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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.
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. The useful four-valued logic of first-degree entailment by Nuel Belnap and Michael Dunn and the notion of a bilattice (a lattice of truth values with two ordering relations) constitute the basis for further generalizations. By doing so the authors elaborate the idea of a multilattice and, most notably, a trilattice of truth values – a specific algebraic structure with an 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 also determines its own entailment relation. Both semantic ans syntactic ways of formalizing these relations by constructing various logical calculi are considered.
Content Level »Research
Keywords »first-degree entailment - lattice theory - logical semantics - trilattice logics - truth values
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