Difference between revisions of "Taking degrees of truth seriously"
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author=Josep Maria Font| | author=Josep Maria Font| | ||
| − | title= | + | title=Taking degrees of truth seriously| |
journal=Studia Logica| | journal=Studia Logica| | ||
volume=91| | volume=91| | ||
| + | number= | | ||
pages=383-406| | pages=383-406| | ||
year=2009}} | year=2009}} | ||
== Abstract == | == Abstract == | ||
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This is a contribution to the discussion on the role of truth degrees in many-valued 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 Lukasiewicz'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. | This is a contribution to the discussion on the role of truth degrees in many-valued 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 Lukasiewicz'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. | ||
Latest revision as of 07:32, 27 April 2016
| Authors: |
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| Title: | Taking degrees of truth seriously | |
| Journal: | Studia Logica | |
| Volume | 91 | |
| Number | ||
| Pages: | 383-406 | |
| Year: | 2009 |
Abstract
This is a contribution to the discussion on the role of truth degrees in many-valued 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 Lukasiewicz'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.
