Abstract
The operators of first-order logic, including negation, operate on whole formulae. This makes it unsuitable as a tool for the formal analysis of reasoning with non-sentential forms of negation such as predicate term negation. We extend its language with negation operators whose scope is more narrow than an atomic formula. Exploiting the usefulness of subatomic proof-theoretic considerations for the study of subatomic inferential structure, we define intuitionistic subatomic natural deduction systems which have several subatomic operators and an additional operator for formula negation at their disposal. We establish normalization and subexpression property results for the systems. The normalization results allow us to formulate a proof-theoretic semantics for formulae composed of the subatomic operators. We illustrate the systems with applications to reasoning with combinations of sentential negation, predicate term negation, subject term negation, and antonymy.
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DOI 10.1007/s10849-020-09325-4
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References found in this work BETA

The Logical Basis of Metaphysics.Michael DUMMETT - 1991 - Harvard University Press.
A Natural History of Negation.Laurence Horn - 1989 - University of Chicago Press.
A Natural History of Negation.Jon Barwise & Laurence R. Horn - 1991 - Journal of Symbolic Logic 56 (3):1103.

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