COLOG-88 pp 198-231 | Cite as

Gentzen-type systems and resolution rules part I propositional logic

  • G. Mints
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 417)


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Abdali M.,Manna Z.: Nonclausal temporal deduction, Lecture Notes in Computer Sci. 193, Springer-Verlag, Berlin, Heidelberg, New York (1985), 1–15Google Scholar
  2. 2.
    Auffray Y.: Linear strategy for propositional modal resolution. Inform. Process. Lett. 28, (1988), N2, 87–92Google Scholar
  3. 3.
    Bazylev Ju.: Resolution theorem prover for S4. (Russian). To appear in Proc. Soviet Academy of Sci., Techn. Cybernet.Google Scholar
  4. 4.
    Cavalli R., Fariñas C.L.: A decision method for linear temporal logic. Lecture Notes in Computer Sci. 170, (1984), 113–127Google Scholar
  5. 5.
    Chan M.C.: The recursive resolution method for modal logic. New Gener. Comput. 5, (1987), N2, 155–184Google Scholar
  6. 6.
    Chang C., Lee R.: Symbolic Logic and Mechanical Theorem Proving. Academic Press, New York, 1973Google Scholar
  7. 7.
    Ceitin G.S.: On the complexity of proofs in propositional calculus. English translation: Seminars in Math.. Plenum Publishers, 8, (1970)Google Scholar
  8. 8.
    Cialdea M.: Some remarks on the possibility of extending resolution proof procedures to intuitionistic logic. Inform. Process. Lett. 22, (1986), N2, 87–90Google Scholar
  9. 9.
    Cialdea M., Fariñas del Cerro C.L.: A modal Herbrand's property. Z. Math. Logik Grundlag. Math. 32, (1986), N6, 523–530Google Scholar
  10. 10.
    Curry H.: Foundations of Mathematical Logic, McGraw-Hill, New York, 1963Google Scholar
  11. 11.
    Fariñas del Cerro C.L.: Un principle de résolution en logique modale. RAIRO Inform. Theor. 18, (1984), N2, 161–170Google Scholar
  12. 12.
    Fariñas del Cerro C.L.: Resolution modal logic. Automated Reasoning in non-classical logic. Logique et Anal. 110/111, (1985)Google Scholar
  13. 13.
    Fariñas del Cerro C.L.: MOLOG: A system that extends PROLOG with modal logic. New Gener. Comput., 4, (1986), 35–51Google Scholar
  14. 14.
    Farinas del Cerro C.L., Herzig A.: Linear Modal Deductions. Lecture Notes in Computer Sci., 310. Springer-Verlag, Berlin, Heidelberg, New York (1989), 487–489Google Scholar
  15. 15.
    Fitting M.: First order modal tableaux. J. Autom. Reasoning, (1988), N4, 191–213Google Scholar
  16. 16.
    Fitting M.: Resolution for intuitionistic logic. Methodologies for Intelligent Systems. pp 400–407, North-Holland, Amsterdam, 1987Google Scholar
  17. 17.
    Kleene S.: Introduction to Metamathematics. North-Holland, Amsterdam, 1952Google Scholar
  18. 18.
    Kleene S.C.: Permutability of inferences in Gentzen's calculi LK and LJ. Memoirs of the American Math. Soc. 10, (1952)Google Scholar
  19. 19.
    Lifschitz W.: What is the inverse method? J. Autom. Reasoning, (1989)Google Scholar
  20. 20.
    Manna Z., Waldinger R.: A deductive approach to program synthesis. J. Assoc. Comp. Mach. Trans. Prog. Lang. Syst. 2, (1980), N1, 90–121Google Scholar
  21. 21.
    Manna Z., Waldinger R.: Special relations in automated deduction. J. Assoc. Comp. Mach., 33, (1986), N1. 1–59Google Scholar
  22. 22.
    Manna Z., Waldinger R.: Deductive synthesis of the unification algorithm. Sci. Comput. Programming, 1, (1981), 5–48Google Scholar
  23. 23.
