Unification with Simple Variable Restrictions and Admissibility of $\Pi_2$-rules
<|reference_start|>Unification with Simple Variable Restrictions and Admissibility of $\Pi_2$-rules: We develop a method to recognize admissibility of $\Pi_{2}$-rules, relating this problem to a specific instance of the unification problem with linear constants restriction, called here "unification with simple variable restriction". It is shown that for logical systems enjoying an appropriate algebraic semantics and a finite approximation of left uniform interpolation, this unification with simple variable restriction can be reduced to standard unification. As a corollary, we obtain the decidability of admissibility of $\Pi_{2}$-rules for many logical systems.<|reference_end|>
@article{almeida2024unification,
    title={Unification with Simple Variable Restrictions and Admissibility of
  $\Pi_{2}$-rules},
    author={Rodrigo Nicolau Almeida, Silvio Ghilardi},
    journal={arXiv preprint arXiv:2406.03265},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.03265},
    primaryClass={math.LO cs.LO}
}