On Specialization of Derivations in Axiomatic Equality Theories

Walicki and Meldal have deened a calculus DEQ (\Disjunctive EQuational calculus") for reasoning about nondeterministic operators when specifying non-deterministic 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 spe-ciic axiom, is constructed. For pure positive speciic 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.