    Maslov S.: Inverse method of establishing deducibility. (Russian). Trudy Mat. Inst. Steklov. 98, (1968), 26–87. (Translated by Amer. Math. Sci.)Google Scholar
  24. 24.
    Maslov S. Ju.: Proof search strategies based on the ordering in a favorable set. Seminars in Math., Plenum Publishers, 16, (1971)Google Scholar
  25. 25.
    Maslov, S. Ju.: Connection between the strategies of the inverse method and the resolution method. Seminars in Math., Plenum Publishers, 16. (1971)Google Scholar
  26. 26.
    Maslov S.: Theory of deductive systems and its applications. MIT Press, Cambridge, 1987Google Scholar
  27. 27.
    Mints G.: Resolution calculi for the non-classical logics. (Russian). 9 Soviet Symp. in Cybernetics. Moscow, VINITI, 1981Google Scholar
  28. 28.
    Mints G.: Resolution calculi for the non-classical logics. (Russian). Semiotics and informatics, 25, (1985), 120–135Google Scholar
  29. 29.
    Mints G.: Resolution calculi for modal logics. (Russian). Proc. Estonian Acad. of Sci. (1986), N3, 279–290Google Scholar
  30. 30.
    Mints G.: Cutfree formalisations and resolution methods for propositional modal logic. VIII Intern. Congress for Logic, Methodology and Philosophy of Science, Moscow 1987, 46–48Google Scholar
  31. 31.
    Murray N.V.: Completely nonclausal theorem proving. Artificial Intelligence 18, (1982), N1, 67–85Google Scholar
  32. 32.
    Murray N., Rosenthal E.: Inference with path resolution and semantic graphs. J. Assoc. Comp. Mach. 34, (1977), N2, 225–254.Google Scholar
  33. 33.
    Nepeivoda N.N.: Prefix semantic tables for modal logics (Russian). Many-valued, relevant and paraconsistent logics. Moscow, 1984, 78–91Google Scholar
  34. 34.
    Ohlbach H.: A resolution calculus for modal logics. Lecture Notes in Computer Sci., 310, Springer-Verlag,Berlin, Heidelberg, New York (1988), 500–516Google Scholar
  35. 35.
    Shvarts G.: Gentzen Style Systems for K45 and K45D. Lecture Notes in Computer Sci. 363, Springer-Verlag,Berlin, Heidelberg, New York (1989) 245–256Google Scholar
  36. 36.
    Traugott: Nested Resolution. Lecture Notes in Computer Sci., 230, Springer-Verlag, Berlin, Heidelberg, New York (1986)Google Scholar
  37. 37.
    Venkatesh G.: A decision method for temporal logic based on resolution. Lecture Notes in Computer Sci. 206, Springer-Verlag, Berlin, Heidelberg, New York (1985), 273–288Google Scholar
  38. 38.
    Volozh B.,Matskin M.,Mints G., Tyugu E.: The PRIZ system and propositional calculus. Cybernetics 18, (1982), N6, 777–788Google Scholar
  39. 39.
    Vorobyev N.N.: A new derivability algorithm in the constructive propositional calculus. Trudy Math. Inst., Steklov. 52, (1958), 193–226. (Russian, the English translation by Appl. Math. Sci.)Google Scholar
  40. 40.
    Wajsberg M.: Untersuchungen ueber den Aussagenkalkuel von A. Heyting, Wiadomosci Matematyczne, 46, (1938), 45–101Google Scholar
  41. 41.
    Zamov N.: Maslov's inverse method and decidable classes. Ann. Pure and Appl. Log., 42, (1989), 165–194Google Scholar
  42. 42.
    Zamov N.: Resolution without Skolemization. Doklady Akad. Nauk SSSR, 293, (1987), N5, 1046–1049Google Scholar
  43. 43.
    Zamov N.: A resolution system for S4. To be submittedGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • G. Mints
    • 1
  1. 1.Institute of CyberneticsEstonian Academy of SciencesTallinnEstonia, USSR

Personalised recommendations