Introduction: Why Explore the Emergence of Intelligence Through Artificial Languages Now?

Modern large language models have acquired remarkable capabilities by learning from the enormous volume of text available on the internet. However, their intelligence remains vulnerable because it is fundamentally based on statistical plausibility.

Structural Limitations of English and Other Natural-Language LLMs

Natural languages such as English contain thousands of years of accumulated human experience, emotion, inconsistency, and imprecision. In AI training, these characteristics create three major barriers.

Noise Caused by Polysemy

A single word can have several meanings, and its role can change significantly depending on the context. Before an AI can solve the underlying logic, it must first spend computational resources organizing and disambiguating meaning.

Ambiguity in Word Order and Omission

Natural-language grammar is full of exceptions. AI models must infer logic from analogue information such as word position and surrounding context. This contributes to hallucinations—plausible but incorrect outputs—during long-range reasoning.

Dilution of Data

No matter how much conventional internet text is provided, the model may remain limited to imitating average patterns of human thought. Such data does not necessarily form a pure logical computation circuit within the model.

The Lineage of Artificial Languages and the Philosophy of Designing Intelligence

To overcome the limitations of natural language, humanity has created various designed languages, commonly known as artificial or constructed languages. The following are three representative examples. Each offers a different possibility as a potential native language for AI.

Esperanto

History and Philosophy

Esperanto was designed by L. L. Zamenhof at the end of the nineteenth century as an international auxiliary language.

Characteristics

Its grammar is highly regular, and new words are derived systematically through affixes. Nouns end in -o, adjectives in -a, and present-tense verbs in -as. Direct objects take the ending -n.

Esperanto can therefore be understood as an idealized form of Western languages built around strict regularity.

From an AI Perspective

Because Esperanto remains close to natural language, it is relatively easy for humans to use. However, in terms of logical precision, it does not move completely beyond the domain of natural language.

Examples

La suno brilas forte.
The sun shines brightly.
suno = sun, brilas = shines, forte = strongly

Ĉiu birdo havas flugilojn.
Every bird has wings.
ĉiu = every, flugilojn = wings, plural and accusative

Akvo fariĝas glacio en malvarmeco.
Water becomes ice in the cold.
fariĝas = becomes, mal- = opposite

La hundo postkuras la katon.
The dog chases the cat.
The -n ending preserves the subject–object relationship even when the word order changes.

Se pluvos, la tero malsekiĝos.
If it rains, the ground will become wet.
-os marks the future tense and expresses the logical consequence.

Lojban

History and Philosophy

Lojban is based on predicate logic, one of the foundations of computer science. It was designed to pursue cultural neutrality and the elimination of ambiguity as far as possible.

Characteristics

Its grammar is mathematically defined in a format compatible with tools such as yacc and bison, allowing machines to parse it with complete structural accuracy.

Each word has a place structure, or set of slots. Once arguments are inserted into those slots, the logical relationship is determined.

Lojban uses unambiguous predicate logic. lo ... ku turns an expression into an entity, while cu connects it to a predicate. Arguments are inserted into a functional place structure.

From an AI Perspective

Lojban is the core language of this project. Because it removes ambiguity, it is particularly well suited to constructing a pure logical circuit inside an AI model using a minimal amount of data.

Examples

lo cipvina cu vofli
A pigeon flies.
A minimal structure in which x1, cipvina, has the property x2, vofli.

ro lo jinme cu dirba
All metals are hard.
ro is a universal quantifier and defines a logical rule.

lo djacu cu litki lo ka ni'u re no ce'i
Water is liquid at a temperature below freezing, such as −20°C.
A complex abstract condition is expressed after lo ka.

ti du lo la'o py. smartphone .py.
This is the object called a smartphone.
ti = this, du = identity

ni'ibo lo tirne cu ke'umru lo dikca
Therefore, iron consumes electricity.
ni'ibo is a connective indicating a logical conclusion.

Ithkuil

History and Philosophy

Ithkuil was developed over several decades by John Quijada. It is an extremely high-density language designed to draw out the limits of human cognitive ability.

Characteristics

It compresses a vast number of grammatical categories—including aspect, voice, mood, expectation, and validity—into a single word. An idea that may require several lines in a natural language can sometimes be expressed in one word.

A single formative can contain an enormous number of dimensions, including case, aspect, voice, expectation, and effectiveness.

