Planning Equivalence Proofs

نویسندگان

  • Lassaad Cheikhrouhou
  • Volker Sorge
چکیده

Di erent axiomatizations of mathematical concepts prove to be useful in a mathematical knowledge base, since each axiomatization of a concept is more or less helpful for the task at hand. To keep the knowledge base consistent, the equivalence of distinct de nitions for some concept must be formally proven. Especially in algebra, where various axiomatizations of an algebraic structure often occur, the proofs of equivalent de nitions are canonical in major simpli cation steps. Starting out with a proof for the equivalence of two distinct de nitions for the group concept, we report in this paper on the rst attempts of proof planning the equivalence of di erent de nitions for algebraic structures in the mega system. We present a proof method that implements the common simpli cation steps of such theorems and give some relevant methods for closing the subgoals of this method.

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تاریخ انتشار 1998