Use Case: Mathematical Proof Validation

GPTProX can be developed to validate mathematical proofs by parsing them into proof trees and identifying logical gaps:

1. Proof Parsing

• The mathematical proof is split into individual inferential steps.
• Each step is converted into logical predicates representing the premises and conclusions.
• These predicates are arranged into a tree structure showing the logical dependencies between steps.

2. Proof Tree Analysis

• The proof tree is traversed to ensure each branch forms a valid logical deduction.
• Facts and axioms are referenced from the knowledge base to validate premises.
• Any missing or invalid steps are flagged as gaps in the tree.

3. Gap Identification

• Gaps are traced back to the specific steps in the original proof text.
• The location and nature of the logical leap is reported.
• For example, "Step 3 concludes P from S, but this deduction is invalid without proving Q."

4. Proof Correction

• Based on identified gaps, the system can request new proof steps to bridge the flawed logic.
• This iterative validation tightens the reasoning until producing a sound proof.

In summary, by systematically parsing proofs into symbolic logic and traversing the resultant reasoning tree, GPTProX pinpoints logical inconsistencies down to the specific inferential jumps in the original proof. This structured dissection of mathematical reasoning allows robust and transparent proof validation.