This model contains LoRA adapter weights for the base model google/flan-t5-xxl. It was trained to translate natural language statements into First-Order Logic (FOL) representations.

Model Details

Model Description

Developed by: Vossel et al. at Osnabrück University
Funded by: Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) 456666331
Model type: Encoder-decoder sequence-to-sequence model (T5 architecture)
Language(s) (NLP): English, FOL
License: This repository contains only LoRA adapter weights, trained using the base model google/flan-t5-xxl, which is released under the Apache 2.0 License. These adapter weights are also released under the Apache 2.0 License.
Finetuned from model: google/flan-t5-xxl

Uses

Direct Use

This model is designed to translate natural language (NL) sentences into corresponding first-order logic (FOL) expressions. Use cases include:

Automated semantic parsing and formalization of NL statements into symbolic logic.
Supporting explainable AI systems that require symbolic reasoning based on language input.
Research in neurosymbolic AI, logic-based natural language understanding, and formal verification.
Integration into pipelines for natural language inference, question answering, or knowledge base population.

Users should verify and validate symbolic formulas generated by the model for correctness depending on the application.

Downstream Use

The LoRA adapter can be further fine-tuned or combined with other models for domain-specific formalization tasks (e.g., legal, biomedical). Suitable for interactive systems requiring formal reasoning.

Out-of-Scope Use

Not designed for general natural language generation.
May struggle with ambiguous, highly figurative, or out-of-domain input.
Outputs should not be used as final decisions in critical areas without expert review.

Recommendations

Validate outputs carefully before use in critical applications.
Be aware of possible biases from training data and synthetic data sources.
Specialized for English NL and FOL; may not generalize to other languages or logics.
Use human-in-the-loop workflows for sensitive tasks.
Intended for research and prototyping, not standalone critical systems.

How to Get Started with the Model

python

import torch
from transformers import T5Tokenizer, T5ForConditionalGeneration

# Load tokenizer and model
model_path = "fvossel/flan-t5-xxl-nl-to-fol"  # or local path if not pushed to HF
tokenizer = T5Tokenizer.from_pretrained(model_path)
model = T5ForConditionalGeneration.from_pretrained(model_path, device_map="auto", torch_dtype=torch.bfloat16)

# Example NL input
nl_input = "All dogs are animals."

# Preprocess prompt
input_text = "translate English natural language statements into first-order logic (FOL): " + nl_input
inputs = tokenizer(input_text, return_tensors="pt", padding=True).to("cuda")

# Generate prediction
with torch.no_grad():
    outputs = model.generate(
        inputs["input_ids"],
        max_length=256,
        min_length=1,
        num_beams=5,
        length_penalty=2.0,
        early_stopping=False,
    )

# Decode and print result
print(tokenizer.decode(outputs[0], skip_special_tokens=True))

Training Details

Training Data

The model was fine-tuned on two datasets:

WillowNLtoFOL: Contains over 16,000 NL-FOL pairs. Published in:
Deveci, İ. E. (2024). Transformer models for translating natural language sentences into formal logical expressions.
Licensed under CC BY-NC-ND 4.0.
MALLS-v0: 34,000 NL-FOL pairs generated by GPT-4, syntactically checked.
Licensed under Attribution-NonCommercial 4.0, subject to OpenAI terms.

Training Procedure

Fine-tuning was performed using LoRA adapters on the pre-trained google/flan-t5-xxl model with:

Prompt-based instruction tuning
Single-GPU training with bf16 mixed precision

Training Hyperparameters

Training regime: bf16 mixed precision
Batch size: 8 (per device)
Learning rate: 1e-4
Number of epochs: 12
Optimizer: AdamW
Adam epsilon: 1e-8
Scheduler: Linear warmup with 500 steps
Gradient accumulation steps: 1
Weight decay: 0.01
LoRA rank (r): 16
LoRA alpha: 32
LoRA dropout: 0.05
Target modules: ["q", "k", "v", "o", "wi", "wo"]
Bias: none
Task type: SEQ_2_SEQ_LM
Early stopping patience: 4 epochs
Evaluation strategy: per epoch
Save strategy: per epoch
DDP parameters:
- ddp_find_unused_parameters=False
- ddp_backend="nccl"

Citation

If you use this models for scientific purposes, please cite the following paper:

@misc{vossel2025advancingnaturallanguageformalization,
      title={Advancing Natural Language Formalization to First Order Logic with Fine-tuned LLMs}, 
      author={Felix Vossel and Till Mossakowski and Björn Gehrke},
      year={2025},
      eprint={2509.22338},
      archivePrefix={arXiv},
      primaryClass={cs.CL},
      url={https://arxiv.org/abs/2509.22338}, 
}