弱化与收缩超对称子结构逻辑的可判定性与复杂性
Decidability and Complexity in Weakening and Contraction Hypersequent Substructural Logics
摘要：
我们建立了可判定性的无限多公理扩展的交换全Lambek逻辑与削弱FLew（即IMALLW），有一个切自由hyperprinciple证明演算（具体地说：每一个分析结构规则扩展）。最近建立了其收缩对应物FLec的相应扩展的可判定性，但它们的计算复杂性没有得到回答。在本文的第二部分中，我们引入了足够的长度函数的良好拟序和快速增长的复杂性类，以获得复杂性上界的削弱和收缩扩张。这个结果的一个具体实例产生的第一个复杂性界为突出的模糊逻辑MTL（monoidal t-范数为基础的逻辑）提供了一个长期存在的开放问题的答案。
英文摘要：
We establish decidability for the infinitely many axiomatic extensions of the commutative Full Lambek logic with weakening FLew (i.e. IMALLW) that have a cut-free hypersequent proof calculus (specifically: every analytic structural rule extension). Decidability for the corresponding extensions of its contraction counterpart FLec was established recently but their computational complexity was left unanswered. In the second part of this paper, we introduce just enough on length functions for well-quasi-orderings and the fast-growing complexity classes to obtain complexity upper bounds for both the weakening and contraction extensions. A specific instance of this result yields the first complexity bound for the prominent fuzzy logic MTL (monoidal t-norm based logic) providing an answer to a long-standing open problem.
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