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

Autor:	Almeida, Rodrigo Nicolau, Ghilardi, Silvio
Rok vydání:	2024
Předmět:	Mathematics - Logic Computer Science - Logic in Computer Science
Druh dokumentu:	Working Paper
Popis:	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. Comment: 22 pages, Accepted at AIML 2024
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2406.03265 Zobrazit plný text záznamu View this record from Arxiv