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  1. 1 Logic and Logical Philosophy

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  1. 1 Robles G.

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A simple Henkin-style completeness proof for Gödel 3-valued logic G3

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Robles G.
Logic and Logical Philosophy
|
2014
|
vol. 23
|
issue 4
371–390
EN
A simple Henkin-style completeness proof for Gödel 3-valued propositional logic G3 is provided. The idea is to endow G3 with an under-determined semantics (u-semantics) of the type defined by Dunn. The key concept in u-semantics is that of “under-determined interpretation” (u-interpretation). It is shown that consistent prime theories built upon G3 can be understood as (canonical) u-interpretations. In order to prove this fact we follow Brady by defining G3 as an extension of Anderson and Belnap’s positive fragment of First Degree Entailment Logic.
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