Artificial Intelligence · AI Foundations
Explanation-Based Learning
In AI because a general rule can be extracted from one explained example plus a domain theory — a learning family the inductive ML course does not own.
Forward, Backward and Resolution showed how a machine derives what follows from a knowledge base. This lesson is a different use of that derivation: take one positive example, prove why it is positive using a domain theory you already trust, then drop the constants that were irrelevant to the proof. The result is a general rule you can run on the next case. That is explanation-based learning. It is not inductive learning from a table of rows — the Machine Learning course owns that family — and it is not a decision tree.
- Artificial Intelligence
- Medium level
- 5 concepts
1A rule from one explained case
Explanation-based learning (EBL) starts with three things: a target concept ('this object is a safe mug for the cafe'), one positive example (this particular mug on the counter), and a domain theory (authored facts and rules about openness, concavity, heatproof material). The learner does not count how often mugs have appeared. It builds a proof that this mug satisfies the concept, then rewrites that proof so the next object can be classified by the same reasons.
The intelligence is in the proof, not in the sample size. A second mug that is also a positive example adds nothing if the first proof already covered it. A second mug that is a negative example is a signal that the theory, not the count, is wrong.
| Input | Campus mug |
|---|---|
| Target concept | SafeMug(x) |
| One example | this blue ceramic mug |
| Domain theory | open, concave, heatproof ⇒ safe mug |
2The theory has to already know why
The domain theory is a knowledge base in the sense of Forward, Backward and Resolution: facts about this mug, and rules that connect those facts to SafeMug. A typical campus theory says: an object that is open at the top, concave, and made of a heatproof material is a safe mug; ceramic is heatproof; this object is open, concave, and ceramic. Backward chaining from SafeMug(this) succeeds in three steps.
If the theory does not mention heatproof, the proof cannot use it, and the learned rule will not test for it. EBL will not invent the missing axiom from the glaze on the mug. That is the knowledge-engineering bottleneck pointed at a learning procedure: the rule you extract cannot be smarter than the theory you wrote.
| Axiom | Role |
|---|---|
| Open(x) ∧ Concave(x) ∧ Heatproof(x) ⇒ SafeMug(x) | the concept definition |
| Ceramic(x) ⇒ Heatproof(x) | a material rule |
| Open(mug), Concave(mug), Ceramic(mug) | facts about this example |
The theory has Open, Concave and Ceramic facts for this mug, but no axiom that ceramic is heatproof, and SafeMug requires heatproof. What can EBL do?
- Learn SafeMug from the glaze, because the mug is a positive example
- Fail to prove SafeMug(mug), so it cannot extract a rule from this example
- Drop the heatproof conjunct and learn Open ∧ Concave ⇒ SafeMug
- Ask for fifty more mugs and switch to a decision tree
No proof, no rule. EBL does not invent the missing Ceramic ⇒ Heatproof axiom, and it does not silently drop a conjunct the target concept requires. More mugs are the inductive family.
3Prove, then drop the constants
The explanation is a proof tree. Backward chaining from SafeMug(mug) opens Open(mug), Concave(mug) and Heatproof(mug). Heatproof(mug) opens Ceramic(mug). All four leaves are facts. That tree is why this mug is a positive example.
Generalisation replaces the constant mug with a variable, and keeps only the leaves that the proof used. The operational rule is: if an object is open, concave and ceramic, it is a safe mug. Colour, handle shape and the word printed on the side never appeared in the proof, so they do not appear in the rule. Operationality is the extra test: every remaining conjunct must be something the agent can check on a new object without further search — Open, Concave, Ceramic, not 'would a barista approve'.
Figure. The proof tree for this mug. SafeMug opens three conjuncts; Heatproof opens Ceramic. Blue is not a node — the proof never mentioned it. Sage marks the target and the operational leaf that replaced Heatproof.
One EBL pass
- ProveBackward-chain from the target concept on this example until every leaf is a fact.
- GeneraliseReplace the example's constants with variables. Drop features the proof never used.
- OperationaliseKeep only tests the agent can evaluate on the next object. Store that rule.
