Abstract
A first-order language with a defined identity predicate is proposed whose apparatus for atomic predication is sensitive to grammatical categories of natural language. Subatomic natural deduction systems are defined for this naturalistic first-order language. These systems contain subatomic systems which govern the inferential relations which obtain between naturalistic atomic sentences and between their possibly composite components. As a main result it is shown that normal derivations in the defined systems enjoy the subexpression property which subsumes the subformula property with respect to atomic and identity formulae as a special case. The systems admit a proof-theoretic semantics which does not only apply to logically compound but also to atomic and identity formulae—as well as to their components. The potential of the defined systems for a meticulous first-order analysis of natural inferences whose validity crucially depends on expressions of some of the aforementioned categories is demonstrated.
Keywords Identity  Natural deduction  Natural logic  Normalization  Proof-theoretic semantics  Simple rules
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DOI 10.1007/s10849-016-9238-7
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References found in this work BETA

Formal Philosophy. [REVIEW]Richard Montague - 1975 - Canadian Journal of Philosophy 4 (3):573-578.
Natural Deduction: A Proof-Theoretical Study.Richmond Thomason - 1965 - Journal of Symbolic Logic 32 (2):255-256.
Meaning Approached Via Proofs.Dag Prawitz - 2006 - Synthese 148 (3):507-524.
A Note on Harmony.Nissim Francez & Roy Dyckhoff - 2012 - Journal of Philosophical Logic 41 (3):613-628.

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Citations of this work BETA

Proof-Theoretic Semantics.Peter Schroeder-Heister - forthcoming - Stanford Encyclopedia of Philosophy.
Subatomic Negation.Bartosz Więckowski - 2021 - Journal of Logic, Language and Information 30 (1):207-262.

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