Core Concepts

Term	Definition	See Also
Hypervector	A high-dimensional representation of a concept, fact, or relationship. The fundamental data structure of AGISystem2. Can be binary (Dense-Binary) or set-based (SPHDC).	Theory
Geometry	Strategy-defined size parameter for vectors. Dense-Binary uses a bit-length, Sparse-Polynomial (SPHDC) uses a cardinality k, and Metric-Affine uses a byte-channel dimension. The default session strategy is exact (geometry 256).	API
Atom	A named hypervector representing a primitive concept (e.g., "Person", "loves", "John"). Atoms are the building blocks of knowledge.	Syntax
Fact	A bound hypervector encoding a relationship (e.g., "John loves Mary"). Created by binding atoms with position markers.	Syntax
Session	An isolated reasoning context with its own scope, knowledge base, and vocabulary. Sessions are independent and can run in parallel.	API
Knowledge Base (KB)	A bundled hypervector containing all facts learned in a session. Used for query resolution via unbinding.	Theory
Vocabulary	The set of all known atoms in a session. Used for similarity matching when resolving queries.	API

HDC Strategies

Strategy	Representation	Binding	Similarity	Documentation
Dense-Binary	Fixed-length binary vector (d bits)	XOR (cancellable binding)	Hamming	Full docs
SPHDC	Set of k 64-bit integers	Cartesian XOR (statistical)	Jaccard	Full docs, Analysis
Metric-Affine	Byte channels (16–32B typical)	XOR on bytes (cancellable binding) + mean bundling	L1 / baseline-aware similarity	Full docs, HRR Comparison
Metric-Affine Elastic (EMA)	Elastic byte channels (32B+)	XOR on bytes (cancellable binding) + chunked bundling	Channel overlap (max over chunks)	Full docs, EMA Spec
EXACT	Lossless bitset-polynomial (BigInt monomials)	Polynomial bind (unbind differs from bind); quotient-like UNBIND	Witness/overlap scoring (strategy-aware)	Full docs, EXACT Spec

Mathematical Foundations

Concept	Definition	Learn More
GF(2)	Galois Field with two elements {0, 1}. Addition in GF(2) is XOR. Foundation for reversible binding (a xor a = 0).	Full explanation
Jaccard Similarity	Set similarity: |A ∩ B| / |A ∪ B|. Range [0,1]. Used by SPHDC strategy.	Full explanation
Min-Hash	Locality-sensitive hashing for efficient Jaccard estimation. Used for SPHDC sparsification.	Full explanation
Hamming Similarity	Binary vector similarity: 1 - (bit differences / total bits). Range [0,1]. Used by Dense-Binary strategy.	Dense-Binary docs
Holographic Representation	Distributed encoding where information is spread across all dimensions. Enables content-addressable retrieval.	Full explanation

Operations

Term	Definition	Properties
Bind	Creates associations between concepts. Dense-Binary: XOR. SPHDC: Cartesian XOR.	Commutative, Associative, XOR cancellation (reversible for XOR strategies)
Bundle	Combines multiple vectors. Dense-Binary: majority vote. SPHDC: set union + Min-Hash.	Result similar to all inputs, Capacity-limited
Similarity	Measures relatedness. Dense-Binary: Hamming. SPHDC: Jaccard.	1.0=identical, ~0.5=random, 0.0=maximally different
Unbind	Extracts unknown components from composite vectors. XOR-based strategies can reuse bind; others use a distinct unbind.	Key to query resolution

DSL Terms

Term	Syntax	Description
Hole	?name	Unknown value to find in query
Position Vector	Pos1...Pos20	Markers for argument order in relations
Implication	Implies (cond) (result)	Rule for inference
Fact	relation arg1 arg2	Assertion of relationship
Query	relation ?var arg	Question with holes

Reasoning Terms

Term	Definition	See Also
Query	A statement with holes that retrieves matching information from the KB.	API: query()
Proof	A tree of reasoning steps that derives a goal from known facts and rules.	API: prove()
Backward Chaining	Proving a goal by recursively proving the premises of applicable rules.	Theory
Rule	An implication (Implies P Q) used for inference.	Syntax
Transitive Closure	Following chains of relations (e.g., isA Dog Animal, isA Animal LivingThing → isA Dog LivingThing).	Theory
Disjoint Proof	Proving something is NOT the case (e.g., Dog is NOT a Plant if Animal and Plant are disjoint).	Theory

Output & Decoding

Term	Definition	See Also
Decode	Extract operator and arguments from a vector using similarity search against vocabulary.	API: decode()
Generate Text	Convert decoded structure to natural language using templates.	API: generateText()
Elaborate	Generate detailed explanation from a proof result.	API: elaborate()
Summarize	Generate natural language summary of a vector.	API: summarize()

Privacy & Security

Term	Definition	See Also
Secret Atoms	Concept vectors generated from private seed. Cloud cannot decode without the seed.	Privacy-HDC
Structural Leakage	Information revealed by similarity patterns even when atoms are secret.	Privacy-HDC
Federated Aggregation	Combining knowledge from multiple parties without revealing individual contributions.	Privacy-HDC
Homomorphic Property	Ability to compute on encoded data. HDC provides partial homomorphism (not cryptographic security).	Privacy-HDC

Architectural Terms

Term	Definition
HDC Facade	Strategy-agnostic interface to vector operations. Allows switching between Dense-Binary and SPHDC.
Core Layer	Vector operations: Bind, Bundle, Similarity, position vectors.
Runtime Layer	State management: sessions, scopes, vocabulary, executor.
Parser Layer	DSL processing: lexer, parser, AST generation.
Reasoning Layer	Inference: query resolution, proof engine, transitive closure.
Decoding Layer	Output: structural decoder, text generator, phrasing templates.

Thresholds Reference

Threshold	Value	Meaning
Strong Match	> 0.80	High confidence, trust result
Good Match	0.65 - 0.80	Solid match, probably correct
Weak Match	0.55 - 0.65	Marginal, verify if critical
No Match	< 0.55	Near random, don't trust

Acronyms

Acronym	Full Name	Description
HDC	Hyperdimensional Computing	Computing paradigm using high-dimensional vectors
VSA	Vector Symbolic Architecture	Umbrella term for HDC-like systems
SPHDC	Sparse Polynomial HDC	Set-based HDC strategy using k exponents
GF(2)	Galois Field with 2 elements	Algebraic foundation for XOR operations
KB	Knowledge Base	Bundled vector containing all facts
DSL	Domain-Specific Language	AGISystem2's fact/rule language
AST	Abstract Syntax Tree	Parsed representation of DSL code
FHE	Fully Homomorphic Encryption	Cryptographic computation on encrypted data
LSH	Locality-Sensitive Hashing	Hashing that preserves similarity (e.g., Min-Hash)

Guides & Tutorials

Guide	Description
Getting Started	Quick start tutorial: installation, first session, basic queries
NL2DSL Translation	Natural language to DSL translation patterns and API
Technology Comparison	Philosophical comparison with Prolog, theorem provers, Wolfram, expert systems
LLM Integration	Combining AGISystem2 with language models (Claude, GPT)
External Benchmarks	Performance on ProntoQA, FOLIO, LogiQA and other test suites
HRR Comparison	How AGISystem2 relates to Holographic Reduced Representations

Related Pages

Strategy Comparison

Aspect	Dense-Binary	SPHDC
Default geometry	2048 bits	k=4 exponents
Memory per vector	256 bytes	32 bytes
Binding reversibility	Exact	Statistical
Best for	Deep reasoning chains	Large vocabularies, low memory
Full documentation	Dense-Binary	SPHDC, Analysis