The book presents a thoroughly elaborated logical theory of generalized
truth-values understood as subsets of some established set of (basic)
truth values. After elucidating the importance of the very notion of a
truth value in logic and philosophy, we examine some possible ways of
generalizing this notion. The useful four-valued logic of first-degree
entailment by Nuel Belnap and the notion of a bilattice (a lattice of
truth values with two ordering relations) constitute the basis for
further generalizations. By doing so we elaborate the idea of a
multilattice, and most notably, a trilattice of truth values - a
specific algebraic structure with information ordering and two distinct
logical orderings, one for truth and another for falsity. Each logical
order not only induces its own logical vocabulary, but determines also
its own entailment relation. We consider both semantic and syntactic
ways of formalizing these relations and construct various logical
calculi.