Skip to main content
SpringerLink
Log in

Early History and Perspectives of Automated Deduction

  • Conference paper
Book cover KI 2007: Advances in Artificial Intelligence (KI 2007)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4667))

Included in the following conference series:

Abstract

With this talk we want to pay tribute to the late Professor Gerd Veenker who deserves the historic credit of initiating the formation of the German AI community. We present a summary of his scientific contributions in the context of the early approaches to theorem proving and, against this background, we point out future perspectives of Automated Deduction.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Andrews, P.B.: Theorem proving via general matings. Journal of the ACM 28, 193–214 (1981)

    Article  MATH  Google Scholar 

  • Antonsen, R., Waaler, A.: Liberalized variable splitting. J. Automated Reasoning (2007)

    Google Scholar 

  • Bibel, W., Eder, E.: Decomposition of tautologies into regular formulas and strong completeness of connection-graph resolution. Journal of the ACM 44(2), 320–344 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  • Beth, E.W.: Semantic entailment and formal derivability. Mededlingen der Koninklijke Nederlandse Akademie van Wetenschappen 18(13), 309–342 (1955)

    MathSciNet  Google Scholar 

  • Beth, E.W.: On machines which prove theorems. Simon Stevin Wis- en Naturkundig Tijdschrift 32, 49–60, Reprinted in [SW83, 76–90] (1958)

    Google Scholar 

  • Bibel, W.: Matings in matrices. Comm. ACM 26, 844–852 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  • Bibel, W.: Automated Theorem Proving, 2nd edn. Vieweg Verlag, Braunschweig (1987)

    MATH  Google Scholar 

  • Bibel, W.: Lehren vom Leben – Essays über Mensch und Gesellschaft. In: Sozialwissenschaft, Deutscher Universitäts-Verlag, Wiesbaden (2003)

    Google Scholar 

  • Bibel, W.: Transition logic revisited, 2004 (submitted)

    Google Scholar 

  • Bibel, W.: Research perspectives for logic and deduction. In: Stock, O., Schaerf, M. (eds.) Reasoning, Action and Interaction in AI Theories and Systems. LNCS (LNAI), vol. 4155, pp. 25–43. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  • Bibel, W.: Wissenssysteme und Komplexitätsbewältigung. In: Leiber, T. (ed.) Denken und Handeln in einer komplexen Welt – Festschrift zum 60. Geburtstag von Professor Klaus Mainzer, Hirzel Verlag, Stuttgart (2007)

    Google Scholar 

  • Blake, A.: Canonical Expressions in Boolean Algebra. PhD thesis, University of Chicago, Illinois (1937)

    Google Scholar 

  • Brüning, W.: Grundlagen der Strengen Logik. Königshausen und Neumann, Würzburg (1996)

    Google Scholar 

  • Cordeschi, R.: The role of heuristics in automated theorem proving – J.A. Robinson’s resolution principle. Mathware & Soft Computing 3, 281–293 (1996)

    Google Scholar 

  • Davis, M.: A computer program for Presburger’s algorithm. In: Summaries of talks presented at the Summer Institute for Symbolic Logic, Princeton NJ, pp. 215–233, Institute for Defense Analysis (1957), Also contained in [SW83, 41–48]

    Google Scholar 

  • Davis, M.: Eliminating the irrelevant from mechanical proofs. In: Proc. Symposium for Applied Mathematics XV, Providence, RI, pp. 15–30 (1963), Also contained in [SW83, 315–330]

    Google Scholar 

  • Davis, M.: The Prehistory and Early History of Automated Deduction. In: Siekmann, J., Wrightson, G. (eds.) Automation of Reasoning 1 – Classical Papers on Computational Logic 1957–1966, pp. 1–28. Springer, Berlin (1983)

    Google Scholar 

  • Dunham, B., Fridshal, R., Sward, G.L.: A non-heuristic program for proving elementary logical theorems. In: First International Conference on Information Processing, Paris, pp. 282–285. Unesco House (1960), Also contained in [SW83, 93–98]

