The Role of Representation for Specification and Communication in Mathematical Assistants

Jacques Calmet, Karsten Homann

Date: July 17th (Wednesday)
Time:
Abstract
It is well known that mathematicians switch to different views of a problem when needed. They can represent a problem at a formal, conceptual, heuristic, algorithmic or constraint level whenever necessary. To represent Mathematics within several formalisms has been the subject of many research projects. However, only few knowledge-based systems manage translations of representations between theories.

The goal of this talk is twofold. One the one hand, we report on a hybrid knowledge representation and reasoning system called MANTRA. The system provides four different knowledge representation methods - first-order logic, terminological language, semantic networks, and production rules - distributed into a three levels architecture. Specifications of mathematical domains of computation and their inherently related type inference mechanisms can be transformed into knowledge bases.

On the other hand, we argue that a main requirement when designing future environments is the capability to cooperate and to integrate by communicating mathematical knowledge among/through mathematical services based upon restart-able computation and reasoning. Therefore, structures representing intermediate results in any kind of mathematical computation must also be considered.

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