Definitions of new symbols merely abbreviate expressions in logical frameworks, and no new facts (regarding previously defined symbols) should hold because of a new definition. In Isabelle/HOL, definable symbols are types and constants. The latter may be ad-hoc overloaded, i.e. have different definitions for non-overlapping types. We prove that symbols that are independent of a new definition may keep their interpretation in a model extension. This work revises our earlier notion of model-theoretic conservative extension and generalises an earlier model construction. We obtain consistency of theories of definitions in higher-order logic (HOL) with ad-hoc overloading as a corollary. Our results are mechanised in the HOL4 theorem prover.

中文翻译：

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具有特设超载的HOL模型理论保守扩展的机械化

新符号的定义仅是逻辑框架中的缩写，并且由于新定义，任何新事实（关于先前定义的符号）均不成立。在Isabelle / HOL中，可定义符号是类型和常量。后者可能是临时重载的，即对于非重叠类型具有不同的定义。我们证明，独立于新定义的符号可以将其解释保留在模型扩展中。这项工作修订了我们较早的模型理论保守扩展的概念，并概括了较​​早的模型构造。我们以临时重载作为必然结果，获得了高阶逻辑（HOL）中定义理论的一致性。我们的结果在HOL4定理证明器中得以机械化。