From this mug to a rule
Facts: Open(mug), Concave(mug), Ceramic(mug), Blue(mug). Theory as in the axioms table. Target SafeMug(x).
- Prove SafeMug(mug)Open ∧ Concave ∧ Heatproof, and Ceramic ⇒ Heatproof
- Leaves usedOpen(mug), Concave(mug), Ceramic(mug)
- Drop Blue(mug) — unusednot in the proof
- Generalise mug → xOpen(x) ∧ Concave(x) ∧ Ceramic(x) ⇒ SafeMug(x)
Pro tip. Blue was true of the example and is still true. It is absent from the rule because the proof never needed it. That is the whole point of explaining first.
Coding lab. Prove this mug, drop Blue runs in the app, with checks on your output.
4Not a pile of rows
Inductive learning takes many labelled examples and no domain theory, and returns a hypothesis that fits those rows — a linear score, a tree, a net. The Machine Learning course is that family. Decision trees, the thing this AI paper must not clone, live there. EBL takes one labelled example and a theory, and returns a rule that the theory already entailed.
The two families answer different shortages. If you have rows and no theory, you cannot run EBL. If you have a theory and one explained case, collecting a thousand extra mugs is wasted work. A hybrid that uses EBL to propose a rule and induction to check it on held-out cases is allowed; it is still two families, not a reason to re-teach impurity.
| Family | Needs | Returns | Owned by |
|---|---|---|---|
| Inductive | many labelled rows | a hypothesis that fits the rows | the ML course |
| EBL | one example + a theory | a rule the theory already entailed | this lesson |
A teammate wants to 'do EBL' on 800 labelled loan rows with no axioms about credit. What should you tell them?
- That is inductive learning — EBL has no theory to prove a row is a default
- 800 rows are enough for EBL to generalise
- They should build a decision tree and call it an explanation
- They should pick one row and drop the other 799
EBL without a domain theory cannot build a proof. One row plus 799 discarded rows is still not a theory. A tree that fits the 800 is the ML course, and naming it 'explanation' does not change the family.
5When the theory is the method — and when it lies
Reach for EBL when an expert can write the axioms and you want a faster operational test than proving each new case from scratch. The cafe can check Open, Concave, Ceramic on the next mug in one glance; it should not re-run the whole backward chain. That is why expert-system shells historically stored EBL-extracted rules next to the original KB.
Do not reach for it when the theory is incomplete or false. If ceramic is not actually heatproof in the microwave the cafe uses, the extracted rule will classify those mugs as safe and will do so for every ceramic object, not just the one on the counter. A second example cannot repair a false axiom. Fix the theory, then extract again. Uncertainty and Bayes, later in this course, is the family for 'the axiom is only probably true'.
| Situation | Move |
|---|---|
| Trusted axioms, slow proof on each new case | Extract an operational rule |
| Many rows, no axioms | Inductive learning (ML course) |
| Axioms that are only probably true | Uncertainty, not a sharper EBL rule |
Notes
- Explanation-based learning takes one positive example and a domain theory, builds a proof that the example is positive, then generalises the proof.
- The theory, not a pile of rows, is what licenses a rule from a single case.
- If the theory is wrong, the learned rule is confidently wrong — EBL does not discover new physics.
Exam traps & shortcuts
- One example plus a theory is EBL. Many examples and no theory is inductive learning — the ML course.
- Operationality is the test of the finished rule: every test in it must be something the agent can check on a new case.
- A missing or false axiom in the theory is not repaired by seeing a second cup.
Recap
Hold these points before uncertainty.
- One example
- Target concept, one positive case, a domain theory. The proof is the learning.
- Theory
- No Ceramic ⇒ Heatproof axiom means no proof and no rule. EBL does not invent physics.
- Generalise
- Drop unused features (Blue). Replace mug with x. Keep operational tests.
- Not inductive
- Many rows, no theory: ML course. One case plus axioms: this lesson. Do not clone trees.
Practise Explanation-Based Learning
Reading is free and needs no account. Practice, mocks and progress live in the app.
- 2 quick checks with worked explanations
- Timed mocks scored with the real marking scheme
- Readiness tracked per topic, kept on your device