SGDL AI and THE ARIADNE EXOLANGUAGE
A revolutionary autonomous system of symbolic spatial reasoning for the next generation of artificial intelligence
How to Reason About Forms ?
The Ariadne Exolanguage Advantage
The name of the Exolanguage, Ariadne, allow us to optimally recycle the legal protections we already possess and add meaning to the name of the Canadian entity part of the SGDL ecosystem. Furthermore, the Exolanguage will benefit in early 2026 from the publication of work on boustrophedonic geometry.
Morphogenesis
The new term morphogenesis allows us to now cover all kinds of forms, including crystalline ones.
Non-Anthropomorphic and Self-Evolving
The expression "non-anthropomorphic and self-evolving" is essential an is in direct relation to LeCun's concept of advanced artificial intelligence.
The Vision
"The goal of the startup is to bring about the next big revolution in AI: systems that understand the physical world, have persistent memory, can reason, and can plan complex action sequences."
1. What and for whom?
Foundations of Ariadne
1.1 Autonomous System
The Ariadne Exolanguage* is an autonomous system of symbolic spatial reasoning.
1.2 Unified Mechanism
It stems from a mechanism, discovered in the 1990s at the University of Montreal, that unifies the five pillars of spatial knowledge in machines through elementary arithmetic: Logic, Topology, Morphogenesis, Indexing, and Encoding.
Core Characteristics
01
Triple System
It is a triple system that enables the representation, generation, and communication of spatial information.
02
Machine-First Design
Initially designed specifically for machines (AI2AI), it is inherently non-anthropomorphic and self-evolving.
03
Domain-Specific Language
It belongs to the class of mathematically oriented Domain-Specific Languages (DSLs).
2. How?
Technical Architecture
2.1 It consists of a functional programming engine, a non-polygonal volumetric graphics visualization engine, and a spatial information encoding engine, all driven by a logical inference engine and a domain-specific inference engine.
1
Geometric Calculations
All geometric calculations are performed using combinatorial geometry and n-dimensional algebraic or synthetic projective geometry.
2
Topological Calculations
All topological calculations are performed by arithmetic compilation of inferences in Form Arithmetic, the theoretical core language of the exolanguage.
3
Operational Modes
Depending on the real-time constraints of the various calculations, the system operates in symbolic, rational, or irrational mode (floating-point numbers).
The Key to Spatial Reasoning
2.5 The key to logical decision-making in spatial reasoning is the absence of special cases: projective programming without divisions, without machine infinity, and topological programming without the limitations of classical algebraic and simplicial topologies.
Why the name Ariadne?
Ariadne is perfect for this type of system because it evokes the thread, the labyrinth, and the discovery of a path in a monstrously complex space, which is precisely our use case.
3. Ariadne User Guide
Unified Geometric Spatial Representation
The Ariadne exolanguage offers a unique system for unifying the geometric spatial representation of physical World Models, mapping them, and endowing their digital twins with intelligence. The starting point for this unification is the representation of the entire geometry of terrains, vehicles, robots, aircraft, satellites, and structures, built from a single geometric modeling primitive belonging to the family of projective implicit surfaces.
In simplified terms, these surfaces behave like modeling clay elements governed by pure geometric constraints (Computer Aided Design) or by constraints derived from the physical behavior of the bodies, for example, collision simulation using contact dynamics. These primitives are then assembled to form more complex geometric objects whose topology is entirely arithmeticized.
Implicit Spatial Information
Minimal Memory Consumption
This method of working with implicit spatial information allows for minimal memory consumption and significant optimization of computation time.
In this context, the enormous, traditional data structures describing even the smallest shape (e.g., a cube) disappear and are replaced by simple arithmetic expressions, enabling the most complex simulation processes, from supercomputers to embedded systems.
Spatial Information Encoding
The encoding of all spatial information can then be performed, with all topology and geometry reduced to integers.
Multi-Precision Integer Arithmetic
To achieve this, multi-precision integer arithmetic (Bignums) is used, allowing the Ariadne exolanguage to first transform all geometric and topological representations into simple Bignums. These Bignums are then aggregated into larger Bignums, incorporating all metadata, until a single Bignum is obtained.
Geometric & Topological Representations
Transform to Bignums
Aggregate with Metadata
Single Bignum
This information encoding mechanism offers significant advantages in controlling communication flows: encoding and decoding. In addition to its inherent natural compression properties, Ariadne's encoding system allows for the continuous encryption of data streams. It achieves this in an original way by repurposing the core capabilities of its multidimensional indexing system.
The Swiss Army Knife of Information Processing
Based on major breakthroughs in Space Filling Curve theory, this system effectively acts as a Swiss Army knife for information processing.
Unified Encoding & Encryption
A unified system for encoding and encrypting data streams
Spatial Databases
A universal system for implicitly structured spatial databases
Universal Mapping
A universal system for mapping objects in space, with "object" being used in its broadest sense
In this sense, it unifies the mathematical tools of traditional terrain mapping (GIS) and those associated with mapping manufactured objects (CAD-CAM). Spatial reasoning processes can then be implemented. The previously mentioned theoretical vehicle for the unification of logic and topology is the pivotal element that allows us to shift from the world of logical inferences to the world of business or physical inferences.
The Two-Faced Janus System
The intriguing and surprising aspect of the Ariadne exolanguage is that it systematically uses the same arithmetic formalism to formalize spatial reasoning itself, as well as the objects on which this reasoning is applied. The field of space robotics is obviously the area that immediately benefits from this two-faced Janus-like system.
For example, robotic planning optimization problems coupled with Coverage Path Planning problems lie at the intersection of reasoning challenges faced with complex spatial environments whose geometries, topologies, and maps evolve in time and space. Clearly, physical World Models and their virtual digital twins must evolve in parallel, in a coordinated and, of course, synchronized manner within a real-time context.
The Future of Spatial Intelligence
The Ariadne exolanguage uses an internal virtual lidar mechanism coupled with physical lidars to link physical World Models to logical World Models. In short, thanks to the various mechanisms presented above, the Ariadne exolanguage uses entirely new approaches to spatial information representation, initially and deliberately devoid of any anthropomorphic connotations.
In a world and future where the exploration and colonization of spatialized worlds will most likely be reserved for machines, a different linguistic system (exo) dedicated solely to machines and their communications (AI2AI) probably offers the only guarantee for the independence of planetary missions under the control of new, efficient, and frugal reasoning systems.