Nucleoid

Logic Language for World Models 🌱🐋🌍

💭 Hallucinations are a major challenge in LLM reasoning because natural language is unstructured. By nature, LLMs are pattern engines that reason more effectively over structured entities and relationships, enabling more reliable, near-deterministic results.

⚡ Nucleoid is designed with a minimally tokenized syntax for logic representation and a declarative execution model, eliminating the need for LLMs to manually manage control flow, state propagation, and other imperative constructs. In addition, Nucleoid is a next-generation logic programming language built on structured objects and their relationships, extending the traditional Knowledge Graph.

• Near-Deterministic: Structured, reliable reasoning.
• Logic Graph: Executable knowledge graph.
• Minimum-Token Syntax: Token-efficient declarative syntax.

Hello World :zap:

Socrates is mortal without being told so

# There is a Human type with a name
class Human(name: str):
    this.name = name

# Every human is mortal
$Human.mortal = true

# Socrates is a Human
socrates = Human("Socrates")

# Therefore, Socrates is mortal
assert(socrates.mortal, true)

Design Theory 📐

Language Reference

docs/README.md is the language reference: statements and state, variables and dependencies, expressions, types and instances, properties, class-level rules, blocks and scope, control flow, functions, transactions, built-in objects, error messages, and a syntax summary.

It is assembled from the NUC documents in docs/, indexed by NUC 0 with the conventions in NUC 1. nucleoid.spec.md is normative; where the two disagree, the specification wins.

docs/examples.md covers the same ground as complete programs, each one runnable as written.

A Nucleoid program is a set of statements that remain true. An assignment is not an instruction that runs once and finishes, it is a relationship the runtime records and maintains.

An assignment states a relationship, not a result

a = 1
b = a + 2

a = 3

assert(b, 5)

b is never stale. It is the sum of a and 2, so changing a brings it up to date, and the same holds for properties, class-level rules and everything else the reference covers.

Every example in the reference is executable: tests/reference.md is its executable form and runs under cargo test, as do the snippets on this page.

Nucleoid Chat Video

Neuro-Symbolic AI

A world model is what a system knows about a domain: which entities exist, how they relate, which rules hold across all of them, and what follows once something changes. In an LLM that model is implicit, spread across the weights, and that is where hallucination begins, because a model that cannot be inspected cannot be corrected and cannot be held to its own rules. Neuro-Symbolic AI is how the model is made explicit, and it is why the two components below are complementary rather than competing.

Neuro-Symbolic AI is an approach that integrates the strengths of both neural networks and symbolic AI to create systems that can learn from data and also reason logically. By combining these two components, Neuro-Symbolic AI aims to leverage the intuitive, pattern-recognition capabilities of neural networks along with the logical, rule-based reasoning of symbolic AI. This integration offers a more holistic AI system that is both adaptable and able to explain its decisions, making it suitable for complex decision-making tasks where both learning from data and logical reasoning are required. Here’s how it breaks down:

Neural Networks: The Learning Component

Neural networks in Neuro-Symbolic AI are adept at learning patterns, relationships, and features from large datasets. These networks excel in tasks that involve classification, prediction, and pattern recognition, making them invaluable for processing unstructured data, such as images, text, and audio. Neural networks, through their learning capabilities, can generalize from examples to understand complex data structures and nuances in the data.

Symbolic AI: The Reasoning Component

The symbolic component of Neuro-Symbolic AI focuses on logic, rules, and symbolic representations of knowledge. Unlike neural networks that learn from data, symbolic AI uses predefined rules and knowledge bases to perform reasoning, make inferences, and understand relationships between entities. This aspect of AI is transparent, interpretable, and capable of explaining its decisions and reasoning processes in a way that humans can understand.

World Models: The State Component

Neural networks learn and symbolic AI reasons, but reasoning needs something to reason over, and that is the world model: the entities, relationships and rules a system currently holds to be true. In Nucleoid the model is not a passive knowledge base that is read from and written to, it is a logic graph that the runtime keeps true on its own. A rule stated over a type holds for every instance of it, including instances created long afterwards, and a change to any value propagates to everything derived from it, so the model is never left holding a fact together with its own stale consequence.

Rules also decide which worlds are admissible. A statement and every rule it triggers form a single transaction, and if any rule rejects the change, the transaction is rolled back and the state is exactly as it was, so an update that would contradict the model is never partially applied. A world model built this way cannot drift into a state that violates its own laws.

This is what makes the model usable by a language model. It is written incrementally, one statement at a time, in a syntax that costs few tokens, and it can be queried long after it was written, by another session or another model, because the meaning lives in the graph rather than in the context window.

Declarative Language: 6GL Programming Language

Nucleoid is a 6GL programming language, and Nucleoid acts as the ubiquitous language in Neuro-Symbolic AI for specifying the desired outcomes of a program without detailing the procedural methods to achieve these outcomes. This type of language is essential for articulating logical rules, constraints, and relationships that underpin symbolic reasoning within the