A Simple Logic of Concepts

Journal of Philosophical Logic:1-26 (forthcoming)
  Copy   BIBTEX

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.

Similar books and articles

Interpretations of intuitionist logic in non-normal modal logics.Colin Oakes - 1999 - Journal of Philosophical Logic 28 (1):47-60.
The Dynamification of Modal Dependence Logic.Pietro Galliani - 2013 - Journal of Logic, Language and Information 22 (3):269-295.
A spatial modal logic with a location interpretation.Norihiro Kamide - 2005 - Mathematical Logic Quarterly 51 (4):331.
A modal interpretation of the logic of interrogation.Rani Nelken & Chung-Chieh Shan - 2006 - Journal of Logic, Language and Information 15 (3):251-271.
Natural Deduction for Modal Logic with a Backtracking Operator.Jonathan Payne - 2015 - Journal of Philosophical Logic 44 (3):237-258.
Kripke semantics for modal substructural logics.Norihiro Kamide - 2002 - Journal of Logic, Language and Information 11 (4):453-470.
Deontic Modals.Jennifer Carr - 2017 - In Tristram McPherson & David Plunkett (eds.), The Routledge Handbook of Metaethics. Routledge. pp. 194-210.
Actuality and the a priori.Fabio Lampert - 2018 - Philosophical Studies 175 (3):809-830.
Incompleteness Results in Kripke Bundle Semantics.Kazuaki Nagaoka & Eiko Isoda - 1997 - Mathematical Logic Quarterly 43 (4):485-498.

Analytics

Added to PP
2022-11-23

Downloads
76 (#161,218)

6 months
76 (#13,911)

Historical graph of downloads
How can I increase my downloads?

Author Profiles

Thomas Icard
Stanford University
Larry Moss
Indiana University

Citations of this work

No citations found.

Add more citations

References found in this work

The Language of Thought.J. A. Fodor - 1978 - Critica 10 (28):140-143.
The semantic conception of truth and the foundations of semantics.Alfred Tarski - 1943 - Philosophy and Phenomenological Research 4 (3):341-376.
Generalized quantifiers and natural language.John Barwise & Robin Cooper - 1981 - Linguistics and Philosophy 4 (2):159--219.
Conjoining Meanings: Semantics Without Truth Values.Paul M. Pietroski - 2018 - Oxford, United Kingdom: Oxford University Press.
A Natural History of Negation.Jon Barwise & Laurence R. Horn - 1991 - Journal of Symbolic Logic 56 (3):1103.

View all 25 references / Add more references