A natural deduction is an instruction on how to use binary logic to move from one line to another, during a linear sequential proof. Every natural deduction, is one of the tautologies of propositional logic. As an example of a natural deduction, consider the hypothetical syllogism HS.
Hypothetical Syllogism HS:If A then B, if B then C; therefore If A then C.
Consider the following deduction of hypothetical syllogism HS, which employs the natu...
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A natural deduction is an instruction on how to use binary logic to move from one line to another, during a linear sequential proof. Every natural deduction, is one of the tautologies of propositional logic. As an example of a natural deduction, consider the hypothetical syllogism HS.
Hypothetical Syllogism HS:If A then B, if B then C; therefore If A then C.
Consider the following deduction of hypothetical syllogism HS, which employs the natural deduction known as modus ponens, in order to 'deduce' that hypothetical syllogism is a natural deduction.Let A,B,C denote arbitrary statements.
QED
As can be seen, this proof that hypothetical syllogism is a natural deduction, relied on the reasoning agent already knowing that modus ponens is a natural deduction.
Modus Ponens MP: If A then B, A; therefore B
Thus, in order for a reasoning agent to learn that hypothetical syllogism is a valid natural deduction from this deduction (alternatively reasoning event), the reasoning agent...
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