Current AI (probabilistic LLMs) CANNOT (by design) generate 100% reliable reasoning. UMIND is a NeSy architecture based on the new universal logic language ULOGIC. UMIND is designed to generate verified knowledge, not hallucinations. UMIND is the engine behind the LEOX (Logic Expert Operator) agent.
The root problem of LLMs is not about scale or data, it is the architecture itself. An LLM does not maintain logical state. Its "reasoning" is the generation of statistically coherent text. This is the cause of structural hallucination (not accidental), and of inconsistencies. CoT (Chain of Thought) strategies offer better answers, but they are only simulations of reasoning and are not reliable (because the underlying generative mechanism is the same).
Formal languages like LEAN, Coq (and similar ones) attempt to solve this problem. Their verification power is absolute BUT they have a fundamental flaw: their alien syntax is guided by flawed "type theory," something non-existent in real mathematics that disorients LLM interfaces (and people). The zero-shot auto-formalization rate with Lean is below 15% in the best current models. A fact: "Human-mathematicians" don't understand Lean either.
The neuro-symbolic fracture occurs precisely at the interface (LLM → Verifier). It is the bottleneck that no current system has solved autonomously. The problem is not computing power; it is an incompatibility between two different systems: LLMs (semantics by analogy) vs. Verifier (structural-formal-strict).
ULOGIC-MIND's bet is that the solution does not lie in connecting an LLM with Lean, but in re-designing the linguistic formalism (new ULOGIC language) to make it suitable for LLMs. Furthermore, it is necessary to solve historical problems in mathematics and logic: getting rid of the flawed type theory, and creating a natural set theory without contradictions as a basis for fluid reasoning.
The structural defects of verified reasoning in AI
ULOGIC-MIND is an AI capable of 100% reliable exact reasoning. The human intuits, suggests, and guides; the AI autonomously finds proofs (subject to context rules), verifies them with 100% accuracy, and creates a document (TekDoc: Transportable Encapsulated Knowledge) with the proofs and algorithms. Finally, the TekDoc is added to the global verified knowledge repository (TekHub) for future reuse.
Establish the first universal "Typeless" language capable of translating human ambiguity into verifiable code.
Replace the probabilistic "Black Box" of LLMs with a Neuro-Symbolic architecture with full traceability.
Transform scientific knowledge from "static PDFs" to interconnected "Computable Objects".
Agents capable not only of verifying, but of discovering new truths through evolutionary strategies.
From Natural Language to Formal Logic. Frictionless.
Step-by-step mathematical validation. Zero hallucinations.
Global repository of living and linked knowledge.
LEOX (Logical Expert Operator) is not a chatbot. It is a research collaborator connected to the UMIND Kernel. It helps formalize intuitions, search for knowledge (TekDocs) in the TekHub, interconnect it, compose it, and generate 100% verified proofs in advanced mathematics, science, business, and technology of any complexity level. Your organization defines the operational rules and LEOX will follow them with 100% guarantees without failures (0% errors). LEOX uses the internal logic language ULOGIC and the UMIND engine.
You don't need to learn any formal language.
Are you a mathematician? Write math as you always have. Do you have strict rules for financial, industrial, or other processes? Define your rules and ask in your everyday language.
LEOX takes your input and handles everything internally. The ULOGIC engine auto-formalizes
completely invisibly to you, the Kernel verifies every step with absolute certainty, and you receive
the result in standard mathematical notation.
Writes math in informal language and standard notation.
Auto-formalizes the input into the formal language ULOGIC.
Executes deterministic verification. 100% mathematical accuracy.
Translates the verified result back to standard mathematical language.
Receives a mathematically proven and guaranteed proof.
All the power of formal proof. Without a learning curve.
Universal Logic Language (The hidden grammar of informal reasoning)
"A Foundational Shift in AI Reasoning"
Articles about ULOGIC-LANGUAGE in: https://ulogiclang.ai
ULOGIC breaks current paradigms: It is an EXACT UNIVERSAL LANGUAGE with sufficient capacity to express mathematical and scientific reasoning of any complexity level. It unifies logic, computation, and auto-metalinguistics. It has no interpretation in anything external to itself. It does not use the artificiality of types, predefined alphabetic variables, or traditional formal logic conventions. ULOGIC is the "deep grammar underlying mathematics and computation", not a translation into an alien typed language like LEAN. Mathematicians, logicians, and programmers have always spoken in ULOGIC (even if they didn't know it) ... and they can continue writing math normally because agents like LEOX know how to auto-formalize them automatically and scalably.
