Title: A sound and complete axiomatic system for compound accessible relations

Authors: Sujie Guan

Addresses: Information Engineering, NanChang Institute of Technology, Nanchang, Jiangxi, China

Abstract: Approximation spaces are deemed as frames for the modal logic. Given two equivalence relations R₁ and R₂. R₁ and R₂ can be mapped to the modalities ͸₁ and ͸₂, respectively. For any formula A, ͸A ≡ ͸₁A ˅ ͸₂A or ͸A ≡ ͸₁A ˄ ͸₂A, where ͸ corresponds to an accessible relation R. Obviously, R may not be an equivalence relation and it is difficult to give an axiomatic system for ͸. So a sound and complete axiomatic system is given for the propositional modal logic, where the accessibility relation R for modality ͸ is the join of the accessibility relations R₁, R₂. Obviously, this paper presents a generalised modal logic in which the modality ͸ corresponds to two accessible relations, and has stronger knowledge representation ability and stronger formal ability.

Keywords: accessibility relation; axiomatic system; soundness and completeness.

DOI: 10.1504/IJWMC.2024.139790

International Journal of Wireless and Mobile Computing, 2024 Vol.27 No.1, pp.41 - 46

Received: 07 Jan 2023
Accepted: 30 Mar 2023
Published online: 05 Jul 2024 *

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