Affiliations: [a] State Key Laboratory of Software Development Environment, Beijing University of Aeronautics and Astronautics, China
| [b] Key Laboratory of Intelligent Information Processing, Institute of Computing Technology, Chinese Academy of Sciences, China
| [c] School of Computer and Control Engineering, University of Chinese Academy of Sciences, China
Correspondence:
[*]
Corresponding author. Wang Yuhui. Tel.: +86 18801496117 or +86 01062600538; E-mail: [email protected].
Note: [1] This work was supported by the Open Fund of the State Key Laboratory of Software Development Environment under Grant No. SKLSDE-2010KF-06, Beijing University of Aeronautics and Astronautics, and by the National Basic Research Program of China (973 Program) under Grant No. 2005CB321901.
Abstract: Given a lattice L, an L-modalized propositional logic will be proposed in which each element a ∈ L is associated with a modality [a], and a Gentzen-typed deduction system
GL
will be given so that the the system is sound and complete with the L-valued semantics, where [a] A means that the truth-value of formula A is a. Moreover, the distributivity and modularity of
GL
will be discussed.
Keywords: The Belnap logic, the modality, lattice, distributivity of a deduction system, modularity