Example

Tram-mpoi'X

This word may express a complex concept such as a form of existential despair caused by a story not worth knowing reaching an unpleasant conclusion.

From an AI Perspective

Ithkuil may offer the highest logical density in the world. However, there are physically too few example sentences available as training data. At present, it is therefore unsuitable for training an AI system from scratch.

Additional Examples

Tram-mpoi'X
A story caused existential despair by reaching an unpleasant conclusion.
This compresses both context and emotion.

Pshiwu-al
A flock of imperfect, multicolored birds took flight simultaneously but chaotically.

Ait-pila'i-f
I intuitively understand that this water is the source of life, although not as an objectively established fact.

Ua-ssar-i
A series of complex physical phenomena forms causal relationships in a way that the observer did not expect.

Oum-re
A state in which the concept of justice has completely lost its meaning because of the collapse of society.

Chapter 2: The Project’s Core Strategy—Distilling Intelligence Through Lojban

As discussed in the previous chapter, Ithkuil possesses an extraordinarily advanced logical structure. However, its complexity has prevented the creation of a sufficient number of example sentences.

Esperanto, by contrast, has produced an enormous body of literature through a worldwide community that has continued since before World War II. Nevertheless, because its underlying philosophy is the unification of European languages, it intentionally retains many characteristics inherited from those natural languages. It therefore offers little benefit as a replacement for English in LLM training.

Lojban, however, currently represents one of the most complete artificial languages designed to eliminate ambiguity. It is comparatively easy to learn, and several books have already been published in the language.

Modern LLMs can also generate grammatically accurate Lojban sentences almost without interruption and in virtually unlimited quantities. For these reasons, the first target of this research was narrowed to Lojban.

Compatibility Between Predicate Logic’s Slot Structure and Neural Networks

Lojban’s defining characteristic is that every predicate, or gismu, has a strict place structure such as:

x1 does something to x2 under condition x3, and so on.

Ambiguity in Natural Language

Consider the English sentence:

John gave a book.

The recipient is not stated. Whether payment or some other exchange was involved also depends on context. The structure is therefore incomplete and unstable.

Precision in Lojban

The Lojban predicate dunda, meaning “to give,” consistently uses three arguments:

• x1: the giver
• x2: the thing given
• x3: the recipient

For the AI model learning this structure, specifically a Transformer, the behavior is almost identical to a function parameter definition in programming.

The neural network can learn rapidly and accurately which tokens fill which slots whenever a specific predicate token appears. This relationship can be identified through attention.

The following are representative structural characteristics of Lojban that can significantly support reasoning in an LLM.

Strict Separation Between Entities and Predicates: lo ... ku and cu

In natural language, the boundary between nouns and verbs can be unclear. For example, the English word “run” can function as either a noun or a verb.

Lojban physically separates these roles at the syntactic level.

lo ... ku — Sumti

Anything enclosed by lo ... ku always functions as an argument or term. As soon as the AI encounters this structure, it can determine that the enclosed content is an object of logical computation.

cu — Separator

The particle cu, placed before a predicate, serves as a signal that an operation is beginning.

Contribution to Reasoning

When assigning attention, an LLM can identify with complete structural certainty that the token immediately following cu is a function and that the content inside lo ... ku represents a variable.

The model no longer needs to spend resources calculating whether a word is a subject, a noun, or the present-tense form of a verb, as it would in natural language.

Explicit Case Roles Through Place Structures

One of the greatest weaknesses of natural language is that grammatical case—who did what to whom—depends on uncertain elements such as prepositions and word order.

Lojban’s Structure

Every predicate has its own predefined slots.

For example, klama, meaning “to go,” always has the following structure:

• x1: the person or entity going
• x2: the destination
• x3: the point of origin
• x4: the route
• x5: the means of transportation

Contribution to Reasoning

As soon as an LLM reads the token klama, it can identify which subsequent element fills each slot from x1 to x5, potentially from the model’s early layers without requiring processing through many Transformer blocks.

This structurally reduces opportunities for hallucination in logical puzzles involving the substitution or rearrangement of terms, such as syllogisms.

Fixed Quantifier Scope: ro and su'o

Many reasoning errors in natural language result from incorrectly interpreting the scope of quantifiers such as “all” and “at least one.”

Ambiguity in Natural Language

Consider the sentence:

Every student didn’t pass the exam.