Neuro-Symbolic Intelligence (NeSy) for scientific discovery.
The creative component.
Reads natural language, proposes hypotheses, and translates semi-formal and informal language into strict ULOGIC. Searches for proofs.
Creates and composes new knowledge.
The deterministic judge.
Verifies the TekDoc document written in ULOGIC. Guarantees logical consistency without hallucinations. A verified proof follows the rules of "your context-system".
100% absolute certainty (0% errors)
HUMAN presents in informal or semi-formal language ⟶
⟶ NEURO auto-formalizes ⟶ NEURO generates proofs and ideas ⟶ Symbolic KERNEL verifies ⟶ NEURO corrects ⟶
⟶ Generated Truth (valid TekDoc document) → TekDoc saved in TekHub for reuse ⟶
⟶ NEURO presents result to human ⟶ HUMAN evaluates relevance ⟶ INNOVATION AND DISCOVERY
The evolution towards an industrial autonomous discovery architecture
Completion and Improvements of the verifying Kernel in Rust to guarantee memory safety and massive parallelism.
Model training (Fine-Tuning) via Reinforcement Learning against the Kernel (AlphaZero style).
The "GitHub" of verified knowledge.
A centralized platform where .tkd documents (TekDocs) are stored, versioned, and cryptographically linked.
The Public TekDocs Network will allow auto-verifying the correctness of proposals and papers, as well as guaranteeing (c) copyright.
Beyond probabilistic AI: Toward an infrastructure of exact knowledge and Effective Freedom.
We reject AGI as a fallible human clone. We build a deterministic Super-Assistant. We transcend statistical LLMs (L1/L2) toward Exact Reasoning (C3) and Scientific Paradigm Discovery (C5).
The altruistic USM Foundation safeguards the ULOGIC standard and the Public TekHub as global common goods, while UlogicMind ensures sustainability by providing 0% error infrastructure to large corporations.
Technology subordinated to human dignity. Those who contribute to open science use tools for free; corporations profiting privately finance the system. Demonstrable truth as a democratic shield.
Explore the detailed Roadmap, Standard Governance, and the UPL License.
A new architecture for computational reasoning.
| Project | NeSy Strategy | Differentiating Technical Features |
|---|---|---|
| DeepMind (AlphaProof) | LLMs generating tactics for Lean (HOL) | Massive search power (RL + MCTS) over an established and community-audited formalism. Extreme friction: Rigid type-based syntax. |
| Lean/Coq Communities | AI Assistance in Classical Formal Languages | Mature theoretical foundation (HoTT, CIC). World's largest ecosystem of verified libraries. Prohibitive learning curve and structural rigidity. |
| IBM Research (LNNs) | Logical Neural Networks | Graded fuzzy reasoning, tolerance for uncertainty in noisy real-world data. Difficulty scaling to creative natural language. |
| ULOGIC-MIND | "Typeless" & Decoupled NeSy Architecture | ULOGIC-LANGUAGE formalism designed from scratch for LLM-native self-formalization. Eliminates syntactic friction in the LLM⟶verifier interface. Solves historical logical problems and lays the groundwork for self-formalizable natural fluid reasoning. |
Technical details of the project
Unlike FOL, where syntax is logic, ULOGIC separates **Representation** (String) from **Expression** (Abstract Object). This enables the AI to auto-formalize natural language without sacrificing rigor.
ULOGIC is a **Typeless** language with internal operational semantics. It eliminates the friction of traditional typed languages, allowing for a reasoning fluidity impossible for systems like Lean or Coq.
We do not depend on external interpretations (Tarski). ULOGIC is its own metalanguage, verifying truth through the internal structure of the **Abstract Expressions** managed by the Kernel.
While others publish static PDFs, we generate cumulative **Computable Objects**. Every verified Expositive Block (ExpEB) in the TekHub is a piece of logical software ready for global use.