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Studia Logica

, Volume 91, Issue 3, pp 383–406 | Cite as

Taking Degrees of Truth Seriously

  • Josep Maria Font
Article

Abstract

This is a contribution to the discussion on the role of truth degrees in manyvalued logics from the perspective of abstract algebraic logic. It starts with some thoughts on the so-called Suszko’s Thesis (that every logic is two-valued) and on the conception of semantics that underlies it, which includes the truth-preserving notion of consequence. The alternative usage of truth values in order to define logics that preserve degrees of truth is presented and discussed. Some recent works studying these in the particular cases of Łukasiewicz’s many-valued logics and of logics associated with varieties of residuated lattices are also presented. Finally the extension of this paradigm to other, more general situations is discussed, highlighting the need for philosophical or applied motivations in the selection of the truth degrees, due both to the interpretation of the idea of truth degree and to some mathematical difficulties.

Keywords

Suszko’s Thesis many-valued logic logical values truth values truth degrees logics preserving degrees of truth semantics abstract algebraic logic 

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© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Department of Probability, Logic and Statistics, Faculty of MathematicsUniversity of BarcelonaBarcelonaSpain

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