Truth and Falsehood: An Inquiry Into Generalized Logical Values

Dordrecht, Netherland: Springer (2011)
  Copy   BIBTEX


The book presents a thoroughly elaborated logical theory of generalized truth-values understood as subsets of some established set of 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 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.



    Upload a copy of this work     Papers currently archived: 91,271

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Relevant generalization starts here (and here = 2).Dmitry Zaitsev & Oleg Grigoriev - 2010 - Logic and Logical Philosophy 19 (4):329-340.
Logic and truth : Some logics without theorems.Jayanta Sen & Mihir Kumar Chakraborty - 2008 - Studia Philosophica Estonica 1 (1):104-117.
True and False: An Exchange.Roberto Casati & Achille C. Varzi - 2000 - In André Chapuis & Anil Gupta (eds.), Circularity, Definition, and Truth. Indian Council of Philosophical Research. pp. 365-370.
An Approach to Uncertainty via Sets of Truth Values.George Gargov - 1995 - Notre Dame Journal of Formal Logic 36 (2):235-268.
Epicurus on Truth and Falsehood.Alexander Bown - 2016 - Phronesis 61 (4):463–503.


Added to PP

16 (#875,539)

6 months
7 (#411,145)

Historical graph of downloads
How can I increase my downloads?

Author Profiles

Yaroslav Shramko
Kryvyi Rih State Pedagogical University, Ukraine
Heinrich Wansing
Ruhr-Universität Bochum

Citations of this work

What is a Paraconsistent Logic?Damian Szmuc, Federico Pailos & Eduardo Barrio - 2018 - In Walter Carnielli & Jacek Malinowski (eds.), Contradictions, from Consistency to Inconsistency. Cham, Switzerland: Springer.
Metainferential duality.Bruno Da Ré, Federico Pailos, Damian Szmuc & Paula Teijeiro - 2020 - Journal of Applied Non-Classical Logics 30 (4):312-334.
Semantics and Truth.Jan Woleński - 2019 - Cham, Switzerland: Springer Verlag.
Routley Star and Hyperintensionality.Sergei Odintsov & Heinrich Wansing - 2020 - Journal of Philosophical Logic 50 (1):33-56.

View all 24 citations / Add more citations

References found in this work

Word and Object.Willard Van Orman Quine - 1960 - Cambridge, MA, USA: MIT Press.
Ontological relativity and other essays.Willard Van Orman Quine (ed.) - 1969 - New York: Columbia University Press.
Meaning and Necessity: A Study in Semantics and Modal Logic.Rudolf Carnap - 1947 - Chicago, IL, USA: University of Chicago Press.
Modal Logic: An Introduction.Brian F. Chellas - 1980 - New York: Cambridge University Press.

View all 219 references / Add more references