In Pietroski (2018) a simple representation language called SMPL is introduced, construed as a hypothesis about core conceptual structure. The present work is a study of this system from a logical perspective. In addition to establishing a completeness result and a complexity characterization for reasoning in the system, we also pinpoint its expressive limits, in particular showing that the fourth corner in the square of opposition (“Some_not”) eludes expression. We then study a seemingly small extension, called SMPL⁺, which allows for a minimal predicate-binding operator. Perhaps surprisingly, the resulting system is shown to encode precisely the concepts expressible in first-order logic. However, unlike the latter class, the class of SMPL⁺ expressions admits a simple procedural (context-free) characterization. Our contribution brings together research strands in logic—including natural logic, modal logic, description logic, and hybrid logic—with recent advances in semantics and philosophy of language.

在 Pietroski (2018) 中，引入了一种称为 SMPL 的简单表示语言，将其解释为关于核心概念结构的假设。目前的工作是从逻辑的角度对该系统进行研究。除了为系统中的推理建立完整性结果和复杂性表征外，我们还指出了其表达限制，特别是表明对立方块中的第四个角（“ Some_not ”）无法表达。然后我们研究一个看似很小的扩展，称为 SMPL ⁺，它允许最小的谓词绑定运算符。也许令人惊讶的是，结果系统被证明可以精确地编码可在一阶逻辑中表达的概念。然而，与后一类不同的是，SMPL ^+的类expressions 承认一个简单的程序（无上下文）特征。我们的贡献汇集了逻辑的研究分支——包括自然逻辑、模态逻辑、描述逻辑和混合逻辑——以及语义学和语言哲学的最新进展。