Deduction in AGISystem2 is geometric containment. If concept A's region is entirely inside concept B's region, then "A IS_A B" is deductively true. This transforms classical syllogistic logic into spatial computation.

Simple Deduction Animal Mammal Dog Dog ⊂ Mammal ⊂ Animal ∴ Dog IS_A Animal ✓ Deduction Process 1. Query: "Dog IS_A Animal?" Encode query point from "Dog" + IS_A + "Animal" 2. Direct check Is Dog's diamond inside Animal's diamond? 3. Transitive check Dog→Mammal→Animal chain exists? Result: TRUE_CERTAIN Confidence: 0.95 (geometric containment)

Deduction checks if one region contains another. "Dog IS_A Animal" is true because Dog's bounded diamond is geometrically inside Animal's. The Reasoner first checks direct containment, then follows IS_A chains for transitive deduction.

How It Works

The Reasoner handles deductive queries in two steps:

  1. Direct containment – Check if the subject's bounded diamond is inside the object's diamond using geometric inclusion tests
  2. Transitive chaining – For IS_A relations, follow the taxonomy chain (Dog→Mammal→Animal) and check containment at each step

The geometric test uses masked L1 distance: the subject is inside the object if the distance from subject's center to object's boundary is less than object's radius, on all relevant dimensions.

Confidence Levels

ResultMeaningGeometric Interpretation
TRUE_CERTAIN Definitely true Subject completely inside object
TRUE_PROBABLE Likely true Subject mostly inside, minor overlap outside
UNKNOWN Insufficient information No containment path found
FALSE_PROBABLE Likely false Subject mostly outside object
FALSE_CERTAIN Definitely false Subject completely disjoint from object

Example Queries

# Direct deduction
ASK "Dog IS_A Animal?"
# → TRUE_CERTAIN (Dog ⊂ Mammal ⊂ Animal)

# Failed deduction
ASK "Cat IS_A Dog?"
# → FALSE_CERTAIN (disjoint regions)

# Unknown (missing link)
ASK "Widget IS_A Animal?"
# → UNKNOWN (Widget not in knowledge base)

Comparison with Classical Logic

Classical LogicAGISystem2 Geometry
All A are B Region(A) ⊂ Region(B)
A → B (implication) Diamond(A) inside Diamond(B)
Modus ponens Point in A → Point in B
Transitive inference Chain of containments

Related Documentation