Finding Finite Models in Multi-Sorted First Order Logic

TL;DR

This paper extends finite model finding methods to multi-sorted first order logic, introducing techniques that significantly reduce search space and improve the efficiency of finding finite models in this setting.

Contribution

It proposes new SAT encoding techniques that guide domain growth in multi-sorted logic, effectively managing the increased search complexity.

Findings

Significantly reduced search space in multi-sorted logic models

Effective domain growth guidance improves model finding efficiency

Implementation in Vampire proves practical and scalable

Abstract

This work extends the existing MACE-style finite model finding approach to multi-sorted first order logic. This existing approach iteratively assumes increasing domain sizes and encodes the related ground problem as a SAT problem. When moving to the multi-sorted setting each sort may have a different domain size, leading to an explosion in the search space. This paper focusses on methods to tame that search space. The key approach adds additional information to the SAT encoding to suggest which domains should be grown. Evaluation of an implementation of techniques in the Vampire theorem prover shows that they dramatically reduce the search space and that this is an effective approach to find finite models in multi-sorted first order logic.