Truth and Falsehood: An Inquiry into Generalized Logical Values [Paperback]

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.Here is a thoroughly elaborated logical theory of generalized truth-values, presenting the idea of a trilattice of truth values  a specific algebraic structure with information ordering and two distinct logical orderings, one for truth and another for falsity.1 Truth Values2 Truth Values and the Slingshot Argument3 Generalized Truth Values: From FOUR2 to SIXTEEN34 Generalized Truth Values: SIXTEEN3 and BeyondAxiom Systems for Trilattice LogicsSequent Systems for Trilattice LogicsIntuitionistic Trilattice LogicsGeneralized Truth Values and Many-valued Logics: HarmoniousMany-valued Logics .Generalized Truth Values and Many-valued Logics: Suszkos ThesisFurther DevelopmentsReferencesIndex

The book presents a thoroughly elaborated logical theory of generalized truth values understood as subsets of some established set of (basic) truth entities. After elucidating the importance of the very notion of a truth value in logic and philosophy,?the authors?examine some possible ways of generalizing this notion.l3œ