983).The Computer Modelling of Mathematical Reasoning. Academic Press, London.

    Google Scholar 

  8. Bundy, A. (1985). Discovery and Reasoning in Mathematics.Proceedings of the 9th IJCAI. Morgan Kaufman, Los Altos.

    Google Scholar 

  9. Cellucci, C. (1985). Proof Theory and Complexity.Synthese. 62.

  10. Cellucci, C. (1986). Using Full First-order Logic as a Programming Language, workshopLogic and Computer Science: New Trends and Applications. Turin.

  11. Cellucci, C. (1987). La Logica e l'intelligenza artificiale, in Riuniti (ed.)Ulisse. Rome.

  12. Davis, M. (1983). The Prehistory and Early History of Automated Deduction, in [25], 1.

  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. Feigenbaum, E.A. (1984). Knowledge Engineering: The Applied Side, in [18].

  15. Genesereth, M.R. and N.J. Nilsson (1987).Logical Foundations of Artificial Intelligence. Kaufmann, Los Altos.

    Google Scholar 

  16. Gödel, K. (1959). Uber eine bisher noch nicht benützte Erweiterung des finiten Standpunktes.Logica, Studia Paul Bernays Dedicata. Griffon, Neuchâtel.

    Google Scholar 

  17. Groner, M., R. Groner and W.F. Bischof (eds) (1983).Methods of Heuristics. Erlbaum, Hillsdale, New Jersey.

    Google Scholar 

  18. Hayes, J.E. and D. Michie (eds) (1984).Intelligent Systems: The Unprecedented Opportunity. Ellis Horwood, Chichester.

    Google Scholar 

  19. Kreisel, G. (1977). On the Kind of Data Needed for a Theory of Proofs, in Barwise et al. (eds)Logic Colloquium. Amsterdam.

  20. Kreisel, G. (1970). Hilbert's Programme and the Search for Automatic Proof Procedures, inSymposium on Automatic Demonstration, Lecture Notes in Mathematics. Springer.

  21. Loveland, D.W. (1983). (1983). Automated Theorem Proving: A Quarter Century Review, in [4].

  22. Reichgel, T.H. (1987). A Review of McDermott'sCritique of Pure Reason. InAI Communications. 1.

  23. Robinson, J.A. (1984). Logical Reasoning in Machines, in [18].

  24. Shepherdson, J.C. (1984). The Calculus of Reasoning, in [18].

  25. Siekmann, J. and B. Wrightson (eds) (1983).Automation of Reasoning, 1–2. Springer, Berlin.

    Google Scholar 

  26. Wang, H. (1960). Towards Mechanical Mathematics.IBM Journal of Research and Development. 4.

  27. Wang, H. (1981).Popular Lectures on Mathematical Logic. Van Nostrand, New York.

    Google Scholar 

  28. Wang, H. (1983). Computer Theorem Proving and Artificial Intelligence, in [4].

  29. Wilder, R. (1981).Mathematics as a Cultural System. Pergamon, Oxford.

    Google Scholar 

  30. Wos. L. and L. Henschen (1983). Automated Theorem Proving 1965–1970, in [25], 2.

  31. Wos, L. (1987). Some Obstacles to the Automation of Reasoning, and the Problem of Redundant Information.Journal of Automated Reasoning. 3.

Download references

Author information

Authors and Affiliations

  1. Department of Sociology, University of Rome, Italy

    Furio Di Paola

Authors
  1. Furio Di Paola
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Di Paola, F. Human-oriented and machine-oriented reasoning: Remarks on some problems in the history of Automated Theorem Proving. AI & Soc 2, 121–131 (1988). https://doi.org/10.1007/BF01891376

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01891376

Keywords

Search

Navigation