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

The Logical Basis of Metaphysics.Michael Dummett, Hilary Putnam & James Conant - 1994 - Philosophical Quarterly 44 (177):519-527.
Formal Philosophy. [REVIEW]Richard Montague - 1975 - Canadian Journal of Philosophy 4 (3):573-578.
Meaning Approached Via Proofs.Dag Prawitz - 2006 - Synthese 148 (3):507-524.
Basic Proof Theory.Roy Dyckhoff - 2001 - Bulletin of Symbolic Logic 7 (2):280-280.

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Proof-Theoretic Semantics.Peter Schroeder-Heister - forthcoming - Stanford Encyclopedia of Philosophy.

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