On specialization of derivations in axiomatic equality theories

  • A. Pliuškevičienė
  • R. Pliuškevičius
  • M. Walicki
  • S. Meldal
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 813)


Walicki and Meldal have defined a calculus DEQ (“Disjunctive EQuational calculus”) for reasoning about nondeterministic operators when specifying nondeterministic systems in an equation-oriented style.

A variant of DEQ, the calculus DEQ* for axiomatic equality theories with cut-like rules introducing as cut formulas only the negative equalities of a specific axiom, is constructed. For pure positive specific axioms (i.e. with empty antecedents) and for so called non-contrary equality theories DEQ* does not contain cut-like rules at all. The variant of the calculus DEQ* without structural rules of contraction and exchange is constructed. A simple cut-elimination procedure for axiomatic equality theories is presented.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    S. Feferman, Lectures on Proof Theory, LNM, 70, Springer, 1969.Google Scholar
  2. 2.
    S. Kanger, A simplified proof method for elementary logic. Comput. Progr. and Formal Systems, North-Holland, Amsterdam, 87–94, 1963.Google Scholar
  3. 3.
    S. Meldal, An abstract axiomatization of pointer types, in Proc. of the 22nd Annual Hawaii International Conference on System Sciences, B.D. Shriver (ed.), IEEE Computer Society Press, vol. 2, 129–134, 1989.Google Scholar
  4. 4.
    A. Pliuškevičienė, Elimination of cut-type rules in axiomatic theories with equality. Seminars in mathematics V.A. Steklov Mathem. Institute, Leningrad, 16, 90–94, 1971.Google Scholar
  5. 5.
    A. Pliuškevičienė, Specialization of the use of axioms for deduction search in axiomatic theories with equality, Seminars in mathematics V.A. Steklov Mathem. Institute, Leningrad, J. Soviet Math. 1, 110–116, 1973.Google Scholar
  6. 6.
    A. Pliuškevičienė, A sequential variant of R.M.Robinson's arithmetic system not containing cut rules. Proc. Steklov Inst. Math., Leningrad, 121, 121–150, 1972.Google Scholar
  7. 7.
    R. Pliuškevičius, Sequential variant of the calculus of constructive logic for normal formulas. Proc. Steklov Inst. Math., 98, 175–229, 1968.Google Scholar
  8. 8.
    M. Rogava, Sequential variants of applied predicate calculi without structural deductive rules. Proc. Steklov Inst. Math. 121, 136–164, 1972.Google Scholar
  9. 9.
    M. Walicki, Algebraic Specifications of nondeterminism, Ph. D thesis, University of Bergen, 1993.Google Scholar
  10. 10.
    M. Walicki, S. Meldal, A complete calculus for the multialgebraic and functional semantics of nondeterminism, (submitted for publ.) 1993.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • A. Pliuškevičienė
    • 1
  • R. Pliuškevičius
    • 1
  • M. Walicki
    • 2
  • S. Meldal
    • 2
  1. 1.Institute of Mathematics and InformaticsVilniusLithuania
  2. 2.Department of Informatics HiBUniversity of BergenBergenNorway

Personalised recommendations