    Google Scholar 

  • Dunham, B., North, J.H.: Theorem testing by computer. In: Proc. Sympos, Brooklyn NY, pp. 173–177. Polytechnic Press (1963) Also contained in [SW83, 271–275]

    Google Scholar 

  • Davis, M., Putnam, H.: A computing procedure for quantification theory. Journal of ACM 7, 201–215 (1960), Also contained in [SW83, 125–139]

    Google Scholar 

  • Eisinger, N.: Completeness, Confluence, and Related Properties of Clause Graph Resolution. Pitman, London (1991)

    Google Scholar 

  • Feferman, S.: Alfred tarski and a watershed meeting in logic: Cornell, 1957. In: Hintikka, J., et al. (eds.) Philosophy and Logic – In search of the Polish tradition. Synthese Library, vol. 323, pp. 151–162. Kluwer Acad. Publ., Dordrecht (2003), http://math.stanford.edu/~feferman/papers/cornell.pdf

    Google Scholar 

  • Frege, G.: Begriffsschrift. Louis Nebert, Halle (1879)

    Google Scholar 

  • Gelernter, H.: Realization of a geometry theorem-proving machine. In: Proc. First Intern. Conf. on Information Processing (IFIP), Paris, pp. 273–282. UNESCO House (1959), Also contained in [SW83, 99–122]

    Google Scholar 

  • Gilmore, P.C.: A proof method for quantification theory: Its justification and realization. IBM J. Research Develop. 4, 28–35 (1960)

    Article  MATH  MathSciNet  Google Scholar 

  • Gilmore, P.C.: An examination of the geometry theory machine. Artificial Intelligence 1, 171–187 (1970)

    Article  MATH  Google Scholar 

  • Goldfarb, W.D. (ed.): J. J. Herbrand — Logical writings. Reidel, Dordrecht (1971)

    Google Scholar 

  • Hilbert, D., Ackermann, W.: Grundzüge der Theoretischen Logik. Springer, Heidelberg (1928)

    MATH  Google Scholar 

  • Herbrand, J.J.: Recherches sur la théorie de la démonstration. In: Travaux Soc. Sciences et Lettres Varsovie, Cl. 3 (Mathem., Phys.) (1930), Engl. transl. in [Gol71]

    Google Scholar 

  • Hintikka, K.J.J.: Form and content in quantification theory. Acta Philosophica Fennica 8, 7–55 (1955)

    MathSciNet  Google Scholar 

  • Hoffmann, G.-R., Veenker, G.: The unit-clause proof procedure with equality. Computing 7(1-2), 91–105 (1971)

    Article  MATH  MathSciNet  Google Scholar 

  • Kanger, S.: Provability in Logic. PhD thesis, University of Stockholm (1957)

    Google Scholar 

  • Kneale, W., Kneale, M.: The Development of Logic. Clarendon Press, Oxford (1984)

    Google Scholar 

  • Letz, R., Schumann, J., Bayerl, S., Bibel, W.: SETHEO — A high-performance theorem prover for first-order logic. Journal of Automated Reasoning 8(2), 183–212 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  • McCarthy, J.: The Wang algorithm for the propositional calculus programmed in LISP. In: McCarthy, J. (ed.) Symbol Manipulating Language Memo 14, Artificial Intelligence Project, MIT, Cambridge MA (1959), Quoted in [Wan60a, p.232]

    Google Scholar 

  • McCharen, J., Overbeek, R., Wos, L.: Problems and experiments for and with automated theorem proving programs. IEEE Transactions on Computers C-25, 773–782 (1976)

    Article  Google Scholar 

  • Newell, A., Shaw, J.C., Simon, H.A.: The logic theory machine. IRE Trans. Information Theory IT-2, 61–79 (1956), Also contained in [SW83, 49-73]

    Google Scholar 

  • Papon, P.: Die Wissenschaft, Zeichen der Zeit. FTE Info – Magazin über europäische Forschung (An interview) 50, 9–11 (2006)

    Google Scholar 

  • Prawitz, D., Prawitz, H., Voghera, N.: A mechanical proof procedure and its realization in an electronic computer. J. ACM 7, 102–128 (1960)

