Order-sorted type systems supporting
inheritance hierarchies and subtype polymorphism
are used in theorem proving, AI, and declarative programming.
The satisfiability problems
for the theories of: (i) order-sorted uninterpreted function
symbols, and (ii) of such symbols modulo a subset
of associative-commutative ones are reduced
to the unsorted versions of such problems
at no extra computational cost. New results on order-sorted
rewriting are needed to achieve this reduction.
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