In the literature on self-referential paradoxes one of the hardest and most challenging problems is that of revenge. This problem can take many shapes, but, typically, it besets non-classical accounts of some semantic notion, such as truth, that depend on a set of classically defined meta-theoretic concepts, like validity, consistency, and so on. A particularly troubling form of revenge that has received a lot of attention lately involves the concept of validity. The difficulty lies in that the non-classical logician cannot accept her own definition of validity because it is given in a classical meta-theory. It is often suggested that this mismatch between the consequence relation of the account being espoused and the consequence relation of the meta-theory is a serious embarrassment. The main goal of the paper is to explore whether certain substructural accounts of the paradoxes can avoid this sort of embarrassment. Typically, these accounts are expressively incomplete, since they cannot assert in the object language that certain invalid arguments are in fact invalid. To overcome this difficulty I develop a novel type of hybrid proof-procedure, one that takes invalidities to be just as fundamental as validities. I prove that this proof-procedure enjoys a number of interesting properties and I analyze the prospects of applying it to languages capable of expressing self-referential statements.

在关于自我指称悖论的文献中，最困难和最具挑战性的问题之一是复仇。这个问题可以采取多种形式，但通常会困扰一些语义概念（例如真理）的非经典解释，这些语义概念取决于一组经典定义的元理论概念，例如有效性，一致性等。最近引起了广泛关注的一种特别令人困扰的复仇形式涉及有效性的概念。困难在于非古典逻辑学家不能接受她自己的有效性定义，因为它是在古典元理论中给出的。经常有人提出，被拥护账户的结果关系与元理论的结果关系之间的这种不匹配是一种严重的尴尬。本文的主要目的是探讨悖论的某些子结构解释是否可以避免这种尴尬。通常，这些帐户在表达上是不完整的，因为它们无法用对象语言断言某些无效参数实际上是无效的。为了克服这一困难，我开发了一种新型的混合证明程序，该程序将无效性与有效性同等重要。我证明了该证明程序具有许多有趣的特性，并且分析了将其应用于能够表达自我参照陈述的语言的前景。为了克服这一困难，我开发了一种新型的混合证明程序，该程序将无效性与有效性同等重要。我证明了该证明程序具有许多有趣的特性，并且分析了将其应用于能够表达自我参照陈述的语言的前景。为了克服这一困难，我开发了一种新型的混合证明程序，该程序将无效性与有效性同等重要。我证明了该证明程序具有许多有趣的特性，并且分析了将其应用于能够表达自我参照陈述的语言的前景。