    Article  MATH  MathSciNet  Google Scholar 

  • Prawitz, D.: An improved proof procedure. Theoria 26, 102–139 (1960), Also contained in [SW83, 159–199]

    Google Scholar 

  • Robinson, A.: Proving theorems (as done by man, logician, or machine). In: Summaries of Talks Presented at the Summer Institute for Symbolic Logic, Communic. Res. Div., Princeton, New Jersey, Institute for Defense Analysis (1957), Also contained in [SW83, 74–76]

    Google Scholar 

  • Alan Robinson, J.: Gamma I: A general theorem proving program for the IBM 704. Technical Report ANL-6447, Argonne National Laboratory, Chicago, IL (1961)

    Google Scholar 

  • Alan Robinson, J.: Theorem proving on the computer. Journ. ACM 10(2), 163–174 (1963), Also contained in [SW83, 372–383]

    Google Scholar 

  • Alan Robinson, J.: A machine-oriented logic based on the resolution principle. Journal of ACM 12, 23–41 (1965), Also contained in [SW83, 397–415]

    Google Scholar 

  • Robinson, J.A.: PROOF=GUARANTEE+EXPLANATION. In: Hölldobler, S. (ed.) Intellectics and Computational Logic – Papers in Honor of Wolfgang Bibel. Applied Logic Series, vol. 19, pp. 277–294. Kluwer, Dordrecht (2000)

    Google Scholar 

  • Schütte, K.: Ein System des verknüpfenden Schließens. Archiv f. Mathematische Logik und Grundlagen der Wissenschaften 2, 55–67 (1956)

    Article  MATH  Google Scholar 

  • Siekmann, J., Wrightson, G. (eds.): Automation of Reasoning — Classical Papers on Computational Logic 1957-1966, vol. 1. Springer, Berlin (1983)

    Google Scholar 

  • Veenker, G.: Ein Entscheidungsverfahren für den Aussagenkalkül und seine Realisation in einem Rechenautomaten. Grundl.stud. aus Kybernetik u. Geisteswiss 4, 127–136 (1963)

    Google Scholar 

  • Veenker, G.: Beweisalgorithmen für die Prädikatenlogik. Computing 2(3), 263–283 (1967)

    Article  MATH  MathSciNet  Google Scholar 

  • van Orman Quine, W.: A proof procedure for quantification theory. J. Symbolic Logic 20, 141–149 (1955)

    Article  Google Scholar 

  • van Orman Quine, W.: A way to simplify truth functions. American Mathematical Monthly 62, 627–631 (1955)

    Article  MathSciNet  Google Scholar 

  • Wang, H.: Proving theorems by pattern recognition, Part I. Comm. ACM 3, 220–234 (1960), Also contained in [SW83, 229–243]

    Google Scholar 

  • Wang, H.: Toward mechanical mathematics. IBM Journ. Res. Develop. 4, 2–22, Also contained in [SW83, 244–264] (1960)

    Google Scholar 

  • Wos, L., Carson, D., Robinson, G.A.: The unit preference strategy in theorem proving. In: AFIPS Conf. Proc., Washington DC, vol. 26, pp. 615–621. Spartan Books (1964)

    Google Scholar 

  • Wos, L., Henschen, L.: Automated theorem proving 1965–1970. In: Siekmann, J., Wrightson, G. (eds.) Automated Reasoning 2 – Classical Papers on Computational Logic 1967–1970, vol. 2, pp. 1–24. Springer, Berlin (1983)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Darmstadt University of Technology, Also affiliated with the University of British Columbia,  

    Wolfgang Bibel

Authors
  1. Wolfgang Bibel
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Joachim Hertzberg Michael Beetz Roman Englert

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Bibel, W. (2007). Early History and Perspectives of Automated Deduction. In: Hertzberg, J., Beetz, M., Englert, R. (eds) KI 2007: Advances in Artificial Intelligence. KI 2007. Lecture Notes in Computer Science(), vol 4667. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74565-5_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-74565-5_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74564-8

  • Online ISBN: 978-3-540-74565-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation