This is an overview of the recent results of interaction of Boolean valued analysis and vector lattice theory.

Several verification methods involve reasoning about multi-valued systems, in which an atomic proposition is interpreted at a state as a lattice element, rather than a Boolean value. The automata-theoretic approach for reasoning about Boolean-valued systems has proven to be very useful and powerful. We develop an automata-theoretic framework for reasoning about multi-valued objects, and describ...

Problem 36 of the third edition of Birkhoo's Lattice theory 2] asks whether the MacNeille completion of uniquely complemented lattice is necessarily uniquely complemented. We show that the MacNeille completion of a uniquely complemented lattice need not be complemented. Questions regarding the axiomatics of Boolean algebras led Huntington to conjecture , in 1904, that every uniquely complemente...