AI has proven to be extraordinary effective for solving certain types of intellectual problems that we thought before only our brains could solve. The number of applications is tremendous: engineering, medicine, banking, law etc. Nevertheless the underlying statistical methods are entirely based on inductive reasoning. I am curious about whether or not machines can be taught deductive reasoning.
Let me take the law of falling bodies as an example. Aristotle first proposed that heavier objects fall faster than lighter ones. Without any knowledge of modern physics and just the everyday life experience, Aristotle's law seems reasonable: heavier objects do tend to fall faster than lighter ones. Galileo Galilei was the first to prove this law wrong by imagining what would happen if two bodies were to fall in the vacuum and proved by deduction that the Aristotle's law was contradictory. He did not perform any experiment nor did he have access to the vacuum. It seems impossible to infer the law of falling bodies from examples. You have to question the logical consequences of the intuitive Aristotle's law to understand that it can not be right: bodies must fall at the same speed in the vacuum, meaning that frictions only are responsible for the observed differences.
Now, if a machine were trained with examples of falling bodies on Earth and was asked to propose a law to explain the phenomenon, we can imagine that it would answer something similar to Aristotle: it would report correlations between mass and falling speed. How can we teach machines to produce deductive reasoning? Are there efforts in that direction today? With what results?