Truth and Falsehood

An Inquiry into Generalized Logical Values

  • Yaroslav Shramko
  • Heinrich Wansing

Part of the Trends in Logic book series (TREN, volume 36)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Yaroslav Shramko, Heinrich Wansing
    Pages 1-18
  3. Yaroslav Shramko, Heinrich Wansing
    Pages 19-40
  4. Yaroslav Shramko, Heinrich Wansing
    Pages 41-62
  5. Yaroslav Shramko, Heinrich Wansing
    Pages 63-91
  6. Yaroslav Shramko, Heinrich Wansing
    Pages 93-112
  7. Yaroslav Shramko, Heinrich Wansing
    Pages 113-141
  8. Yaroslav Shramko, Heinrich Wansing
    Pages 143-170
  9. Yaroslav Shramko, Heinrich Wansing
    Pages 189-214
  10. Yaroslav Shramko, Heinrich Wansing
    Pages 215-226
  11. Back Matter
    Pages 227-246

About this book

Introduction

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.

Keywords

first-degree entailment lattice theory logical semantics trilattice logics truth values

Authors and affiliations

  • Yaroslav Shramko
    • 1
  • Heinrich Wansing
    • 2
  1. 1.Dept. PhilosophyState Pedagogical UniversityKrivoi RogUkraine
  2. 2.Inst. PhilosophieTU DresdenDresdenGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-007-0907-2
  • Copyright Information Springer Science+Business Media B.V. 2012
  • Publisher Name Springer, Dordrecht
  • eBook Packages Humanities, Social Sciences and Law
  • Print ISBN 978-94-007-0906-5
  • Online ISBN 978-94-007-0907-2
  • About this book