AGISystem2 represents knowledge geometrically: facts are points, concepts are regions, and reasoning is distance computation. This approach bridges symbolic AI (precise but brittle) and neural AI (flexible but opaque) by providing structured, inspectable, and auditable representations.

Core Idea: Meaning as Geometry

When text enters the system, it is parsed into Subject-Relation-Object triples. The encoder converts each part to a vector, applies relation-specific permutations, and combines them with saturating arithmetic. The result is a point in a high-dimensional space. See Language Layer for encoding details.

Bounded Diamonds

Why not just boxes? In high dimensions, boxes have most of their volume in unrealistic corners. The L1 ball trims these corners while the box enforces hard per-dimension constraints. A relevance mask specifies which dimensions participate in distance calculations. See Geometry Layer for implementation details.

Dimensional Partitions

This partitioning supports the separation of facts from values described in Bias & Values. Theory layers can adjust axiology dimensions without corrupting factual knowledge, enabling reasoning under different ethical frameworks or legal jurisdictions.

Why Geometry Works

Approach	Strengths	Weaknesses
Symbolic (rules)	Precise, auditable, explainable	Brittle, requires complete rules
Neural (embeddings)	Flexible, learns from data	Opaque, hard to audit
Geometric (conceptual spaces)	Precise + flexible, inspectable regions	Requires dimension design

Geometric representation offers:

• Incremental learning – New facts shift centers and expand bounds without retraining
• Graded truth – Distance from center indicates confidence (not just true/false)
• Explicit contradictions – Non-overlapping regions indicate incompatible concepts
• Auditable reasoning – Every decision traces to distances and inclusions

High-Dimensional Engineering

AGISystem2 uses int8 vectors with hundreds to thousands of dimensions. This design is informed by hyperdimensional computing research:

• Near-orthogonality – Random high-dimensional vectors are nearly orthogonal, enabling superposition
• Permutation binding – Roles are encoded by permuting dimensions, not adding dimensions
• Saturating arithmetic – Int8 with saturation prevents overflow and ensures determinism
• LSH retrieval – Locality-sensitive hashing enables fast approximate search

See Geometry Layer for VectorSpace, MathEngine, and BoundedDiamond implementations.

Relation to OWL and Semantic Web

AGISystem2 borrows vocabulary from OWL/RDF but changes the representation:

OWL Concept	AGISystem2 Equivalent
Class	Bounded diamond region
Individual	Point (encoded fact)
SubClassOf	IS_A relation, nested regions
ObjectProperty	Relation with permutation
Entailment	Inclusion check (point in region)

Key differences:

• OWL uses logical inference; AGISystem2 uses distance computation
• OWL is bivalent (true/false); AGISystem2 supports graded membership
• OWL lacks native non-monotonic reasoning; AGISystem2 uses theory layers

OWL vocabularies can be imported as relation names and IS_A hierarchies. See Relations for how relations map to geometric operations.

Related Documentation

Architecture

• Geometry Layer – VectorSpace, MathEngine, BoundedDiamond
• Knowledge Layer – ConceptStore, ClusterManager, TheoryStack
• Reasoning Layer – How geometric operations become inference

Theory

• Reasoning – Deduction, abduction, analogy as geometry
• Relations – Relation types and custom verbs
• Bias & Values – Fact/value separation
• Ontology Dimensions – Factual dimension catalogue
• Axiology Dimensions – Value dimension catalogue

Wiki

• Conceptual Spaces Wiki – Background theory
• Bounded Diamonds – Shape details
• Hyperdimensional Computing – HD computing background
• Permutation Binding – Role encoding