Truth and Falsehood: An Inquiry into Generalized Logical Values

✍ Scribed by Yaroslav Shramko, Heinrich Wansing

• Publisher: Springer
• Year: 2012
• Tongue: English
• Leaves: 261
• Series: Trends in Logic 36
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xiii
Truth Values....Pages 1-18
Truth Values and the Slingshot Argument....Pages 19-40
Generalized Truth Values: From FOUR 2 to SIXTEEN 3 ....Pages 41-62
Generalized Truth Values: SIXTEEN 3 and Beyond....Pages 63-91
Axiom Systems for Trilattice Logics....Pages 93-112
Sequent Systems for Trilattice Logics....Pages 113-141
Intuitionistic Trilattice Logics....Pages 143-170
Generalized Truth Values and Many-Valued Logics: Harmonious Many-Valued Logics....Pages 171-187
Generalized Truth Values and Many-Valued Logics: Suszko’s Thesis....Pages 189-214
Further Developments....Pages 215-226
Back Matter....Pages 227-246

✦ Subjects

Logic; Mathematical Logic and Foundations; Mathematical Logic and Formal Languages