Entailment Calculus as the Logic Basis of Automated Theorem Finding in Scientific Discovery

Jingde Cheng

Any scientific discovery must include an epistemic process to gain knowledge of or to ascertain the existence of some empirical and/or logical entailments previously unknown or unrecognized. The epistemic operation of deduction in an epistemic process of an agent is to fred new and valid entailments logically from some premises which are known facts and/or assumed hypothesis. Automated theorem fmding can be regarded as the automation of deduction operations of an agent. This paper discusses the logical basis of automated theorem finding from the viewpoint of relevant logic. The paper points out why classical mathematical logic and/or its various extensions are not suitable logical tools for solving the problem, and shows that paradox-free relevant logics are more hopeful candidates for the purpose.

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