ENGLISH

Truth and Falsehood: An Inquiry into Generalized Logical Values

By Heinrich Wansing , Yaroslav Shramko

Book information

Publisher
Springer
Year
2012
ISBN
9400709064, 9789400709065
DOI
10.1007/978-94-007-0907-2
Google Books ID
6WMS1mqP8ZUC
Language
english
Format
PDF
Filesize
2 MB (2058457 bytes)
Series
Trends in Logic 36
Pages
261\261
Topic
Mathematics Logic
Orientation
portrait
Paginated
yes
Scanned
no
Time added
2012-02-14 18:00:00
Logic; Mathematical Logic and Foundations; Mathema

Description

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.

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