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نویسنده
چکیده
In this paper we propose a methodology for developing representation formalisms for mathematical knowledge bases. We propose to equip knowledge bases with a hierarchy of logical systems that are linked by logic morphisms. These mappings relativize formulae and proofs and thus support translation of the knowledge to the various formats currently in use in automated deduction. On the other hand they deene higher language features from simpler ones and ultimately serve as a means to found the whole knowledge base in axiomatic set theory. The viability of this approach is proven by developing a sorted record-calculus with dependent sorts and labeled abstraction that is well-suited both for formalizing mathematical practice and supporting eecient inference services. This \mathematical vernacular" is an extension of the sorted-calculus from Koh94] by records, dependent record sorts and selection sorts.
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