Learning a rule vs reasoning with one
Four of our sub-faculties all involve rules, and are easy to confuse. They differ on two things: whether you’re told the rule, and where the evidence comes from.
| Sub-faculty | Rule told to you? | Where the evidence comes from | Your job |
|---|---|---|---|
| Rule induction Learning · LearningBench | No | A set of examples, all shown before you start | Guess the rule, then judge new cases |
| Learning from feedback Learning · Two machines | No | Your own choices, one outcome at a time | Adjust your choices as results come in |
| Deductive reasoning Reasoning · Wason | Yes | Nothing to learn | Work out what the rule strictly implies |
| Abstract rule induction Problem solving · ARC | No | Worked examples (before → after), shown before you start | Find the rule, then produce the answer yourself |
01 · Learning
Rule induction: from examples to a rule
You study strings like KL, KRRL, KZL and KRRZL, which all follow a hidden grammar that nobody states. Then you sort new strings into “follows the rule” and “breaks it”.
You never act on the world, and every piece of evidence is in front of you before you start. The skill is generalising: spotting what the examples share and applying it to cases you haven’t seen.
02 · Learning
Learning from feedback: learning by doing
Nothing is shown first. You pick one of two machines, see whether it paid out, and pick again, twenty times. The evidence exists only because you made choices, and it is noisy: the better machine sometimes loses, and its first pull is a deliberate miss.
Two things make it hard:
- deciding when to try the other machine and when to stick with the one that seems better;
- not overreacting to luck.
What you learn is which option is better, not a rule you could write down.
Learning from feedback on the Learning page · Binz & Schulz (2023)
03 · Reasoning
Deductive reasoning: from a rule to its consequences
The rule is handed to you, for example “if a card has a vowel on one side, it has an even number on the other”. There is nothing to discover. The question is which cards you must turn over to test it.
The hard part is following the logic strictly. Most people pick the card that would confirm the rule, not the one that could break it.
Deductive reasoning on the Reasoning page · Wason selection task
04 · Problem solving
Abstract rule induction: induction plus doing
As in rule induction, the rule is hidden and you get the examples first. Here each example is a pair, a grid before and after, and you don’t just judge a new case: you build the answer cell by cell.
That takes seeing the grid, finding the rule and carrying it out. Combining several faculties is why the framework puts ARC under Problem solving rather than Learning.
Abstract rule induction on the Problem solving page · ARC-AGI
05 · The core contrast
Induction vs deduction
Induction goes from cases to a rule, and its conclusion can be wrong even when you reason well: the next example may not fit. Deduction goes from a rule to cases, and if you reason correctly the conclusion is certain.
06 · Summary
In one line each
- Rule induction: examples first, guess the rule.
- Learning from feedback: no examples, learn from what your choices bring.
- Deductive reasoning: rule given, work out what follows.
- Abstract rule induction: examples first, guess the rule, then build the answer.