There has been a longstanding dispute over which formalism is the best for representing knowledge in AI. The well-known "declarative vs. procedural controversy" is concerned with the choice of utilizing declarations or procedures as the primary mode of knowledge representation. The ongoing debate between symbolic AI and connectionist AI also revolves around the question of whether knowledge should be represented implicitly (e.g., as parametric knowledge in deep learning and large language models) or explicitly (e.g., as logical theories in traditional knowledge representation and reasoning). To address these issues, we propose a general framework to capture various knowledge representation formalisms in which we are interested. Within the framework, we find a family of universal knowledge representation formalisms, and prove that all universal formalisms are recursively isomorphic. Moreover, we show that all pairwise intertranslatable formalisms that admit the padding property are also recursively isomorphic. These imply that, up to an offline compilation, all universal (or natural and equally expressive) representation formalisms are in fact the same, which thus provides a partial answer to the aforementioned dispute.

翻译：人工智能领域长期存在关于何种形式化方法最适合表示知识的争论。著名的"陈述式与过程式之争"关注以声明还是过程作为知识表示的主要模式。符号人工智能与联结主义人工智能之间的持续辩论，也围绕着知识应隐式表示（例如作为深度学习和大型语言模型中的参数化知识）还是显式表示（例如作为传统知识表示与推理中的逻辑理论）这一问题展开。为解决这些问题，我们提出了一个通用框架来捕捉我们感兴趣的各种知识表示形式化方法。在该框架中，我们发现了一类通用知识表示形式化方法，并证明所有通用形式化方法都是递归同构的。此外，我们证明了所有具有填充性质且可相互转换的形式化方法同样具有递归同构性。这些结果表明，经过离线编译处理后，所有通用（或自然且表达能力等价）的表示形式化方法本质上是相同的，从而为上述争议提供了部分解答。