模糊命题的多维三层逻辑的语义

Semantics of Fuzzy Propositional Multi-Dimension Three-Layer Logic

考虑模糊概念与模糊逻辑的多种性,基于带对偶非的三角模逻辑,提出了一种新的模糊命题的逻辑,称为模糊命题的多维三层逻辑.特别地,记n维三层逻辑为L_(n-3-3).首先,引入了模糊命题的首层n维真向量、中层3维真向量、末层经典真向量的概念;然后,提出了L_(n-3-3)逻辑悲观c-重言式、L_(n-3-3)逻辑乐观c-重言式、L_(n-3-3)逻辑期望c-重言式、L_(n-3-3)逻辑重言式、L_(n-3-3)逻辑悲观c-经典重言式、L_(n-3-3)逻辑乐观c-经典重言式与L_(n-3-3)逻辑期望c-经典重言式概念,并且讨论了L_(n-3-3)逻辑的性质.最后提供了LN-L2-3-3逻辑的规律.

Considering multiple characteristics of fuzzy concept and fuzzy logics,based on trian-gle norms with involution negation,the paper proposes a new kind of fuzzy propositional logics.It is called fuzzy propositional multi-dimension three-layer logic.In particular,n-dimension three-layer logic is denoted by L_(n-3-3).Firstly,some concepts for fuzzy propositions,such as the first-layer n-dimension truth-vector,the middle-layer 3-dimension truth-vector and the end-layer classical truth-vector,are introduced.Then,some concepts,such as L_(n-3-3) logic pessimism c-Tautology,L_(n-3-3) logic optimism c-Tautology,L_(n-3-3) logic expectation c-Tautology,L_(n-3-3) logic Tautology,L_(n-3-3) logic pessimism c-classical Tautology,L_(n-3-3) logic optimism c-classical Tautology and Ln-33 logic expectation c-classical Tautology also are presented,and the proper-ties of L_(n-3-3) logic are discussed.Finally,the logical laws of LN-L2-3-3 are provided.