Truth and Falsehood: An Inquiry into Generalized Logical Values (Trends in Logic Book 36) 2012th Edition by Yaroslav Shramko (PDF)

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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⭐The content of the book is very interesting. The one star is for the Kindle edition. It is absurd that a book this expensive has been rendered into Kindle so shoddily! Some symbols are missing entirely, leaving you to guess what they are. All equations are rendered microscopically small, so that you have to zoom just to read them. Even some italicized words are shrunk this way for no apparent reason!

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