The Logic Verification Engine is a modular Python package designed to simulate, analyze, and mathematically audit logical systems. Moving beyond simple calculations, this engine prioritizes System Integrity by providing automated tools to verify tautologies and programmatically prove logical equivalences.
This toolkit serves as a foundation for transitioning abstract discrete mathematics into verifiable software constraints, essential for Safety-Critical Systems and Natural Language Processing (NLP).
logic-verification-engine/
├── engine/ # Core Logic Package
│ ├── __init__.py # Package Initializer
│ ├── logic_gates.py # Boolean operations and Truth Table generation
│ └── quantifiers.py # Universal (∀) and Existential (∃) verification
├── README.md
└── .gitignore
- Gate Simulation: Full support for AND, OR, NOT, NAND, NOR, XOR, and XNOR operations.
- Equivalence Verification: Implements the Tautology Test to confirm if two compound statements are logically identical by evaluating the biconditional: P ↔ Q.
- Universal (∀) & Existential (∃) Engines: Evaluates predicates across variable domains to identify global constraints or specific supporting evidence.
- Traceable Verification: Unlike standard boolean returns, the engine identifies and returns the specific Counterexample (for ∀) or Supporting Evidence (for ∃) that triggered the result.
- De Morgan Consistency Audit: An internal verification layer that programmatically proves the mathematical consistency of negations (e.g., ¬[∀x P(x)] ≡ ∃x ¬P(x)).
In engineering, "it works" is insufficient; "it is provable" is the standard. This engine is built with an Audit Layer that ensures software operations strictly follow the laws of discrete mathematics. By returning the specific data point that falsifies a universal statement, the engine provides the Transparency required for debugging complex automated decision-making systems.
Author: Josh Hasam