A Simple Logic of Concepts

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...

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Bibliographic Details
Published in:Journal of philosophical logic 2023-06, Vol.52 (3), p.705-730
Main Authors: Icard, Thomas F., Moss, Lawrence S.
Format: Article
Language:English
Subjects:
Binding
Cognition & reasoning
Education
Hypotheses
Language
Linguistics
Logic
Natural language
Philosophy
Philosophy of language
Semantics
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Summary: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.
ISSN:0022-3611
1573-0433
DOI:10.1007/s10992-022-09685-1