Truth and Falsehood, 2012 An Inquiry into Generalized Logical Values Trends in Logic Series, Vol. 36

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.

1 Truth Values 2 Truth Values and the Slingshot Argument 3 Generalized Truth Values: From FOUR2 to SIXTEEN3 4 Generalized Truth Values: SIXTEEN3 and Beyond Axiom Systems for Trilattice Logics Sequent Systems for Trilattice Logics Intuitionistic Trilattice Logics Generalized Truth Values and Many-valued Logics: Harmonious Many-valued Logics . Generalized Truth Values and Many-valued Logics: Suszko’s Thesis Further Developments References Index

Surveys and unifies various philosophical and formal treatments of truth values Discusses central issues such as the relation between truth values and consequence relations Systematically develops both semantically and proof-theoretically a theory of generalized truth values as subsets of already established truth values.