Gentzen-type sequent calculus for modal logic S5
Year: 2025
Type: article
Abstract: We consider a Gentzen-type cut-free sequent calculus GS5 for the modal logic S5 with a restriction on backward applications of modal rule $(\Box \Rightarrow )$. Using Schütte’s method of reduction trees, we prove that the calculus is complete for S5. We also prove that all rules are invertible and the cut rule is admissible in the calculus. We show that any backward proof search terminates, obtaining a decision procedure for S5 using the introduced calculus GS5.
Source: Logic Journal of IGPL
Authors: R Alonderis, H Giedra
Institution: Vilnius University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $4,533
OpenAlex ID: W4408490245