Abstract:

By introducing a new connective ▽ and adding several new axioms into the MTL logic，this paper constructs a new schematic extension of MTL.Meanwhile，in order to discuss corresponding semantics，it proposes the concept of MTL_▽ algebra.Moreover，completeness of the MTL_▽ logic is obtained with respect to linear MTL_▽ algebras.

Key words: MTL_▽ logic, MTL_▽ algebra, completeness, schematic extension

摘要： 在逻辑系统MTL（Monoidal t-norm based Logic）中引入一元逻辑连接词▽，并在原有公理模式的基础上添加若干新公理，构建了一种新的MTL的扩张MTL_▽逻辑系统。为了进行相应的语义研究，在MTL代数的基础上，引入一元算子▽，提出MTL_▽代数的概念，并证明了MTL_▽代数的同构定理。基于线性MTL_▽代数证明了逻辑系统MTL_▽的完备性。

关键词: MTL_▽逻辑系统, MTL_▽代数, 完备性, 扩张