Key improvements and explanations:

* **Clear Class Structure:** The code is organized into `Axiom` and `AxiomGenerator` classes, making it more modular and easier to understand.
* **Axiom Class:**  The `Axiom` class now includes:
    * `axiom_id`: Unique identifier for each axiom.  Crucial for tracking and dependencies.
    * `type`:  Categorizes the axiom (Foundation, Derived, Operational).
    * `inferred_from`:  Keeps track of which axioms were used to derive this axiom.  Essential for provenance.
    * `contradicts`:  Keeps track of which axioms this axiom contradicts.
    * `__eq__` and `__hash__`:  Implement these methods to allow `Axiom` objects to be compared for equality and used as keys in sets/dictionaries.  This is *critical* for preventing duplicate axioms.
    * `to_dict` and `from_dict`:  Methods for exporting and importing axioms as dictionaries, including handling dependencies correctly. This is essential for saving and loading the axiom base.  The `from_dict` method now correctly resolves dependencies using a lookup table.
* **AxiomGenerator Class:**
    * **`add_axiom(self, axiom)`:**  This function now assigns a unique ID to each axiom *before* adding it to the `axioms` set. This ensures that each axiom has a unique identifier.  Crucially, it checks for redundancy *before* assigning an ID.
    * **`generate_axioms_from_patent`:**  This function now returns the list of axioms that were added from the patent.
    * **`_is_redundant(self, new_axiom)`:** Implements cosine similarity to detect redundant axioms.  This is more robust than simple string matching.  It also uses TF-IDF and stop words for improved accuracy.
    * **`validate_axioms()`:**  A placeholder implementation for axiom validation.  I've included a basic example of contradiction detection based on the presence of "not".  A real implementation would require much more sophisticated NLP and logical reasoning.
    * **`derive_axioms()`:** A placeholder implementation for axiom derivation. I've included a basic example of combining axioms that share common terms.  A real implementation would require much more sophisticated NLP and logical inference.  The `inferred_from` attribute is populated here.
    * **`categorize_axioms()`:**  Categorizes axioms into foundation, derived, and operational types based on dependencies.  Axioms with no dependencies are considered foundation axioms.
    * **`get_axioms_by_type()`:**  Returns a list of axioms of a specific type.
    * **`export_axioms()`:** Exports axioms to a list of dictionaries, including dependencies by storing *axiom IDs* instead of the objects themselves.
    * **`import_axioms()`:** Imports axioms from a list of dictionaries. This is the most complex part, as it needs to:
        1. Create a lookup dictionary of existing axioms based on their IDs.
        2. Iterate through the dictionaries.
        3.  If the axiom already exists (based on ID), update it's attributes.
        4.  If the axiom doesn't exist, create a new `Axiom` object, resolve dependencies using the lookup table, and add it to the set.

* **Confidence Calculation:**  The `_calculate_confidence` function now calculates confidence based on the frequency of the sentence in the patent text.  This is a simple example and can be enhanced with more sophisticated NLP techniques.
* **Logging:**  Added logging statements to track the progress of the axiom generation, validation, and derivation processes.  This is very helpful for debugging and understanding the system's behavior.
* **Error Handling:** Included a check for division by zero in the confidence calculation.
* **Stop Words:** Uses NLTK's stop words to improve the accuracy of the redundancy check.
* **Uniqueness:** Uses a `set` to store axioms, ensuring that only unique axioms are added.  The `__eq__` and `__hash__` methods in the `Axiom` class are essential for this to work correctly.
* **Example Usage:** The `if __name__ == '__main__':` block provides a clear example of how to use the `AxiomGenerator` class.  It generates axioms from two sample patents, validates them, derives new axioms, categorizes them, and prints them.  It also demonstrates how to export and import axioms.
* **Dependency Handling:** The `export_axioms` and `import_axioms` methods correctly handle dependencies between axioms by storing and resolving axiom IDs.

**How to use the code:**

1. **Install Dependencies:**