MBase: representing knowledge and context for the intergration of mathematical software systems

  • Authors:

  • Micheal Kohlhase;Andreas Franke

  • Affiliations:

  • Carnegie Mellon Univ., Pittsburgh, PA;Saarland Univ., Saarbrücken, Germany

  • Venue:
  • Journal of Symbolic Computation - Calculemus-99: integrating computation and deduction
  • Year:
  • 2001

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Abstract

In this article we describe the data model of the MB ASE system, aweb-based, distributed mathematical knowledge base. This system isa mathematical service in MATHWEB that offers a universalrepository of formalized mathematics where the formalrepresentation allows semantics-based retrieval of distributedmathematical facts. We classify the data necessary to representmathematical knowledge and analyze its structure. For the logicalformulation of mathematical concepts, we propose a methodology fordeveloping representation formalisms for mathematical knowledgebases. We propose to concretely equip knowledge bases with ahierarchy of logical systems that are linked by logicmorphisms. These mappings relativize formulae and proofs andthus support translation of the knowledge to the various formatscurrently in use in deduction systems. On the other hand theydefine higher language features from simpler ones and ultimatelyserve as a means to found the whole knowledge base in axiomatic settheory. The viability of this approach is proven by developing asorted record-λ-calculus with dependent sorts and labeledabstraction that is well-suited both for formalizing mathematicalpractice and supporting efficient inference services. This"mathematical vernacular" is an extension of a sortedλ-calculus by records, dependent record sorts and selectionsorts. 2001 Academic Press.