@inbook{dcfed152f0704269969a67d3669e7a41,

title = "The Representation of Negative Terms with Euler Diagrams",

abstract = "In the common use of logic diagrams, the positive term is conveniently located inside the circle while its negative counterpart is left outside. This practice, already found in Euler{\textquoteright}s original scheme, leads to trouble when one wishes to express the non-existence of the outer region or to tackle logic problems involving negative terms. In this chapter, we discuss various techniques introduced by Euler{\textquoteright}s followers to overcome this difficulty: some logicians modified the data of the problem at hand, others amended the diagrams, and another group changed the mode of representation. We also consider how modern diagrammatic systems represent negation.",

keywords = "Euler diagram, Negation, Syllogism, Venn diagram",

author = "Reetu Bhattacharjee and Amirouche Moktefi and Pietarinen, {Ahti Veikko}",

note = "Funding Information: Acknowledgments This research benefitted from the support of ERC project “Abduction in the age of Uncertainty” (PUT 1305, Principal Investigator: Prof. Ahti-Veikko Pietarinen) as well as the fellowship grant received in 2018 by Reetu Bhattacharjee in the frame of the European Regional Development Fund{\textquoteright}s Doctoral Studies and internationalization Program (which is carried out by Archimedes Foundation) for short-term research at Tallinn university of Technology, Tallinn, Estonia and the Post Doctoral research grant “Quod erat videndum: heuristic, logical and cognitive aspects of diagrams in mathematical reasoning” as part of the research project MIUR -“Departments of Excellence”, call 2017 - Faculty of Humanities at Scuola Normale Superiore, Pisa, Italy received by Reetu Bhattacharjee in 2022. Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.",

year = "2023",

month = jan,

day = "12",

doi = "10.1007/978-3-030-94452-0_3",

language = "English",

isbn = "9783030944513",

series = "Studies in Universal Logic",

publisher = "Springer - Birkh{\"a}user Cham",

pages = "43--58",

editor = "Jean-Yves B{\'e}ziau and Jean-Pierre Descl{\'e}s and Amirouche Moktefi and Pascu, {Anca Christine}",

booktitle = "Logic in Question",

edition = "1st",

}