The theory of the square of opposition was developed based on a logical structure coming from Aristotelian logic, a square, which was expanded into more complex geometrical objects: hexagons, octagons, polyhedra, and even four-dimensional objects. It has been continuously studied for two thousand years and it can also be found in works by Gottlob Frege. Such a logical construction can be applied to many fields, ranging from metalogic to highway code, through economics, music, physics, color theory, and theology. This volume contains new advances on the different aspects of this theory: its history, philosophy, application, and mathematical shapes.

 

The articles in this volume will be of interest to researchers and students in logic, mathematics, and philosophy alike.

Jean-Yves Beziau is a Swiss logician, philosopher and mathematician and has a PhD in mathematics and a PhD in philosophy. He has been living and working in different places: France, Brazil, Poland, Corsica, California (UCLA, Stanford, UCSD), and Switzerland. He is currently a professor at the University of Brazil in Rio de Janeiro, the former Director of Graduate Studies in Philosophy and the former President of the Brazilian Academy of Philosophy. He is the creator of the World Logic Day, yearly celebrated on January 14 (UNESCO international days), the World Logic Prizes Contest, the founder and Editor-in-Chief of the journal Logica Universalis and South American Journal of Logic, the book series Logic PhDs, Studies in Universal Logic and area logic editor of the Internet Encyclopedia of Philosophy. He has published about 200 research papers and 30 edited books and Special Issues of Journals.

 

Julio Michael Stern received his B.Sc. (1981) and M.Sc. (1983) in physics from the University of São Paulo (USP), followed by an M.Eng. (1990) and Ph.D. (1991) in operations research from Cornell University, and a Livre-Docência (2002) in computer science from USP. He is currently a full professor of applied mathematics at USP (since 2010). Stern has served as a research fellow at CNPq (2006–2025), the President of the Brazilian Chapter of the International Society for Bayesian Analysis (2010–2011), and the President of the IME-USP Research Council (2017–2020). He is a member of the Advisory Committee of the Brazilian Jurimetrics Association (since 2017) and of the Brazilian Academy of Philosophy (since 2019).