Admissible inference rules of temporal intransitive logic with the operator "tomorrow"

Vitaliy V. Rimatsky, Olga V. Ganchukova

Siberian Federal University, Krasnoyarsk, Russian Federation

Abstract: We investigates non-transitive temporal logic with the "tomorrow" operator. In this logic, the operator "necessary" $\Box$ coincides with the operator “possible” $\Diamond$ (or almost coincides in reflexive case). In addition to the basic properties of the reflexive non-transitive logic ${{\mathcal L}}^r$ (decidability, finite approximability), admissible rules of this logic are investigated. The main result consists in proving the structural completeness of this logic and its tabular extensions.

Keywords: modal logic, frame and model Kripke, admissible and globally admissible inference rule.

UDC: 510.643; 517.11

Received: 29.04.2023
Received in revised form: 18.12.2023
Accepted: 26.02.2024

Language: English