Does this mean that no student passed, or that some students did not pass?

Precision in Lojban

Quantifiers such as ro, meaning “all,” and su'o, meaning “at least one,” are always placed directly before the relevant term. Their scope is closed syntactically.

Contribution to Reasoning

When the AI processes a proposition such as “All A are B,” it can identify precisely which part of the expression is governed by “all.”

This prevents confusion between universal affirmative propositions and particular affirmative propositions, one of the logical distinctions with which LLMs commonly struggle.

Abstraction Markers: ka, ni, and du'u

LLMs often have difficulty distinguishing facts, propositions, and properties. Lojban wraps these concepts in dedicated markers.

lo du'u ...
Packages the fact or content that something is the case into a single term.

lo ka ...
Extracts a property or abstract concept.

Contribution to Reasoning

When the AI processes the sentence “He likes running,” it receives a clear tag such as lo ka bajra, representing the abstract property of running.

The model can therefore distinguish the action itself from a description of the action and move accurately between different levels of meta-logical reasoning.

Closing Recursive Structures with Terminators: ku, vau, and kei

For a Transformer, determining where a clause ends within a long sentence can be difficult. This is related to the broader challenge of maintaining information across long structures.

Lojban’s Structure

Lojban frequently uses terminators such as:

• ku, which closes a structure beginning with lo
• vau, which marks the end of a sentence-level predicate structure
• kei, which closes an abstraction

These markers are often omitted in ordinary human usage. For AI training data, however, explicitly retaining them is recommended.

Contribution to Reasoning

These terminators perform a role similar to a closing brace, }, in a programming language.

They allow the AI to physically delimit the range over which attention should be applied. Even in deeply nested sentences, the model can continue parsing the structure without losing its logical position.

Conclusion: For an LLM, Lojban Is Like Pre-Structured JSON

If learning natural language is comparable to understanding a mass of tangled threads while simultaneously trying to untangle them, learning Lojban is comparable to reading a spreadsheet that has already been organized.

When training a model from scratch on a 1660 Ti, the reason the AI can acquire reasoning ability at remarkable speed is not simply that the AI is intelligent. It is because Lojban is already optimized for a form that intelligence can process efficiently.

Chapter 3: Experiment Overview and Results

This experiment did not use an existing pretrained base model such as Llama or GPT-4 that had already learned from enormous volumes of internet text.

Only the mathematical architecture was borrowed. The model was trained entirely from scratch, beginning with no stored knowledge.

Task

Three-valued logic puzzles using Lojban vocabulary, including:

• class inheritance relationships
• transitivity of relations
• separation of irrelevant noise
• evaluation of counterexamples and contradictions

Model Architecture

Custom GPT-2:

• 6 layers
• 8 attention heads
• embedding size of 512

Vocabulary Size

1,019 unique tokens:

• 997 real Lojban root words
• 5 variables
• structural words and special tokens

Training Environment

Local environment using:

• NVIDIA RTX 5090
• AdamW optimizer
• learning rate of (lr = 5 \times 10^{-4})

Number of Training Steps

10,000 steps with a batch size of 16.

Final Average Loss

1.7376

Evaluation Result

The model achieved 100% accuracy on the prepared reasoning test cases.

Four Reasoning Scenarios for Testing Three-Valued Logic

The important point in this experiment is that the AI did not simply learn to answer “yes” or “unknown.”

It mastered three-valued logic, enabling it to identify when a proposition is explicitly false and logically contradicts the premises.

Let us examine the four logic puzzles that were provided to the model.

To make them easier for humans to understand, the elegant vowel pattern of Lojban pro-sumti—ko'a, ko'e, and ko'i—is represented using the variables A, E, and I.

• ko'a → A
• ko'e → E
• ko'i → I

Every scenario also contains deliberately inserted irrelevant facts, or noise information, intended to disrupt the AI’s judgment.

Shared Premises

• A is a dog, gerku.
• Every dog belongs to the class of animals, danlu. This represents class inheritance.
• E is taller than A, expressed with zmadu ... lo ka clani.
• A is taller than I.
• E is a flag, lanci. This is irrelevant noise information.

The height relationship can therefore be summarized as:

E > A > I

After reading these premises, the model produced perfect answers to the following four questions.

Scenario 1: Class-Inheritance Judgment — True

Question

Is A an animal?

