This wiki collects the theoretical and algorithmic concepts that underpin AGISystem2. Each page connects philosophical and mathematical ideas to the concrete way the system implements geometric reasoning, layered theories, and value-aware control.

Architecture Documentation

For system implementation details, see the Architecture section:

Layer	Description
Geometry Layer	VectorSpace, MathEngine, BoundedDiamond, RelationPermuter
Knowledge Layer	ConceptStore, ClusterManager, TheoryStack, TheoryLayer
Reasoning Layer	Reasoner, Retriever, BiasController, ValidationEngine
Language Layer	Sys2DSL Parser, Grammar, Encoder, Query Compiler
Storage	StorageAdapter, persistence, file formats
Configuration	Profiles, parameters, tuning
Sys2DSL	The domain-specific language for facts, questions, and theory programs

Theory & Guides

For conceptual foundations, see the Theory section:

Topic	Description
Conceptual Spaces	Theory of geometric knowledge representation
Reasoning	How reasoning modes map to geometric operations
Bias & Values	Fairness modes and value-aware reasoning
Explainability	Provenance traces and audit support
Learning	Concept evolution and adaptation
Relations	Relations, custom verbs, and permutation encoding
Limits	What the system does not do

Reasoning and Logic

Concept	Description
Abduction	Reasoning to the best explanation: inferring plausible causes from observations.
Induction	Generalising from examples into rules by enveloping points in the conceptual space.
Deduction	Deriving conclusions from premises, seen as checking inclusion between conceptual volumes.
Analogy	Transferring relations between domains by applying learned vector offsets.
Non-Monotonic Logic	Reasoning that allows withdrawing conclusions when new information appears.
Counterfactuals	"What-if" questions evaluated through temporary theories.
Deontic Logic	Modelling obligations and permissions with forbidden and obligatory volumes.
Narrative Consistency	Keeping stories coherent over time and aligned with normative theories.
Symbolic Execution	Exploring branches to find contradictions and counterexamples.
Abstract Interpretation	Static analysis via controlled abstractions.
Expert Systems	Rule-based predecessors with explicit knowledge and traceable explanations.

Knowledge, Values and Governance

Concept	Description
Conceptual Spaces	Representing knowledge as points and volumes in a continuous space.
Ontology	The factual layer of dimensions that structures the objective world.
Axiology	The layer of values and moral judgements, separated from ontology for audit.
Symbol Grounding	Anchoring symbols in experience and geometry.
Pragmatics	How context influences the interpretation of facts and questions.
Bias	Systematic preferences that must be controlled explicitly.
Veil of Ignorance	Rawlsian principle for fair scenarios.
Auditability	Reconstructing and verifying every reasoning step.
Trustworthy AI	Criteria that make the system acceptable in critical domains.

Geometric and Algorithmic Foundations

Concept	Description
Hyperdimensional Computing	Representing information via superposition and permutations.
Locality-Sensitive Hashing	Fast nearest-neighbour search in high-dimensional spaces.
Permutation Binding	Using permutations to bind subjects, relations and objects.
Masked L1 Distance	Distance measure with masks that ignore specific subspaces.
Bounded Diamonds	The shape of concepts: intersections of boxes and L1 balls.
Theory Layers	Knowledge layers that can be stacked to handle context and contradictions.
Validation	Checking answers and theories for consistency.
Memory Management	Usage tracking, forgetting, and priority boosting.

Syntax & CLI

For practical usage:

• Syntax Reference – Complete command syntax
• Relations – All relation types
• CLI Overview – Command-line interfaces
• Raw CLI – Structured command interface
• Chat Interface – Natural language interface