@article{4d8ff21c429a48089e3aefcc30fef049,
title = "On the Logical Philosophy of Assertive Graphs",
abstract = "The logic of assertive graphs (AGs) is a modification of Peirce{\textquoteright}s logic of existential graphs (EGs), which is intuitionistic and which takes assertions as its explicit object of study. In this paper we extend AGs into a classical graphical logic of assertions (ClAG) whose internal logic is classical. The characteristic feature is that both AGs and ClAG retain deep-inference rules of transformation. Unlike classical EGs, both AGs and ClAG can do so without explicitly introducing polarities of areas in their language. We then compare advantages of these two graphical approaches to the logic of assertions with a reference to a number of topics in philosophy of logic and to their deep-inferential nature of proofs.",
keywords = "Assertion, Assertive graphs, Classical vs. non-classical logical graphs, Deep inference, Existential graphs, Inferentialism, Peirce",
author = "Daniele Chiffi and Pietarinen, {Ahti Veikko}",
note = "Funding Information: The work of the first author is supported by the Portuguese Foundation for Science and Technology, project (PTDC/MHC-FIL/0521/2014), and the Estonian Research Council PUT1305 Abduction in the Age of Fundamental Uncertainty. The work of the second author is partly supported by the Russian Academic Excellence Grant “5-100”, Formal Philosophy and the Estonian Research Council PUT1305 Abduction in the Age of Fundamental Uncertainty. This work has been presented at The First Int. Logic Day, Tallinn University of Technology, Tallinn, Estonia; Assertion and Belief, University of Padua, Italy; Department of Computer Science Seminar, University of T{\"u}bingen, Germany; 9th Interational Conference on the Theory and Applications of Diagrams, Edinburgh, Scotland; Around Peirce, 6th World Congress and School on Universal Logic, Vichy, France; Grupo de Investigaci{\'o}n en L{\'o}gica, Lenguaje e Informaci{\'o}n (GILLIUS), University of Sevilla, Spain; Philosophy Seminar, Nazarbayev University. We thank the audience of these events for valuable suggestions, among them F. Bellucci, M. Capraru, M. Carrara, J.-M. Chevalier, C. De Florio, M. Fontaine, C. Bar{\'e}s G{\'o}mez, V. Morato. {\'A}. Nepomuceno, M. Plebani, P. Schroeder-Heister, G. Sundholm, L. Tranchini, T. Uustalu. Above all, our thanks go to the two reviewers of the present journal for helpful comments that led to a number of improvements. Publisher Copyright: {\textcopyright} 2020, Springer Nature B.V.",
year = "2020",
month = dec,
doi = "10.1007/s10849-020-09315-6",
language = "English",
volume = "29",
pages = "375--397",
journal = "Journal of Logic, Language and Information",
issn = "0925-8531",
publisher = "Springer Netherlands",
number = "4",
}