Induction in AGISystem2 is geometric envelope expansion. Given multiple examples of a concept, the system computes a bounded diamond that contains them all. This transforms learning from examples into finding the minimal enclosing shape.

How It Works

The ClusterManager handles induction when new facts arrive:

1. Encode the example – Convert "Rover IS_A Dog" into a vector point
2. Find existing concept – Look for a "Dog" diamond in the knowledge base
3. Expand or create – If found, expand the diamond to include the new point. If not, create a new diamond centered on this point.

Expansion adjusts the diamond's center, min/max bounds, and radius to include the new point while keeping the shape minimal.

Incremental Learning

Unlike batch learning algorithms, AGISystem2's induction is incremental. Each new example updates the concept immediately:

# First dog
ASSERT Rover IS_A Dog
# Creates initial "Dog" diamond centered on Rover

# More examples expand it
ASSERT Buddy IS_A Dog
ASSERT Max IS_A Dog
ASSERT Luna IS_A Dog
# Diamond grows to encompass all

# Query generalization
ASK "Fido IS_A Dog?"
# TRUE if Fido's vector falls inside the Dog diamond

Splitting Concepts

If examples are too spread out, the ClusterManager may split a concept into multiple subconcepts rather than creating one huge diamond. This happens when:

• The radius would exceed a threshold
• Points cluster into distinct groups
• Including new points would overlap with conflicting concepts

Comparison with Deduction

Aspect	Deduction	Induction
Direction	General → Specific	Specific → General
Geometry	Containment check	Envelope construction
Certainty	Guaranteed if premises true	Probable (may have exceptions)
Operation	Query (read)	Assert (write)

Related Documentation

• ClusterManager – Expansion and splitting logic
• Bounded Diamonds – The shapes being constructed
• Deduction – Using induced concepts for queries
• Learning Theory – How concepts evolve over time
• Analogy – Transferring structure between induced concepts