A Simple Logic of Concepts

Journal of Philosophical Logic (forthcoming)
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Abstract

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.

Author Profiles

Thomas Icard
Stanford University
Larry Moss
Indiana University

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