Relations & Custom Verbs

Relations are the verbs of the knowledge system. They connect subjects to objects and determine how vectors are combined during encoding. This page explains how relations work geometrically, lists the built-in relation types, and describes how to define custom verbs.

How Relations Work

Encoding a fact: The object vector is permuted according to the relation, then added to the subject vector with saturating arithmetic. Different relations use different permutations, keeping the dimensionality fixed while encoding role information.

Each relation has a unique permutation table that reorders vector dimensions. When encoding "Dog IS_A Animal", the system:

Gets the base vector for "Dog"
Gets the base vector for "Animal"
Applies the IS_A permutation to "Animal"
Adds the permuted vector to "Dog" with saturation

This produces a single point that represents the fact. See RelationPermuter for implementation details.

Relation Properties

Inverse Relations

Many relations have inverses. If A CAUSES B, then B CAUSED_BY A. Inverse relations use inverse permutations, so the encoding is consistent in both directions.

Symmetric Relations

Some relations are symmetric: SIMILAR_TO is the same in both directions. Symmetric relations reuse the same permutation for both subject and object roles.

Transitive Relations

Relations like IS_A support transitivity: if Dog IS_A Mammal and Mammal IS_A Animal, then Dog IS_A Animal. The Reasoner handles transitivity through chain checking.

Built-in Relations

Taxonomic Relations

Relation	Inverse	Meaning	Example
`IS_A`	`HAS_INSTANCE`	Type/class membership	Dog IS_A Animal
`PART_OF`	`HAS_PART`	Mereological containment	Wheel PART_OF Car
`SUBCLASS_OF`	`SUPERCLASS_OF`	Class hierarchy	Mammal SUBCLASS_OF Animal

Causal Relations

Relation	Inverse	Meaning	Example
`CAUSES`	`CAUSED_BY`	Direct causation	Fire CAUSES Smoke
`ENABLES`	`ENABLED_BY`	Precondition	Key ENABLES Door_Opening
`PREVENTS`	`PREVENTED_BY`	Inhibition	Vaccine PREVENTS Disease

Spatial Relations

Relation	Inverse	Meaning	Example
`LOCATED_IN`	`CONTAINS`	Spatial containment	Paris LOCATED_IN France
`NEAR`	`NEAR`	Proximity (symmetric)	Library NEAR School
`ABOVE`	`BELOW`	Vertical position	Sky ABOVE Ground

Temporal Relations

Relation	Inverse	Meaning	Example
`BEFORE`	`AFTER`	Temporal ordering	Monday BEFORE Tuesday
`DURING`	`CONTAINS_TEMPORALLY`	Temporal containment	Meeting DURING Morning
`OVERLAPS`	`OVERLAPS`	Partial overlap (symmetric)	Event1 OVERLAPS Event2

Deontic Relations

Relation	Inverse	Meaning	Example
`PERMITS`	`PERMITTED_BY`	Permission	License PERMITS Driving
`PROHIBITS`	`PROHIBITED_BY`	Prohibition	Law PROHIBITS Theft
`OBLIGATES`	`OBLIGATED_BY`	Obligation	Contract OBLIGATES Payment
`REQUIRES`	`REQUIRED_BY`	Requirement	Driving REQUIRES License

Property Relations

Relation	Meaning	Example
`HAS_PROPERTY`	Attribute assignment	Water HAS_PROPERTY liquid
`HAS_VALUE`	Numeric value	Water HAS_VALUE temp=100
`HAS_ATTRIBUTE`	Named attribute	Car HAS_ATTRIBUTE color=red

Similarity Relations

Relation	Symmetric	Meaning	Example
`SIMILAR_TO`	Yes	General similarity	Dog SIMILAR_TO Wolf
`DIFFERENT_FROM`	Yes	Explicit distinction	Cat DIFFERENT_FROM Dog

Custom Verbs

AGISystem2 supports defining custom relations beyond the built-in set. Custom verbs enable domain-specific knowledge representation.

Defining a Custom Verb

# In Sys2DSL
DEFINE_RELATION TREATS inverse=TREATED_BY transitive=false

# Usage
ASSERT Aspirin TREATS Headache
ASK "What TREATS Headache?"

Custom Verb Properties

Property	Description	Default
`inverse`	Name of inverse relation	None (unidirectional)
`symmetric`	Same in both directions	false
`transitive`	Chains apply (A→B→C means A→C)	false
`permutation_seed`	Seed for deterministic permutation	Hash of name

Domain Examples

# Medical domain
DEFINE_RELATION TREATS inverse=TREATED_BY
DEFINE_RELATION CONTRAINDICATED_WITH symmetric=true
DEFINE_RELATION METABOLIZED_BY inverse=METABOLIZES

ASSERT Aspirin TREATS Pain
ASSERT Aspirin CONTRAINDICATED_WITH Warfarin
ASSERT Aspirin METABOLIZED_BY Liver

# Legal domain
DEFINE_RELATION GOVERNS inverse=GOVERNED_BY
DEFINE_RELATION SUPERSEDES inverse=SUPERSEDED_BY transitive=true

ASSERT GDPR GOVERNS DataProcessing
ASSERT Regulation_2023 SUPERSEDES Regulation_2020

Natural Language Mapping

The Chat Interface maps natural language phrases to relations:

Natural Language	Relation
"is a", "are", "is a type of"	IS_A
"has", "contains", "includes"	HAS_PART
"causes", "leads to", "results in"	CAUSES
"is caused by", "comes from"	CAUSED_BY
"is in", "located in"	LOCATED_IN
"requires", "needs"	REQUIRES
"allows", "permits"	PERMITS
"prohibits", "forbids"	PROHIBITS
"is before", "precedes"	BEFORE
"is similar to", "is like"	SIMILAR_TO

Geometric Interpretation

Different relations create different geometric patterns. IS_A creates nested regions (subsets). CAUSES creates directional links between separate regions. SIMILAR_TO implies proximity in the space.

AGISystem2 – Relations & Custom Verbs