Algebra Seminar talk
2022-06-10
Miroslav Haviar
Dualities for bilattices and their applications
Abstract:
Bilattices provide an algebraic tool for simultaneously modelling knowledge and truth; they are algebras $L$ with two lattice structures,
a "knowledge lattice" $(L, \le_k)$ (ranging from "no information" to "full information") and
a "truth lattice" $(L, \le_t)$ (ranging from "false" to "true"), together
with an involutive negation which is an order automorphism of the
knowledge order and a dual order automorphism of the truth order.
In the talk I will present a family of varieties of bilattices and use natural duality to analyse them.
An expanded abstract can be found here: haviar2022.pdf.