Unification with Simple Variable Restrictions and Admissibility of $\Pi_{2}$-rules

Rodrigo Nicolau Almeida; Silvio Ghilardi

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arXiv · 2406.03265

Unification with Simple Variable Restrictions and Admissibility of $\Pi_{2}$-rules

Rodrigo Nicolau Almeida·Silvio Ghilardi

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Abstract

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.

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BibTeX RIS

Rodrigo Nicolau Almeida, Silvio Ghilardi. 2024-06-05. Unification with Simple Variable Restrictions and Admissibility of $\Pi_{2}$-rules. https://arxiv.org/abs/2406.03265

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