# Finding Finite Models in Multi-Sorted First Order Logic

arXiv: https://arxiv.org/abs/1604.08040 · HTML: https://mlsanity.com/paper/1604.08040/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Apr 2016.

## Built on by (most cited first, 1 of 1)

- [Using Symmetries to Lift Satisfiability Checking](https://mlsanity.com/paper/2311.03424/) (2023)

## Abstract (arXiv)

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.