Modal theorem proving

  • Martín Abadi
  • Zohar Manna
Nondassical Deducation
Part of the Lecture Notes in Computer Science book series (LNCS, volume 230)


We describe resolution proof systems for several modal logics. First we present the propositional versions of the systems and prove their completeness. The first-order resolution rule for classical logic is then modified to handle quantifiers directly. This new resolution rule enables us to extend our propositional systems to complete first-order systems. The systems for the different modal logics are closely related.


Modal Operator Modal Logic Classical Logic Proof System Predicate Symbol 
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  1. [AM1]
    M. Abadi and Z. Manna, “Nonclausal temporal deduction,” in Logics of Programs (R. Parikh, ed.), Springer-Verlag LNCS 193, 1985, pp. 1–15.Google Scholar
  2. [AM2]
    M. Abadi and Z. Manna, “A timely resolution,” Proceedings of the Symposium on Logic in Computer Science (LICS), 1986.Google Scholar
  3. [Fa1]
    L. Fariñas del Cerro, “Temporal reasoning and termination of programs,” Eighth International Joint Conference on Artificial Intelligence, 1983, pp. 926–929.Google Scholar
  4. [Fa2]
    L. Fariñas del Cerro, “Un principe de résolution en logique modale,” RAIRO Informatique Théorique, Vol. 18, No. 2, 1984, pp. 161–170.Google Scholar
  5. [Fa3]
    L. Fariñas del Cerro, “Resolution modal logics,” in Logics and Models of Concurrent Systems (K.R. Apt, ed.), Springer-Verlag, Heidelberg, 1985, pp. 27–55.Google Scholar
  6. [Fi1]
    M. Fitting, Proof Methods for Modal and Intuitionistic Logics, D. Reidel Publishing Co., Dordrecht, 1983.Google Scholar
  7. [Fi2]
    M. Fitting, private communication.Google Scholar
  8. [GK]
    C. Geissler and K. Konolige, “A resolution method for quantified modal logics of knowledge and belief,” in Theoretical Aspects of Reasoning about Knowledge (J. Halpern, ed.), Morgan Kaufmann Publishers, Palo Alto, 1986, pp. 309–324.Google Scholar
  9. [HC]
    G.E. Hughes and M.J. Cresswell, An Introduction to Modal Logic, Methuen & Co., London, 1968.Google Scholar
  10. [HM]
    J.Y. Halpern and Y. Moses, “Knowledge and Common Knowledge in a Distributed Environment,” Third ACM Conference on the Principles of Distributed Computing, 1984, pp. 50–61. A revised version appears as IBM RJ 4421, 1984.Google Scholar
  11. [Ko]
    K. Konolige, A Deduction Model of Belief and its Logics, Ph.D. Thesis, Computer Science Department, Stanford University, 1984.Google Scholar
  12. [Mc]
    D. McDermott, “Nonmonotonic Logic II: Nonmonotonic Modal Theories,” Journal of the ACM, Vol. 29, No. 1, Jan. 1982, pp. 33–57.CrossRefGoogle Scholar
  13. [Mu]
    N.V. Murray, “Completely nonclausal theorem proving,” Artificial Intelligence, Vol. 18, No. 1, January 1982, pp. 67–85.CrossRefGoogle Scholar
  14. [MW1]
    Z. Manna and R. Waldinger, “A deductive approach to program synthesis,” ACM Transactions on Programming, Languages, and Systems, Vol. 2, No. 1, Jan. 1980, pp. 90–121.Google Scholar
  15. [MW2]
    Z. Manna and R. Waldinger, “Special relations in automated deduction,” Journal of the ACM, Vol. 33, No. 1, Jan. 1986, pp. 1–59.CrossRefGoogle Scholar
  16. [MW3]
    Z. Manna and R. Waldinger, “Special relations in program-synthetic deduction,” Report No. STAN-CS-82-902, Computer Science Department, Stanford University, March 1982.Google Scholar
  17. [P]
    A. Pnueli, “The temporal logic of programs,” 18th Annual Symposium on Foundations of Computer Science, 1977, pp. 46–57.Google Scholar
  18. [R]
    J.A. Robinson, “A machine-oriented logic based on the resolution principle,” Journal of the ACM, Vol. 12, No. 1, January 1965, pp. 23–41.CrossRefGoogle Scholar
  19. [W]
    P. Wolper, “Temporal Logic can be more expressive,” 22nd Annual Symposium on Foundations of Computer Science, 1981, pp. 340–348.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Martín Abadi
    • 1
  • Zohar Manna
    • 1
  1. 1.Computer Science DepartmentStanford UniversityUSA

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