On specialization of derivations in axiomatic equality theories
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.
- 1.S. Feferman, Lectures on Proof Theory, LNM, 70, Springer, 1969.Google Scholar
- 2.S. Kanger, A simplified proof method for elementary logic. Comput. Progr. and Formal Systems, North-Holland, Amsterdam, 87–94, 1963.Google Scholar
- 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.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.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.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.R. Pliuškevičius, Sequential variant of the calculus of constructive logic for normal formulas. Proc. Steklov Inst. Math., 98, 175–229, 1968.Google Scholar
- 8.M. Rogava, Sequential variants of applied predicate calculi without structural deductive rules. Proc. Steklov Inst. Math. 121, 136–164, 1972.Google Scholar
- 9.M. Walicki, Algebraic Specifications of nondeterminism, Ph. D thesis, University of Bergen, 1993.Google Scholar
- 10.M. Walicki, S. Meldal, A complete calculus for the multialgebraic and functional semantics of nondeterminism, (submitted for publ.) 1993.Google Scholar