| Truth and Falsehood: An Inquiry Into Generalized Logical Values 2012 Edition Contributor(s): Shramko, Yaroslav (Author), Wansing, Heinrich (Author) |
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ISBN: 9400709064 ISBN-13: 9789400709065 Publisher: Springer OUR PRICE: $104.49 Product Type: Hardcover - Other Formats Published: September 2011 |
| Additional Information |
| BISAC Categories: - Philosophy | Logic - Mathematics | Logic - Computers | Computer Science |
| Dewey: 511.312 |
| Series: Trends in Logic |
| Physical Information: 0.63" H x 6.14" W x 9.21" (1.20 lbs) 250 pages |
| Descriptions, Reviews, Etc. |
| Publisher 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. |