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2006

On the infinite-valued Lukasiewicz logic that preserves degrees of truth

9 years 7 months ago
On the infinite-valued Lukasiewicz logic that preserves degrees of truth
Lukasiewicz's infinite-valued logic is commonly defined as the set of formulas that take the value 1 under all evaluations in the Lukasiewicz algebra on the unit real interval. In the literature a deductive system axiomatized in a Hilbert style was associated to it, and was later shown to be semantically defined from Lukasiewicz algebra by using a "truthpreserving" scheme. This deductive system is algebraizable, non-selfextensional and does not satisfy the deduction theorem. In addition, there exists no Gentzen calculus fully adequate for it. Another presentation of the same deductive system can be obtained from a substructural Gentzen . In this paper we use the framework of abstract algebraic logic to study a different deductive system which uses the aforementioned algebra under a scheme of "preservation of degrees of truth". We characterize the resulting deductive system in a natural way by using the lattice filters of Wajsberg algebras, and also by using a ...
Josep Maria Font, Àngel J. Gil, Antoni Torr
Added 10 Dec 2010
Updated 10 Dec 2010
Type Journal
Year 2006
Where AML
Authors Josep Maria Font, Àngel J. Gil, Antoni Torrens, Ventura Verdú
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