Lojban Input

ko'a cu gerku .i ro gerku cu klesi danlu .i ko'e zmadu ko'a lo ka clani .i ko'a zmadu ko'i lo ka clani .i ko'e cu lanci .i xu ko'a cu danlu

Model Output

jetnu — True

Explanation

From the inheritance relationship stating that every dog is an animal, the model correctly proves that A is an animal.

Scenario 2: Transitivity of Relations — True

Question

Is E taller than I?

Lojban Input

ko'a cu gerku .i ro gerku cu klesi danlu .i ko'e zmadu ko'a lo ka clani .i ko'a zmadu ko'i lo ka clani .i ko'e cu lanci .i xu ko'e zmadu ko'i lo ka clani

Model Output

jetnu — True

Explanation

From the two relationships “E > A” and “A > I,” the model correctly derives the indirect relationship “E > I.”

Scenario 3: Detection of a Category Error — Insufficient Premises or Undecidable

Question

Is the entire class or concept of animals taller than the individual E?

Lojban Input

ko'a cu gerku .i ro gerku cu klesi danlu .i ko'e zmadu ko'a lo ka clani .i ko'a zmadu ko'i lo ka clani .i ko'e cu lanci .i xu danlu zmadu ko'e lo ka clani

Model Output

na'i — Invalid premise or undecidable

Explanation

The model determines that it is inappropriate to compare a set or class with an individual instance using the same property of height, and therefore returns an error-like judgment.

Scenario 4: Logical Negation — False

Question

Is I taller than E?

Lojban Input

ko'a cu gerku .i ro gerku cu klesi danlu .i ko'e zmadu ko'a lo ka clani .i ko'a zmadu ko'i lo ka clani .i ko'e cu lanci .i xu ko'i zmadu ko'e lo ka clani

Model Output

na'e jetnu — False

Explanation

Because the premises establish that E is taller than I, the proposition “I > E” contradicts the established relationship. The model therefore identifies it explicitly as false.

The Role of GPT-2

Some readers may question why the familiar term “GPT-2” appears in an experiment described as training an AI from scratch.

This does not mean that a pretrained GPT-2 model or any of its previously acquired knowledge was used. It means that only the GPT-2 architecture—the structural blueprint—was borrowed.

The relationship is similar to an agar culture medium used in a science experiment.

• GPT-2 architecture: The agar medium, a foundation in which nutrients are properly arranged
• RTX 5090: The incubator that maintains the appropriate conditions and accelerates learning
• Lojban logical data: The specific bacteria being cultured—the logical reasoning engine

The agar itself does not initially contain bacteria. It begins in a sterile state. However, its moisture and nutrients are arranged in a way that supports efficient growth.

The Transformer architecture, the underlying technology behind GPT, works in a similar way. It provides a mechanism for efficiently calculating relationships between words and determining which information deserves attention through self-attention.

Because this well-designed medium already exists, it is possible to place Lojban logical data into it and perform training with suitable hardware.

Even within an extremely short process of only 10,000 steps, a clean and unambiguous logical reasoning structure can grow.

This is not a shortcut or an unfair trick in development. It is a rational and efficient approach that makes full use of a framework—a reusable common structure—in software engineering.

Loss Analysis and the Beauty of Symmetry

One particularly notable result is that the final average loss decreased to 1.7376, even though the training included the difficult task of identifying false propositions using na'e jetnu.

In ordinary language learning, adding another category that the model must distinguish—in this case, the option “false”—often introduces additional uncertainty and may temporarily increase the loss.

In this experiment, however, the loss decreased cleanly.

This can be attributed to the structural symmetry of Lojban, in which grammar and meaning correspond directly on a one-to-one basis.

The value suggests that the relationship between true and false fitted efficiently into the model’s internal parameters and connections.

Summary and Future Directions

This experiment provides one clear answer to the following question:

Are enormous LLMs with hundreds of billions of parameters truly necessary for advanced logical reasoning?

Even when the Transformer framework itself is relatively simple, using Lojban as the input language removes ambiguity from the data.

The experiment demonstrated that a lightweight model with only tens of millions of parameters can be developed into a specialized reasoning engine capable of processing complex three-valued logic with 100% accuracy under the prepared evaluation conditions.

The next area of investigation is how far this model can adapt to:

• multi-step reasoning involving several interacting conditions
• scenarios in which the number of premises changes dynamically
• more complex and previously unseen combinations of logical relationships