Abduction, induction, deduction explained

ChatGPT about: Abduction, induction, deduction

New Math approach: The trio you’re describing corresponds precisely to the Peircean (Charles Sanders Peirce) classification of reasoning:

📝 Summary Table

Inference	Given	Needed
Deduction	input + rule	output
Induction	output + rule	input
Abduction	input + output	rule

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Bad traditional explanation of this triangle

Inference Given Infer CS/Math Analogy
Deduction Input + Rule Output f(x) = y → compute y
Induction Output + Rule Input f(?) = y → find x
Abduction Input + Output Rule f(x) = y → find f

🔧 Synonyms

Synonyms of the above:

• output = result, consequence

  • This is the final product you want to generate or explain — the answer or consequence of applying the operation or function to the input.

• input = arguments, case

  • These are the values or premises you supply to the rule to produce the output. In programming, they’re the parameters you feed into a function.

• rule = operation, function

  • This is the mechanism that transforms input into output. It’s the process, algorithm, or logical structure that tells you how to get from input to output.

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💬 Explanation

Using these synonyms makes the logic more transparent, especially for those coming from mathematics, computer science, or engineering. In AI and logic, many frameworks treat inference steps as computational processes, so thinking of “rules” as “functions” and “inputs” as “arguments” aligns perfectly with how inference engines (and programming languages) actually work.

• Deduction is akin to function application: given inputs and a function (rule), you compute the output.
• Induction is like working backwards: given an output and a function, you try to find which input(s) could produce that output (inverse problem).
• Abduction is about rule discovery: given inputs and outputs, you search for or invent a function that would connect them.

Tip: think of them also as business process graphs (source: https://github.com/yuzutech/kroki): 

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