Лекции Филиппа Лионеля Балбиани, научного сотрудника Института информационных исследований в Тулузе (Франция) 11, 13, 18, 20 декабря 2019

In this course, we will give a survey of the results on unification in modal logic and we will present some of the open problems whose solution will have a great impact on the future of the area.
After an introductory part about unification in equational theories, we will consider the case of Boolean unification [Baader 1998, Martin and Nipkow 1989], we will study the unification problem in Intuitionistic Propositional Logic and transitive normal modal logics like K4 [Gencer 2002, Gencer and de Jongh 2009, Ghilardi 1999, Rybakov 1997, Rybakov 2001], we will introduce the notions of projective and transparent unifiers [Dzik 2003, Dzik 2007, Dzik 2011, Dzik and Wojtylak 2012, Ghilardi 1999, Ghilardi 2000] and we will define study unification [Ghilardi and Sacchetti 2004].
Then, we will present the latest results obtained within the context of unification in description logics [Baader, Borgwardt and Morawska 2012, Baader and Morawska 2009, Baader and Narendran 2001, Fernandez and Gil 2012] and in multimodal, tense and epistemic logics [Babenyshev and Rybakov 2011, Balbiani and Gencer 2017, Balbiani and Tinchev 2017, Dzik 2003].