# A general completeness theorem relating sequents and bivaluations

## Jean-Yves Béziau

### Federal University of Rio de Janeiro, Brazil

In this talk I will present a theorem justifying an intuitive semantical interpretation of rules of sequent proof systems. This theorem is based on the one hand on a generalization of Lindenbuam maximalization theorem and on the other hand on a general semantical theory of bivaluations, not necessarily truth-functional, originally developed by Newton da Costa for paraconsistent systems. I will show that this theorem gives a better understanding of sequent calculus and that it can fruitfully be applied to a wide class of logical systems providing instantaneous completeness results. This is a typical example of work in the line of the universal logic project, of which I will say a few words.

Reference: Logica Universalis, Special Double Issue – Scope of Logic Theorems. Volume 8, Issue 3-4, December 2014.

Jean-Yves Béziau is a professor and researcher of the Brazilian Research Council — CNPq — at the University of Brazil, Rio de Janeiro, Brazil. He works in the field of logic—in particular, paraconsistent logic, the square of opposition and universal logic. He holds a PhD in Philosophy from the University of São Paulo on Logical truth (advisor: Newton da Costa), a MSc and a PhD in Logic and Foundations of Computer Science from Denis Diderot University (advisor: Daniel Andler). He has been working in France, Switzerland, Brazil, Poland and USA (UCLA and Stanford).

He is the Editor-in-Chief and founder of the journal Logica Universalis, the South American Journal of Logic, the Springer book series Studies in Universal Logic, the College Publication book series Logic PhDs and book Encyclopedia of Logic as well as the area editor of logic of the Internet Encyclopedia of Philosophy

He is the organizer of various series of events in logic around the world: UNILOG – World Congress and School on Universal Logic (Montreux 2005, Xi’an 2007, Lisbon 2010, Rio de Janeiro 2013, Istanbul 2015), Square of Opposition (Montreux 2007, Corsica 2010, Beirut 2012, Vatican 2014), Logic in Question (Sorbonne, Paris) 2011, 2012, 2013, 2014).