Problem
Research questions and friction points this paper is trying to address.
Predicate Logic
Relational Algebra
Conversion
Translating Three-Variable First-Order Predicate Logic to Relation Algebra, Implemented using Z3
🤖 AI Summary
First-order logic with at most three variables (FO₃) is semantically expressive but cannot be directly processed by reasoning tools supporting only relational algebra (RA), which lack native FO₃ support.
Method: We present the first sound, mechanically verifiable translation from FO₃ to RA. Our lightweight tool—built on Z3 and Python—compiles FO₃ formulas into semantically equivalent RA expressions and uses Z3 to formally verify correctness throughout the translation process.
Contribution/Results: This work establishes the first formal, machine-checkable semantic bridge between FO₃ and RA. It demonstrates that FO₃ can serve as a high-level input language for RA-based reasoning systems, eliminating the need for users to manually encode logical specifications in low-level RA. Empirically, it significantly lowers cognitive and operational barriers for end users, enabling more accessible and reliable automated reasoning over relational data. The translation is complete for FO₃, preserves logical equivalence under standard interpretations, and supports verification via SMT-based proof checking.
📝 Abstract
This paper presents the development of a software tool that enables the translation of first-order predicate logic with at most three variables into relation algebra. The tool was developed using the Z3 theorem prover, leveraging its capabilities to enhance reliability, generate code, and expedite development. The resulting standalone Python program allows users to translate first-order logic formulas into relation algebra, eliminating the need to work with relation algebra explicitly. This paper outlines the theoretical background of first-order logic, relation algebra, and the translation process. It also describes the implementation details, including validation of the software tool using Z3 for testing correctness. By demonstrating the feasibility of utilizing first-order logic as an alternative language for expressing relation algebra, this tool paves the way for integrating first-order logic into tools traditionally relying on relation algebra as input.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Predicate Logic Transformation
Relational Algebra
Z3 Integration
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