Interactive theorem proving on hierarchically and modularly structured set of very many axioms

Authors:
Michio Honda;Reiji Nakajima
Affiliations:
Dept. of Information Science, Kagawa University, Takamatsu;Research Institute for Mathematical Sciences, Kyoto University, Kyoto
Venue:
IJCAI'79 Proceedings of the 6th international joint conference on Artificial intelligence - Volume 1
Year:
1979

Citing 3
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Putting theories together to make specifications

IJCAI'77 Proceedings of the 5th international joint conference on Artificial intelligence - Volume 2

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Abstract

A large number of axioms are often involved in the proof of a single theorem in many realistic applications of mechanical theorem proving such as formal verification of programs whose program domains are determined by user-defined axioms. There, fully automatic proofs are unrealistic due to the obvious constraints though a powerful machine support is highly desired. It is suggested that some meaningful structuring of theories can ease the difficulties. Several strategies are proposed to enhance efficient interactive non-resolution proofs on hierarchically and modularly structured theories with many axioms. Use of such strategies is illustrated in their application to verification of hierarchical programs with abstraction mechanisms.