We extend Choiceless Polynomial Time (CPT), the currently only remaining promising candidate in the quest for a logic capturing Ptime, so that this extended logic has the following property: for every class of structures for which isomorphism is definable, the logic automatically captures Ptime.

For the construction of this logic, we extend CPT by a witnessed symmetric choice operator. This operator allows for choices from definable orbits. But, to ensure polynomial-time evaluation, automorphisms have to be provided to certify that the choice set is indeed an orbit.

We argue that, in this logic, definable isomorphism implies definable canonization. Thereby, our construction removes the non-trivial step of extending isomorphism definability results to canonization. This step was a part of proofs that show that CPT or other logics capture Ptime on a particular class of structures. The step typically required substantial extra effort.

我们扩展了无选择多项式时间（CPT），这是目前在寻求捕获Ptime的逻辑中唯一剩下的有希望的候选者，因此该扩展逻辑具有以下属性：对于可定义同构的每一类结构，该逻辑自动捕获Ptime。

为了构建这个逻辑，我们通过见证对称选择算子扩展了 CPT。该运算符允许从可定义的轨道中进行选择。但是，为了确保多项式时间评估，必须提供自同构来证明选择集确实是轨道。

我们认为，在这种逻辑中，可定义的同构意味着可定义的经典化。因此，我们的构造消除了将同构可定义性结果扩展到规范化的重要步骤。此步骤是证明 CPT 或其他逻辑在特定类别的结构上捕获Ptime的证明的一部分。该步骤通常需要大量的额外努力。