Subatomic Natural Deduction for a Naturalistic First-Order Language with Non-Primitive Identity

Journal of Logic, Language and Information 25 (2):215-268 (2016)
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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.

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Citations of this work

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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References found in this work

The Logical Basis of Metaphysics.Michael Dummett - 1991 - Harvard University Press.
Natural Deduction: A Proof-Theoretical Study.Dag Prawitz - 1965 - Stockholm, Sweden: Dover Publications.
The Logical Form of Action Sentences.Donald Davidson - 1967 - In Nicholas Rescher (ed.), The Logic of Decision and Action. University of Pittsburgh Press. pp. 81--95.

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