A Deductive Method to Prove Mathematical Theorems

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Mohammad Rezaei, Mojtaba | 2010

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 50100 (02)
University: Sharif University of Technology
Department: Mathematical Sciences Pure Mathematics
Advisor(s): Ardeshir, Mohammad
Abstract:
Automatic theorem proving has been attractive in artificial intelligence (AI). The aim of the usual automatic theorem proving methods is applying of the mathematical logic rules to decide intelligently, and reasoning automatically. In contrast the aim of our research is to apply computers abilities and artificial intelligence methods to simulate human abilities to prove mathematical theorems. For this purpose, we invent a typed formal language (TFL) to describe mathematical theories. The language must be clearly computable and should cover the First Order Logic (FOL) and the usual mathematical sentences. Then some algorithms and inference rules to compare sentences conceptually are introduced. Finally we present architecture of mathematical theorem prover software
Keywords:
Proof Theory ; Automated Deduction ; Formal Language Theory ; Mathematical Logic ; Automatic Theorem Prover ; Automatic Reasoning ; First Order Logic ; Higher Order Logic

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