绝对逻辑：形式逻辑的一种替代框架
Absolute Logic: an alternative framework for formal logic
AI总结：
本文提出绝对逻辑框架，通过统一术语与公式的概念，建立自包含语义学，解决传统一阶逻辑的限制，并整合递归理论约束以平衡表达力与有效性。
摘要：
本文介绍了一种形式逻辑的替代框架，称为“绝对逻辑”，旨在克服标准一阶逻辑（FOL）固有的内在限制和结构相对性。虽然FOL依赖于外部塔斯基结构来赋予意义，并将量化限制在一个预定的领域内，所提出的系统建立了一个不变、自包含的语义学，其中每个符号都有内在的意义。通过将传统的语法二元分化（术语和公式）统一为一个“表达式”的概念，并在形式化的变量-表达式上下文中评估它们，该系统密切模仿了人类数学推导的自然和累积性质。此外，我们通过整合递归理论约束来解决表达力和建设性效用之间的关键平衡，展示了计算理论如何作为必要界限来保持基础有效性。所得到语言的一致性和结构性质被正式确立，为非层级的绝对逻辑系统提供了新的视角。
英文摘要：
This paper introduces an alternative framework for formal logic, termed "Absolute Logic", designed to overcome the intrinsic limitations and structural relativity of standard First-Order Logic (FOL). While FOL relies on external Tarskian structures to assign meaning and restricts quantification to a single, predetermined domain, the proposed system establishes an invariant, self-contained semantics where every symbol possesses an intrinsic meaning. By unifying the traditional syntactic dichotomy between terms and formulas into a single concept of "expression" and evaluating them relative to formalized variable-expression contexts, the system closely mirrors the natural, cumulative nature of human mathematical deduction. Furthermore, we address the critical balance between expressive power and constructive utility by integrating recursion-theoretic constraints, demonstrating how computability theory acts as a necessary bound to preserve foundational validity. The consistency and structural properties of the resulting language are formally established, providing a novel perspective on non-hierarchical, absolute logical systems.
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