The purpose of this paper is to give an easy to understand with step-by-step explanation to allow interested people to fully appreciate the power of natural deduction for first-order logic. Natural deduction as a proof system can be used to prove various statements in propositional logic, but we will see its extension to cover quantifiers which gives it more power over propositional logic in solving more complex, real-world problems. We started by going over logical connectives and quantifiers to agree on the symbols that will be used throughout the paper, as some authors use different symbols to refer to the same thing. Besides, we showed the inference rules that are used the most. Furthermore, we presented the soundness and completeness of natural deduction for first-order logic. Finally, we solved examples ranging from easy to complex to give you different circumstances in which you can apply the proof system to solve problems you may encounter. Hopefully, this paper will be helpful makes the subject easy to understand.
翻译：本文的目的是通过逐步解释,让感兴趣的人能够充分理解自然扣减对一阶逻辑的推理力。自然扣减作为一种验证系统可以用来证明各种推理推理的推理,但我们会看到其延伸,以涵盖在解决更复杂和现实世界的问题方面赋予它比假设逻辑更大的权力的限定符。我们首先通过逻辑连接和限定符,就整个文件将使用的符号达成一致,因为一些作者使用不同的符号来指同一件事。此外,我们展示了最常用的推理规则。此外,我们介绍了第一阶逻辑自然扣减的正确性和完整性。最后,我们从容易到复杂的例子,给了你不同的情况,你可以在其中应用验证系统来解决你可能遇到的问题。希望这份文件有助于让问题容易理解。
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