演绎定理：博弈论中共同实践的问题性质
Deduction Theorem: The Problematic Nature of Common Practice in Game Theory
摘要：
我们认为演绎定理在博弈论的文献中使用运行一个所谓的矛盾证明。在博弈论中，如果我们有$ϕ\vdash φ$的证明，那么我们也有$ϕ\Rightarrow φ$的证明。因此，$ϕ\Rightarrow φ$的证明是从先前已知的陈述推导出来的。然而，我们认为，必须设法建立子句$ϕ$和$φ$的证明，即，它们是已知的真陈述，以表明$ϕ\vdash φ$是可证明的，因此$ϕ\Rightarrow φ$也是可证明的。因此，我们不能假定子句$ϕ$或$φ$是真语句。这立即导致一个错误的结论。除此之外，我们还强调了为什么演绎定理不适用于反证的其他事实。最后，我们提出了一个例子，从工业合作的演绎定理是不正确的应用的后果，所获得的结果矛盾的众所周知的聚集问题。
英文摘要：
We consider the Deduction Theorem used in the literature of game theory to run a purported proof by contradiction. In the context of game theory, it is stated that if we have a proof of $ϕ\vdash φ$, then we also have a proof of $ϕ\Rightarrow φ$. Hence, the proof of $ϕ\Rightarrow φ$ is deduced from a previously known statement. However, we argue that one has to manage to establish that a proof exists for the clauses $ϕ$ and $φ$, i.e., they are known true statements in order to show that $ϕ\vdash φ$ is provable, and that therefore $ϕ\Rightarrow φ$ is provable as well. Thus, we are not allowed to assume that the clause $ϕ$ or $φ$ is a true statement. This leads immediately to a wrong conclusion. Apart from this, we stress to other facts why the Deduction Theorem is not applicable to run a proof by contradiction. Finally, we present an example from industrial cooperation where the Deduction Theorem is not correctly applied with the consequence that the obtained result contradicts the well-known aggregation issue.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
