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.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1007/s10849-020-09325-4
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 59,916
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

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.

View all 29 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Logical Negation.Ignacio Angelelli - 1983 - Review of Metaphysics 36 (4):925-926.
Hegel's Glutty Negation.Elena Ficara - 2015 - History and Philosophy of Logic 36 (1):29-38.
Negation.Ernesto Napoli - 2006 - Grazer Philosophische Studien 72 (1):233-252.
Rules for Subatomic Derivation.Bartosz Więckowski - 2011 - Review of Symbolic Logic 4 (2):219-236.
On Not Being a Dentist.Richard Vallée - 2004 - Manuscrito 27 (1):227-233.
Negation in the Language of Theology – Some Issues.Adam Olszewski - 2018 - Philosophical Problems in Science 65:87-107.
Another Plan for Negation.Nissim Francez - 2019 - Australasian Journal of Logic 16 (5):159.
Empirical Negation.Michael De - 2013 - Acta Analytica 28 (1):49-69.
Negation of the Negation in Logical and Historical Analysis.M. F. Vorob'ev - 1969 - Russian Studies in Philosophy 8 (2):190-205.


Added to PP index

Total views
10 ( #856,282 of 2,433,174 )

Recent downloads (6 months)
10 ( #65,743 of 2,433,174 )

How can I increase my downloads?


My notes