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We are now touching a problem how we add soft computing aspects to logic programming and we have been discussing a new framework for handling incomplete attribute values on logic programs. For handling incomplete information, we depend upon the concept 'Rule of Thumb' and we syntactically introduce a functor set into logic programs. This functor set causes some soft computing aspects to logic programs. In this chapter we first show our new framework, then we apply our realized theorem prover to simulation and diagnosis in digital circuits. We have also realized an user interface for managing a theorem prover, a program translator and a knowledge base with several rules, so every user does not have to know the logic programs and he can easily operate our system.