Truth and Falsehood

An Inquiry into Generalized Logical Values

Yaroslav Shramko, Heinrich Wansing (Autoren)

Buch | Softcover

250 Seiten

2013 | 2012 ed.
Springer (Verlag)
978-94-007-3734-1 (ISBN)

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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

Reihe/Serie	Trends in Logic ; 36
Zusatzinfo	XIV, 250 p.
Verlagsort	Dordrecht
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Geisteswissenschaften ► Philosophie ► Allgemeines / Lexika
	Geisteswissenschaften ► Philosophie ► Logik
	Mathematik / Informatik ► Informatik ► Theorie / Studium
	Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
	Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
ISBN-10	94-007-3734-3 / 9400737343
ISBN-13	978-94-007-3734-1 / 9789400737341
Zustand	Neuware